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1. Scenario Default Scenario Zi Population l Population 1 Z Deteministic projections assume no stochastic fluctuations no inbreeding depression no a limitation of mates no harvest and no supplementation Scenario Default Scenario Population 1 Population 1 Deterministic population growth rate Caution Deterministic growth rate may not be meaningful if functions were used for some demographic rates r 0 1094 lambda 1 1156 RO 1 7229 Generation time for females 4 97 males 4 97 Stable age distribution Age class females males 0 0 164 0 164 0 074 0 059 0 048 0 048 0 039 0 039 Sendto Report Save As Pit The graph given with the Deterministic Results is fairly simple and crude but it shows the exponential growth or decline projected from the life table calculations up to the limit set by the carrying capacity The graph can be sent to your Project Report printed or exported to a file for import into other programs As with all graphs in VORTEX double clicking on the graph opens Chart Properties in which you can customize the graph The deterministic calculations are performed by VORTEX as soon as you save the input values for your model Therefore you can view these results and also the Input Summary text even before you run your simulations It is often helpful and always recommended to look at the deterministic projections before procee
2. 10 20 30 40 50 60 70 80 90 100 Year of Simulation RATE 50 10 SNRAND Y R 100 This is the same as imposing a mean rate of 50 with environmental variation of SD 10 Linear density dependence RATE 50 K N K The rate declines from 50 at N 0 to 0 when N K Demographic Rate Demographic Rate 80 0 F 70 0 f 60 0 50 0 F 40 0 30 0 20 0 10 0 0 0 W144 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 50 0 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 5 0 f 0 0 0 10 20 30 40 50 60 70 80 90 100 Population Size 22 23 24 Density dependence used as the default for breeding in VORTEX RATE 50 20 N K 4 N 1 N The rate peaks near 50 when N is small 50 0 F declines at higher densities and is 30 when N 45 0 K At very small N the rate is also o oo depressed For example it is reduced by 50 g 35 0 when N 1 and reduced by 25 when N 3 2 300 In terms of the coefficients that can be 25 0 entered into the optional density dependence S 20 0 for breeding in VORTEX P 0 50 P K 5 15 0 30 B 4 and A 1 10 0 5 0 0 0 0 10 20 30 40 50 60 70 80 90 100 Population Size Sex specific dispersal rates RATE D S M OR RAND gt 0 35 If the above function is used for the Dispersal Modifier Function then 35 of the females are prevented from dispersing Thus disper
3. Optional Criteria for acceptable mates This option allows the user to specify a constraint on which males are suitable as sires for each female The constraint is specified using a function For these functions specifying mate suitability the standard variables describing individual characteristics e g A for age I for inbreeding or PARITY refer to the values for the potential sire You should use SIRE1 SIRE2 etc and DAM1 DAM2 etc to indicate the IS variables for the sire and dam If you want the function to include a characteristic such as Age of the dam then you need to set and ISvar to that variable e g IS1 A and refer to DAM in the function If the function evaluates to a number between 0 and 1 then the result will be used as the probability that the male is accepted as the mate Examples of the use of this option include 1 lt 0 10 for avoiding mating with a sire than has an inbreeding level greater than 10 SIRE1 gt DAM1 or A gt DAM1 to force the sire to be older than the dam if IS1 is set to age This option can provide a great deal of flexibility in creating complex breeding systems but it can be difficult to specify the constraint function correctly Number of times to try to find a mate If constraints on suitable males to select as mates are specified in the above options related to inbreeding or limitations of pairings then this option will specify how many times the program should select a m
4. sT Project Settings Simulation Input Text Output Tables and Graphs Project Report Custom Plot hd Table Errorbars None SE SD Custom Plot Data Specification Plot x axis up through year 0 for data maximum Plot y axis want the Mean of variable GeneDiv x Scenarios to include z F AbundantPrey A LowEV 7 2Pops 3Pops E 10Pops E MyST1 E MyST3 MyST2 X opulations to be included 2Pops Pop1 2Pops Population2 2Pops Metapopulation 3Pops Pop1 3Pops Population2 3Pops Population3 3Pops Metapopulation Baseline 2Pops Metapopulation 3Pops Metapopulation SSGG0808 Baseline Pop1 Sendto Report Save As Pont Remember that after changing options for a graph you sometimes will need to hit the Update Plot button to get your new options to be shown in the graph 91 Project Report This is a basic Notepad like text Window in which you can build your own Report Text tables and graphs from other screens can often be sent to the Report and you can directly edit the Report as well You can cut and paste from other data fields e g from your Project or Input Section Notes into the Project Report and you can cut and paste between the Project Report and other Windows documents In Text Output Tables and Graphs and on several other scr
5. J Heredity 81 257 266 Brook B W et al 1997 Does population viability analysis soft ware predict the behaviour of real populations A retrospec tive study on the Lord Howe Island woodhen Tricholimnas sylvestris Sclater Biol Conserv 82 119 128 49 Brook B W et al 1999 Comparison of the population viability analysis packages GAPPS INMAT RAMAS and VORTEX for the whooping crane Grus americana Anim Conserv 2 23 31 Brook B W et al 2000 Predictive accuracy of population via bility analysis in conservation biology Nature 404 385 387 Brown J H and Kodric Brown A 1977 Turnover rates in insu lar biogeography effect of immigration on extinction Ecology 58 445 449 Caro T M and Laurenson M K 1994 Ecological and genetic factors in conservation a cautionary tale Science 263 485 486 Caughley G 1994 Directions in conservation biology J Anim Ecol 63 215 244 Charlesworth D and Charlesworth B 1987 Inbreeding de pression and its evolutionary consequences Annu Rev Ecol Syst 18 237 268 Clark T W 1989 Conservation biology of the black footed fer ret Wildlife Preservation Trust International Philadelphia Courchamp E Clutton Brock T and Grenfell B 1999 Inverse density dependence and the Allee effect Trends Ecol Evol 14 405 410 Dietz J M Baker A J and Ballou J D 2000 Demographic evidence of inbreeding depressi
6. 5 0 Division by zero TAN 1 5707963 Tangent of PI 2 ASI N 1 1 Arcsine or arccosine of a value gt 1 or lt 1 e Some mathematically valid functions would be ambiguous or meaningless For example functions of carrying capacity K should not contain K as an independent predictor of itself Functions of K should also not include A age or S sex as parameters because the condition of exceeding the carrying capacity is a population level phenomenon and K is assessed once for each population each year If K is a function of inbreeding I the value of applied in the function will be the mean for the population e There is no limit on the length of a function Often there are multiple functions that will achieve the same purpose A more concise function may be easier to type and may also run faster in the program However it may be easier to see the logic in a more explicit but longer function that evaluates to the same result e Many of the variables that can be used in rate functions will themselves change during each year of the simulation In order to avoid irresolvable circular interdependencies of parameters and rates the population size N sizes of subsets J F M U X W and genetic descriptors of populations G and GDI ST used in functions are updated at the beginning of each life history stage e g Breed Mortality Disperse Harvest Supplement etc for each population in the model For example the popula
7. Conserv Biol 1 143 158 Lacy R C 1993 1994 What is population and habitat viabil ity analysis Primate Conserv 14 15 27 33 Lacy R 1996 Further population modelling of northern white rhinoceros under various management scenarios In Foose T J ed Summary Appendix 3 Northern White Rhinoc eros Conservation Strategy Workshop International Rhino Foundation Cumberland Ohio pp 1 15 Lacy R C 1997 Importance of genetic variation to the viability of mammalian populations J Mammal 78 320 335 Lacy R C 2000 Structure of the VORTEX simulation model for population viability analysis Ecol Bull 48 191 203 Lacy R C and Lindenmayer D B 1995 A simulation study of the impacts of population subdivision on the mountain brushtail possum Trichosurus caninus Ogilby Phalangeri dae Marsupialia in south eastern Australia II Loss of ge netic variation within and between subpopulations Biol Conserv 73 131 142 Lacy R C and Ballou J D 1998 Effectiveness of selection in reducing the genetic load in populations of Peromyscus po lionotus during generations of inbreeding Evolution 52 900 909 Lacy R C and Miller P S 2001 Managing the human animal incorporating human populations and activities into PVA for wildlife conservation In Beissinger S and McCul lough D R eds Population viability analysis Univ of Chicago Press in press Lacy R C Ala
8. ITOT1 ITOT2 etc Total across living individuals of i th individual state variable ISUM1 SUM2 etc Synonyms for TOTi MEAN1 MEAN2 etc Mean across individuals of th individual state variable I MI N1 IMI N2 etc Minimum across individuals ofi th individual state variable I MAX1 MAX2 etc Maximum across individuals of i th individual state variable Note when the above four kinds of variables are used in definitions of Global State Variables the calculations are done over the metapopulation Otherwise they apply to the population PAIRS number of pairs that have been created in that year PAI RS will be updated after each pair has been created This allows you to control the probability of future pairs based on the number already made BROODS broods produced within that year updated as broods are made PROGENY progeny produced within that year updated as progeny are made BREEDRECS pairs last calculated to be needed when Breed to K option is chosen MMI GRANTS individuals dispersing from the population in the current year updated as dispersal occurs but do not use in a function within the Dispersal event as it is unpredictable when the value changes during dispersal EMI GRANTS individuals dispersing into the population in that year HARVESTS individuals harvested in that year updated after each population is harvested SUPPLEMENTS individuals supplemented into the population
9. If you specify allele frequencies for more loci than were in your model see above then the last locus in the allele frequency file will be used to set the initial haplotypes for the mtDNA If you specify alleles for more loci than needed for your requested number of neutral loci plus the mtDNA then additional neutral loci will be modeled with the frequencies you have specified The starting frequencies for mtDNA alleles will still be taken from the last locus in the file If you are modeling more than one population you can repeat the rows of data for each population Here is an example of a file with allele frequencies at three loci for three populations 3 342 33 33 34 25 25 25 25 5 5 4 3 3 3 5 25 75 3 3 4 35 15 35 15 75 25 If you have more populations in your model than data in the allele frequency file then VORTEX will use the last set of frequencies for all subsequent populations Thus if you want all populations to start at the same frequencies you can just give that set of frequencies once in the file When you have supplements VORTEX will use the frequencies specified for population nP 1 in which nP is the number of populations Again however you can omit specification of an extra set of frequencies for any supplements and then VORTEX will use the last set of frequencies that you did provide Note that if there are not enough frequencies specified for the numbers of alleles specified on line 2 then VO
10. The Text Output contains a tab ST Tables to display the summaries of results from Sensitivity Tests that are saved in the stsum file The stsum file can also be opened in Excel if you specify that columns are delimited with semi colons The last few columns of data in the stsum file are the values of SVs that were sampled in each scenario within the series This makes it easy to do further statistical analysis using your favorite statistical package on the ST results Commonly you would want to run a regression analysis or ANOVA of some sort to determine the effect of each SV and possible interactions among them on measures of population viability For probability of extinction an appropriate analysis is often a logistic regression For final population size or population growth rate often a linear regression is appropriate The stdat files give year by year results for each scenario that was run during the ST Although often you will have no need to examine these files they do provide the data needed for analyses at intermediate years of the simulation and they are used for graphing ST results see next section 99 Graphing ST results Graphs of ST results include the same graphs available for all scenarios and some additional plots that are useful for comparing the relative effects of variables tested in a ST All the data that are used for ST graphs are available in files with extension stdat with the same data format as the
11. 1 GenerationTime Preliminary estimate Solve Euler equation by iterative approximation to yield precise Lambda Set r p log Lambda Set Generation Time p og RO rlph FOR each age x Determine stable age distribution Set StableAgeClassSizelp lx 1 SexRatio Lix I Lambda x ECOLOGICAL BULLETINS 48 2000 Add StableAgeClassSize p x to SumStableAgeClassSize p END LOOP JI Repeat age distribution calculations for males but use female based Mx and Lambda FOR each age x Set male survival P x 1 MaleMortality p x FOR each type of catastrophe 11 Adjust P x for catastrophes Multiply P x by CatastropheFrequency pl c CatastropheSurvivalSeverity p 1 CatastopheFrequency p c END catastrophe LOOP Multiply cumulative survivorship L x by P x END LOOP FOR each age x Determine stable age distribution Set StableAgeClassSize p x SexRatio Lix l Lambda x Add StableAgeClassSize p x to SumStableAgeClassSize p END LOOP FOR each age x and sex s Divide SrableAgeClassSize p s x by SumStableAgeClassSizelp END LOOP END FUNCTION CALC_DETERMINISTIC_GROWTH BEGIN FUNCTION GLOBAL_EV_RANDS FOR each type of catastrophe Set GlobalCatastropheRand RAND Select random number to determine if global catastro phe occur See Note 5 END catastrophe LOOP Set GlobalBreedEVRand RANDO 11 Select random number for specifying EV in bre
12. 43 distribution You accomplish this by entering the percentage i e a number between 0 0 and 100 0 for each specified size up to the maximum For example if the maximum litter size is 5 but the average litter is comprised of just 2 individuals you would enter a much higher percentage of females producing smaller litters say 60 produce a litter of 2 but only 5 produce a litter of 5 If you do not use any functions for rates in this table the last row will automatically be filled in so that the percents add to 100 That last row cannot be edited If you do use a function in this table it is then your responsibility to be sure that the rows will sum to 100 If the values sum to more than 100 the excess will be taken from the last value s If the rows sum to less than 100 the missing percents will be add to the last value A clever trick If you want to use a distribution for the number of progeny that is something other than a normal e g Poisson you can do it Just select Use Normal distribution enter your function for the distribution as the mean and then enter 0 for the SD For example to get a Poisson distribution with mean 2 5 you would enter for the mean the function POISSON 2 5 and then enter 0 for SD You can even create a specified distribution like the other option for entering progeny per brood by giving a function that generates that distribution Explaining fully how to do this is beyond the scope of
13. RATE 50 10 V lt 20 Z gt 19 50 0 With ten initial founders and with some 45 0 number of individuals from another source used o 40 0 as supplements at a later stage the breeding rate S gol is 50 for an individual which carries both ofits 2 300 alleles from the initial founders or both from the 25 0 source population of the supplements vs 40 for gt 50 01 individuals which are heterozygous carrying an 3 15 0 allele from each source 10 0 5 0 0 0 l 10 20 30 40 50 Allele Identifier 70 0 28 Genetically based individual variation in 60 0 breeding success 2 E 50 0 RATE 2 sol 50 5 SNRAND R 100 V SNRAN D R 100 Z 3 30 07 In this case breeding rates vary around a 5 20 0 mean of 50 with a standard deviation equal to ial 5 SQRT 2 an 10 20 30 40 50 Allele Identifier 130 Appendix 1 An Overview of Population Viability Analysis Using VORTEX This Appendix presents an overview of processes threatening the health and persistence of wildlife populations the methods of population viability analysis the VORTEX simulation program for PVA and the application of such techniques to wildlife conservation Much of the following material is adapted from Lacy 1993a and Lacy 1993 4 This description was first written to describe VORTEX version 9 Please see the overview of changes from VORTEX 9 to VORTEX 10 below for a summary of new options in VORTEX
14. UNI FORM Random integer A B UNI FORM 1 5 1 0 or2 0 or3 0 or or RAND 4 0 or POISSON Poisson random deviate with POISSON 3 0 0 orl 0 or2 0 or mean m POI SSON1 0 truncated Poisson sampled POISSON1 3 1 0 or2 0 or3 0 or from Poisson with mean m but without 0 value aes SRAND A seeded random number hence SRAND x provides a random number between 0 and 1 with the seed value x SNRAND A seeded random normal deviate hence SNRAND x returns a number from a 0 1 normal distribution with the seed value x SUNI FORM A seeded random uniform hence SUNI FORM a b x provides a random number between a and b inclusive with the seed value x SI UNI FORM A seeded uniform random integer hence SI UNI FORM a b x provides a or SI RAND random number between a and b inclusive with the seed value x SPOI SSON A seeded random number generator hence SPOI SSON m x provides a random number from a Poisson distribution with mean m with seed value X SPOISSON1 A seeded 0 truncated Poisson SPOI SSON1 m x provides a random number greater than 0 from a Poisson distribution with mean m with seed value x Defined Constants PI 3 1415927 SIN PI 4 0 7071067 E 2 7182818 LN E 1 0 115 The operators to create modify and operate on lists will not be used by most VORTEX users but they can be powerful ways to create specific sequences of values These can then be used to s
15. Vortex 10 A stochastic simulation of the extinction process Version 10 0 7 0 Begin a New Project Open a Project Existing Recent Quit Copyright 2014 Chicago Zoological Society User s Manual Written by Robert C Lacy Philip S Miller and Kathy Traylor Holzer 30 January 2015 update Copyright 2015 IUCN SSC Conservation Breeding Group amp Chicago Zoological Society 1 Citations The VORTEX program should be cited as Lacy R C and J P Pollak 2014 Vortex A Stochastic Simulation of the Extinction Process Version 10 0 Chicago Zoological Society Brookfield Illinois USA This manual should be cited as Lacy R C P S Miller and K Traylor Holzer 2015 Vortex 10 User s Manual 19 January 2015 update IUCN SSC Conservation Breeding Specialist Group and Chicago Zoological Society Apple Valley Minnesota USA Citations for the concepts algorithms and program flow although a little out of date because they describe version 9 or earlier but still mostly are accurate descriptions of the standard VORTEX model include Lacy R C 1993 VORTEX A computer simulation model for Population Viability Analysis Wildlife Research 20 45 65 Lacy R C 1993 1994 What is Population and Habitat Viability Analysis Primate Conservation 14 15 27 33 Lacy R C 2000 Considering threats to the viability of small populations Ecological Bulletins 48 39 51 Lacy R C 2000 Structure of the VORTEX s
16. END LOOP ECOLOGICAL BULLETINS 48 2000 END IF Read in Supplement p IF Supplement p Yes Read in First YearSupplementation p Last YearSupplementation p SupplementationIntervallp FOR each age x up to FemaleBreedingAge Read in NumberFemales ToBeSupplemented p x END LOOP FOR each age x up to MaleBreedingAge Read in NumberMales ToBeSupplemented p x END LOOP END IF END FUNCTION READ_POPULATION_PARAMETERS BEGIN FUNCTION CALC_DETERMINISTIC_GROWTH for popula tion p 11 Use standard life table analysis solve the Euler equation to find the deterministic growth rate Set fecundity M MeanLitterSize p 1 SexRatio 11 SexRatio is proportion males at birth FOR each type of catastrophe Adjust M for catastrophes Multiply M by CatastropheFrequency p c CatastropheBreedSeverity p c 1 CatastopheFrequency p c END catastrophe LOOP FOR each age x Set female survival P x 1 FemaleMortality p xJ FOR each type of catastrophe c 11 Adjust P x for catastrophes Multiply P x by CatastropheFrequency p c CatastropheSurvivalSeverity p c 1 CatastopheFrequency p c END catastrophe LOOP Multiply cumulative survivorship L x by P lx IF x gt FemaleBreedingAge Add L x M to SumLxMx Add x L x M to SumAgeLxMx END IF END age LOOP Set RO SumLxMx Set Generation Time p SumAgeLxMx SumLxMx Preliminary estimate Set Lambda RO
17. Scenario Default Scenario y Population Population1 y VORTEX 10 00 01 simulation of population dynamics Project New Project Scenario Default Scenario 12 03 2014 2 populations simulated for 100 years for 100 iterations Sequence of events in each time cycle EV Breed Mortality Age Disperse Harvest Supplement Calc Ktruncation Sendto Report Save As Print The Input Summary will not be updated until you save your Scenario It is always a good idea to scroll through the Input Summary to be sure that you entered all the input values correctly for your scenario and that VORTEX interpreted the inputs as you intended 72 Deterministic Results The second section of Text Output provides both text and a simple graph to display the deterministic projections of population size The text window shows the exponential rate of increase r the annual rate of change A and the per generation rate of change or net replacement rate Ro as determined from life table analysis of the mean rates of reproduction and survival in your model The mean generation time and a stable age distribution calculated from age specific birth and death rates are also given File Simulation Help B amp det st Project Settings i Output Tables and Graphs Project Report Input Summary Output Summary Output Tables ST Tables
18. These state variables must be numeric values or something that can be coded as a numeric value Population state variables may describe characteristics such as measures of habitat quality or habitat suitability for the population elevation or some other descriptor of the habitat or perhaps some statistic e g density that you want to tally during the simulation This option of entering population state variables is provided so that demographic rates such as fecundity mortality and carrying capacity can be specified to be functions of these state variables To create one or more population state variables click the Add button for each variable you will be creating For each variable you then enter into the table a label which can be any text that will help you to remember what parameter you were representing For each PS variable you need to enter two functions or constants to define a an initialization function Init fn the starting value for each population at the beginning of the simulation and b a transition function Transition fn the change in state if any each year of the simulation There is a drop down list for selecting the population to which your PS variable functions will be applied You can Add or Delete a PS variable only from the first population That variable and its initial specifications are then copied over to the later populations You then need to step through each population to adjust the Initiali
19. and c a transition function Transition fn the change in state if any each year of the simulation These functions are entered in the same way as other functions that can be used to specify demographic rates see section on Functions Note that the initialization function is used both for individuals at the start of the simulation and also for any individuals added in later supplementation This provides an easy way to determine if an individual was a supplement because the Init fn can be set to be a special code after year 0 E g Init fn IF Y 0 1 2 will assign 2 to the IS variable for all supplemented individuals One special use of an IS variable is to give a Label of POPULATION in order to use the IS variable to move individuals between populations based on their characteristics Usually there would be ways to accomplish this with Dispersal using a function for the dispersal rate but for certain kinds of movements it might be easier to use the IS variable to change the population Each time that IS variables are updated if there is an IS variable with name POPULATION and if the value of that variable is set to something other than the current population then the individual is moved However if POPULATION is set to a number that is not a population e g 0 then the individual is left in its current population For example a Transition fn of IF I gt 0 20 1 0 would place individuals with inbreeding of F gt 0 20 into population 1
20. and leave all others in their current population This functionality can be used to optimize genetic management of a metapopulation such as with IF MK1 lt MK2 1 2 or if there are 4 populations FIND LOW MK1 MK2 MK3 MK4 MK1 MK2 MK3 MK4 to place each individual into the population where it has the lowest mean kinship An aside blindly moving all individuals to the population where they have the lowest mean kinship can cause some very odd results e g all individuals in population can get instantly moved to population 2 leaving population 1 with no individuals and therefore not a good place to put anyone Caution be sure not to label an IS variable aa POPULATION unless you do want to use it to control movements among populations Note also that population statistics such as N might not be updated in between the updating of the IS variables for each individual so do not use N or M F J etc with this option as a means to move individuals until a population reaches some threshold N will be updated at times however when an individual in a different population is evaluated so if you want to use the N for each population as it existed before the movements of individuals in the IS update started set a PS variable to N and use that PS variable in your IS variable Transition fn MK values are updated as each individual is moved as those values are individual characteristics Default values The table at the bottom of the page allows you
21. and truncate symmetri cally to avoid bias IF Rate gt 0 5 Set UpperLimit 1 200 Set LowerLimit Rate 1 Rate ELSE Set UpperLimit 2 Rate Set LowerLimit 0 END IF ELSE Add EV EVNRand to Rate Let Rate max LowerLimit Rate Let Rate min UpperLimit Rate END IF ELSE END FUNCTION ADJUSTRATE BEGIN FUNCTION MIGRATE FOR each living animal IF not in age range that migrates CONTINUE LOOP with next animal END IF IF not a sex that migrates CONTINUE LOOP with next animal END IF Set MigrationRand RAND Set pSource to population of current animal IF MigrationRand gt CumulativeMigrationProb pSource NumberPopulations CONTINUE LOOP with next animal Does not migrate END IF Obtain Migration Density by evaluating function or using specified constant parameter 11 See Note 3 IF PopulationSize pSource CarryingCapacity pSource lt MigrationDensity CONTINUE LOOP with next animal END IF Obtain MigrationSurvival by evaluating function or using specified constant parameter II See Note 3 Find to which population the animal migrates FOR up to 10 attempts to enter another population 11 The limit of 10 attempts is imposed to prevent an infi nite loop from occurring when all populations are at carry ing capacity IF RAND gt MigrationSurvival Animal dies BREAK from LOOP CONTINUE with next animal END IF FOR each population pDestination IF Mi
22. dat files used for graphing non ST scenarios so the ST results can also be analyzed and graphed in other programs Note that the Tables amp Graphs within ST and the Tables amp Graphs tab within the main PMx program are very similar and that was purposeful but the ST version will use only the stdat data files and the main program will use only the dat data files Therefore the data available to be plotted in the two sections are different O Plot Table ST Analysis MyST1 y N vs Year MyST1 Base 50 40 10 15 a MyST1 1 70 50 26 5947 20 MyST1 2 60 30 28 8974 15 MyST1 3 70 50 85 7157 20 MyST1 4 70 40 97 0497 15 Erorbars None SE sD Samples to include 160 MyST1 Base a 140 MyST1 1 F100 MyST1 2 MyST1 3 100 80 0 MyST1 5 k MyST1 6 ou MyST1 7 X 40 opulations to be included as lines 20 MyST1 Base Pop1 0 MyST1 1 Pop1 0 10 20 30 40 50 60 70 80 90 100 MyST1 2 Pop1 Years MyST1 3 Pop1 MyST1 4 Pop1 aaa Il a SISSS88 n 5520 Le You open the ST Tables amp Graphs by clicking on the Display Graphs button of the Sensitivity Testing setup window The first step in generating graphs is to select from the top left drop down list the ST Analysis for which you want to see the results You then check which of the sampled scenarios from that ST are to be included in the graph If your ST generat
23. ed Viable Populations for Conservation Cambridge Cambridge University Press Latour A 1986 Polar normal distribution Byte August 1986 131 2 Lindenmayer D B and R C Lacy 1995a Metapopulation viability of Leadbeater s Possum Gymnobelideus leadbeateri in fragmented old growth forests Ecological Applications 5 164 182 Lindenmayer D B and R C Lacy 1995b Metapopulation viability of arboreal marsupials in fragmented old growth forests Comparison among species Ecological Applications 5 183 199 Lindenmayer D B and R C Lacy 1995c A simulation study of the impacts of population sub division on the mountain brushtail possum Trichosurus caninus Ogilby Phalangeridae Marsupialia in south eastern Australia I Demographic stability and population persistence Biological Conservation 73 119 129 Lindenmayer D B T W Clark R C Lacy and V C Thomas 1993 Population viability analysis as a tool in wildlife conservation policy A review with reference to Australia Environmental Management 17 745 758 Mace G M and R Lande 1991 Assessing extinction threats Toward a re evaluation of IUCN threatened species categories Conservation Biology 5 148 157 Mace G et al 1992 The development of new criteria for listing species on the IUCN Red List Species 19 16 22 Mace G and S Stuart 1994 Draft IUCN Red List Categories Version 2 2 Species 21 22 13 24 MacNab J 1985 Carrying capacity and related slippe
24. esses Below are a few examples of interactions among threatening processes that can reduce population viability often in unexpected and unexpectedly strong ways Increased dispersal among patches of habitat is usually assumed to help stabilize a metapopulation Increased dis persal can restore genetic variation to previously inbred populations can reduce demographic fluctuations within local populations can rescue demographically weak popu lations Brown and Kodric Brown 1977 and can lead to recolonization of temporarily extirpated local populations However the metapopulation dynamics of small partly isolated and frequently extirpated populations can be highly dependent on spatial temporal and behavioral as pects of the population structure Fahrig and Merriam 1994 For example ifa metapopulation declines to a level at which many of its constituent local populations are very small or extinct then the benefits of dispersal can be re placed by disadvantages Uncompensated emigration from isolated populations can depress local population growth Fahrig and Merriam 1985 and suitable habitat that is temporarily empty can act as a population sink where ani mals fail to find mates Gyllenberg and Hanski 1992 Consequently increased dispersal can accelerate decline of sparsely populated metapopulations Lindenmayer and Lacy 1995 This collapse into a metapopulation vortex may be more likely if dispersal behaviors evolved in a phy
25. is the extinction expected to result primarily from negative average population growth mean deaths exceeding mean births from large fluctuations in numbers from effects of accumulated inbreeding or from a combination of these factors Given that there is considerable uncertainty about several aspects of the species biology and its habitat is the population likely to persist across the plausible ranges of parameters that might characterize the population In particular how sensitive are the population dynamics to varying estimates of reproductive success juvenile survival adult survival effects of natural catastrophes initial population size carrying capacity of the habitat and dispersal among populations Are there critical values for any of these parameters which demarcate a transition from a population that would be considered viable to one that is not Which factors have the greatest influence on the projected population performance If important factors are identified management actions might be designed to improve these factors or ameliorate the negative effects How much change would be required in aspects of the population in order to ensure population survival What would be the effect of removing some individuals from the population Would there be a significant benefit from supplementing the population with individuals translocated from other populations or released from captive breeding stocks Can the population sustain contro
26. not a comma to avoid problems arising from the comma being used as a decimal separator with some regional data settings Hints for speed Functions can be much slower to evaluate than are simple constant values Therefore don t enter 0 25 or 1 4 both interpreted as functions because they are preceded by when you could have entered just 0 25 And don t use the same complicated function in multiple places Instead set a PSvar to that function and then set the various variables to that PSvar This also makes it easier to later edit that function Random numbers RAND NRAND and especially SRAND and SNRAND are very slow Therefore don t use them more than needed For example instead of using SRAND Y 123 three times to get the same random number used in all 3 places which will require 3 calls to the SRAND function each year create a PSvar that RAND and then use this PSvar in all three places so that RAND gets called once per year 108 Using the Function Editor The Function Editor in VORTEX provides a tool for editing testing and graphing functions that you might want to use in your Project The Function Editor can be accessed either by hitting the function icon fx or with ctrl F inom E A a AR Function Evaluator Function Grapher Enter Function 50 50 25 N K 2 N A N Emoto te Xar N Range 1 to 100 Increment 1 Parenthetically ri PA OR 3D Yar A Range 1 to 10 Increment 1 Polish 505
27. o 80 60 _ 59 5 40 E E zZ 1940 be expected to show minimal susceptibility to environ mental variation Observed variation in the numbers of hatchlings from 1976 to 1991 was approximately that which would be expected due solely to the demographic variation that would result from a random annual sam pling of breeders from the pool of adult birds each with a constant probability of reproductive success Mirande et al 1991 Variation across years in first year survival was more than three fold greater than what would be expected due to demographic sampling indicating that the proba bility of chick mortality fluctuates across years due to envi ronmental variation Adult mortality however seemed to fall into two classes in some years mortality was signifi cantly greater than mortality in other years and deviated significantly further from the mean than can be expected from random demographic stochasticity The cause of 9000 8000 7000 6000 4000 3000 Estimated Number Fig 4 Estimated numbers of palila with 90 confidence in tervals from field surveys Adapted from Ellis et al 1992 1000 1980 ECOLOGICAL BULLETINS 48 2000 1982 Whooping Cranes 1938 1995 1950 1960 1970 1980 1990 these years of poor survival is not known as census counts were made only once a year during those years However they would appear to be examples of natural catastrophes If these catastrophe years are
28. results of various possible management options PVA models also have weaknesses and limitations A model of the population dynamics does not define the goals for conservation planning Goals in terms of population growth probability of persistence number of extant populations genetic diversity or other measures of population performance must be defined by the management authorities before the results of population modeling can be used Because the models incorporate many factors the number of possibilities to test can seem endless and it can be difficult to determine which of the factors that were analyzed are most important to the population dynamics PVA models are necessarily incomplete We can model only those factors which we understand and for which we can specify the parameters Therefore it is important to realize that the models probably underestimate the threats facing the population Finally the models are used to predict the long term effects of the processes presently acting on the population Many aspects of the situation could change radically within the time span that is modeled Therefore it is important to reassess the data and model results periodically with changes made to the conservation programs as needed Dealing with uncertainty It is important to recognize that uncertainty regarding the biological parameters of a population and its consequent fate occurs at several levels and for independent reasons Uncertainty can
29. the normal approximation to the binomial when used is truncated symmetrically around the mean Environmental variation VORTEX can model annual fluctuations in birth and death rates and in carrying capacity as might result from environmental variation To model environmental variation each demographic parameter is assigned a distribution with a mean and standard deviation that is specified by the user Annual fluctuations in probabilities of reproduction and mortality are modeled as binomial distributions Environmental variation in carrying capacity is modeled as a normal distribution Environmental variation in demographic rates can be correlated among populations Catastrophes Catastrophes are modeled in VORTEX as random events that occur with specified probabilities A catastrophe will occur if a randomly generated number between zero and one is less than the probability of occurrence Following a catastrophic event the chances of survival and successful breeding for that simulated year are multiplied by severity factors For example forest fires might occur once in 50 years on average killing 25 of animals and reducing breeding by survivors 50 for the year Such a catastrophe would be modeled as a random event with 0 02 probability of occurrence each year and severity factors of 0 75 for survival and 0 50 for reproduction Catastrophes can be local impacting populations independently or regional affecting sets of populations simul
30. 30 0 25 0 20 0 15 0 F 10 0 5 0 F 0 0 Demographic Rate O 10 20 30 40 50 60 70 80 90 100 Age Years 124 9 Increase in mortality with inbreeding RATE 100 50 EXP 1 57 1 The survival rate declines exponentially 90 0 F described by the portion within the 80 0 outermost parentheses while the percent mortality is set at 100 survival This is the equation used by VORTEX to model increased juvenile mortality if there are 3 14 lethal 70 0 60 0 50 0 Demographic Rate equivalents and no recessive lethal alleles SO contributing to inbreeding depression 20011 20 0 H 10 0 0 0 L L L L L 1 L L L 0 10 20 30 40 50 60 70 80 90 100 Inbreeding Coefficient 10 Stepwise increase RATE 10 Y gt 10 10 Y gt 20 10 Y gt 30 10 The rate increases from 50 to 80 at 10 year intervals An alternative way to express the same function would be 90 0 F 80 0 70 0 RATE 50 10 MIN 3 FLOOR Y 1 10 60 0 50 0 40 0 30 0 f Demographic Rate 20 0 10 0 0 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 11 Different rates at different intervals RATE 10 A lt 3 25 A 3 30 A 4 OR A 5 35 A gt 5 AND A lt 1 0 20 A gt 10 AND A lt 15 The rate increases stepwise with age then 50 0 E drops to a lower level for years 10 through 45 0 14 and then drops to zero for animals 15 o oo
31. Allee effect Technically P O is the y intercept that would result from the exponential function if parameter A 0 but it will usually be approximately the breeding rate under ideal conditions It is best to derive the values of P 0 P K A and B from a regression analysis of data on the breeding rate of your population If these data are unavailable but you can estimate P 0 and P K then you may want to explore several different combinations of A and B to come up with a curve that seems appropriate for your population You could use graphics or statistical 39 Adult Females Breeding per Year P N P 0 80 P K 40 K 100 A 0 P 0 80 P K 40 K 100 B 8 30 40 50 60 70 80 90 100 Population Size N Plots of the default density dependence relationship as used by VORTEX in the absence of an Allee effect A 0 panel A in the presence of a steep decrease in breeding success at high population densities B 8 panel B and both a steep decrease in breeding Adult Females Breeding per Year P N P 0 80 P K 40 K 100 A 1 success at high population densities and an Allee 0 10 2 30 40 50 60 70 80 90 100 effect A 1 and B 8 panel C Population Size N software or even graph paper and a calculator to construct a range of hypothetical curves using different combinations of parameters as was done to produce the figures above If you do use density depende
32. Harvest Mortality of males as Supplementation Population 1 Population 2 Genetics Mortality from age 0 to 1 50 50 SD in 0 to 1 mortality due to EV 10 10 Gapiin vehics hos Mortality from age 1 to 2 10 10 SD in 1 to 2 mortality due to EV 3 3 Annual mortality after age 2 10 10 to subsequent populations SD in mortality after age 2 3 3 Mortality of Females Males as In these tables enter the mean mortality rates for each age class and enter also a standard deviation SD for each mean to describe the environmental variation EV in each rate Be aware that if you enter a standard deviation for each mean mortality rate that is at least half of the survival rate 100 mortality rate in occasional years the mortality rate will be set at 100 and the population will immediately go extinct For example if all age specific mortality rates are 50 and the standard deviations are set at 25 then in about 1 in 40 years the mortality rate after adjustment for EV will be 100 since the rate will exceed the mean by 2 standard deviations about 2 5 of the time A substantial literature exists on the many methods by which one can estimate age sex specific mortality rates in wild populations Caughley 1977 is a good text from which to start an exploration of this body of information 45 Estimating mortality rates from sightings of banded Whooping Cranes As of 1991 the last remaining population of the whooping crane Gr
33. If you enter 0 for bin width then VORTEX will analyze your data to try to determine a good bin width for presenting your results Often it does a good job but sometimes it does not and you can always test alternative bin widths to see what resolution of the distribution looks best to you 85 File EEE Help l n ae bel amp Det p ST Project Settings Simulation Input Text Output Tables and Graphs Project Report Frequency Distribution of TE X Plot Table 0 Use O for automatic binning Scenarios to include Ome o F N25K300 Frequency o a Populations to be included Y Current BNNR 80 90 100 110 120 130 140 150 Year Sendto Report Save As Pint _ Edit Line Labels Update Piot _ A frequency distribution of time to extinction with the default Bin Width of 1 year 3 40 50 60 70 Current 80 90 100 110 120 130 140 150 Year Ed File Simulation Help OEA amp Det D ST Project Settings Simulation Input Text Output Tables and Graphs Project Report Frequency Distribution of TE y Plot Table Plot Options Bin width 5 Use O for automatic binning 0 07 0 06 Scenarios to include 0 05 IE N25K300 300 5 0 03 0 02 Populations to be include
34. Implement as a Translocation Under the option to Implement as a Translocation the last population is treated as a holding population for transferring individuals among the other populations An undocumented Special Option allows you to set some other population to be the holding peopulation Any individuals supplemented to populations other than the holding population will be taken from the holding population If not enough individuals are available to meet the specified number of supplements all those that are available will be moved Any supplements into the holding population will be new individuals as is the case for all supplements when the translocation option is not selected The if box allows you to enter 57 conditions as function or number representing a probability under which the individuals supplemented into populations will be treated as translocations taken from the holding population rather than supplemented as new individuals added to the model Percent survival during Translocation This data entry box is linked to the one on the Harvest page and it can be used to specify the survival of individuals during the Translocation Any mortality during Translocation is imposed in addition to any normal mortality and it will occur when the individuals are being moved into the last population Optional criteria for individuals to be released You can specify that individuals must meet criteria to be available for release f
35. Mate Monopolization 42 51 Note that inbreeding can also affect later survival and other aspects of demography To model effects on other demographic rates enter rates as functions of inbreeding Initial Population Size Carrying Capacity Harvest Y EV concordance of reproduction and survival Supplementation PA EV correlation among populations 05 E Inbreeding depression Check this box if you want to include inbreeding depression in your model as a reduction in first year survival among inbred individuals Although most diploid species that have been studied show depressed fitness when inbred you may sometimes want to leave inbreeding depression out of your model so that you can compare results with and without inbreeding depression thereby allowing you to document what impacts inbreeding depression could have on population viability Lethal Equivalents This box asks you to specify the severity of inbreeding depression in your simulated population if the population becomes inbred Enter the impact of inbreeding on first year survival quantified as lethal equivalents per diploid individual See Box below Percent Due to Recessive Lethals Enter here the percent of the total genetic load quantified by the lethal equivalents you entered into the previous box that is due to recessive lethal alleles The number of lethals per founder will be distributed approximately as a Poisson distribution A plausible value on
36. Read in GlobalOrLocal p c END IF Read in CatastropheFrequency p lc Read in CatastropheBreedSeverizy p c Read in CatastropheSurvivalSeverity plc END catastrophe LOOP CALC_DETERMINISTIC_GROWTH p I Calculate deterministic population growth rate genera tion time and stable age distribution from mean birth and death rates Effects of any catastrophes are averaged across years Read in ProportionMalesInBreedingPool p II See Note 4 IF initial numbers of animals are to be distributed according to the stable age distribution Determine initial numbers of animals in each age sex class 1 The stable age distribution would rarely assign whole numbers to each age sex class Integral numbers are assigned that most closely match the desired distribution ELSE does not start at stable age distribution FOR each sex FOR each age up to MaximumAge Read in initial number of animals END LOOP END LOOP END stable age distribution IF ELSE Read in CarryingCapacity p K 11 K may be specified as a function of year or other param eters See Note 3 Read in KEV p Read in Harvest p IF Harvest p Yes Read in FirstYearHarvest p Last YearHarvest p Harvestinterval p FOR each age x up to FemaleBreedingAge 11 For harvest all adults are treated in the same age cat egory Read in NumberFemales ToBeHarvested p x END LOOP FOR each age x up to MaleBreedingAge Read in NumberMales ToBeHarvested p x
37. VORTEX simulation is available within program libraries dll files that can be accessed by other interfaces such as METAMODEL MANAGER available at www vortex 10 org MeMoMa aspx and VORTEX Project files created in any software can be run from a command line version of VORTEX see below The opening window provides options to start a new Project which will initially have a default scenario open an existing previously saved Project or open a list of recently opened Projects for quicker access Vortex 10 A stochastic simulation of the extinction process Version 10 0 7 0 Begin a New Project Open a Project Existing Recent Quit Copyright 2014 Chicago Zoological Society If you start a new Project with the default scenario it is important to go through every input page to change the initial default input values to something that is appropriate for your case The default values let you run a test scenario just to see that VORTEX 1s working for you and the defaults also are often useful indicators of the magnitude and format of a typical input value e g a percent or an integer or a number from 0 to 1 However if you forget to change the default values on an input page while you are creating a scenario for your analysis you may not be getting the scenario that you had intended When you select an existing Project the Open dialog will initially go to the last folder in which you had worked but you can navigate to o
38. VORTEX will show a few summary statistics at the bottom of the graph You can Save or Print the graph or edit it further by accessing graph Properties by double clicking on the graph Close the graph when you are ready to return to the main interface If you want to stop VORTEX in the middle of a simulation for example if it is running very slowly and you think that you had entered something incorrectly and will need to run it again you can try to click often multiple times on the x icon in the corner of the graph of N being generated during the simulation Often this will work because it forces sometimes after a little time VORTEX to crash when Windows can t continue to update the graph If this does not work and you are still desperate to stop VORTEX you can open the Windows Task Manager accessible with Ctrl Alt Del click on the VORTEX Application and then End Task Either of these methods is rather drastic and Windows may give you a meaningless message about trying to find a solution or sending a report about the crash Microsoft has no solution to provide and it won t do anything with such reports VORTEX will shut down and it may leave partial and corrupted output files in your project folder This is a good reason to always save your Project after you make changes before you run the simulation If you do force VORTEX to crash or it does so on its own it is best to fix the data and rerun the simulation even with just
39. any may impact your population You may be able to identify historical catastrophes by examining birth and or death rate data over several past years for your species of interest If you find a demographic rate that is significantly different than that described by normal levels of variation for example at least 2 standard deviations from the mean value you may use that as evidence of a catastrophic event even if the cause was unknown After specifying how many types of catastrophes you want to model you move between catastrophes by selecting from a dropdown list Catastrophe Label You first enter a label for each catastrophe as a way to remind yourself and others what events you were modeling 47 Frequency and extent of occurrence Each catastrophe is specified to be local or global in scope this is applicable only when more than one population is modeled You are given considerable flexibility in how the scope of each catastrophe is specified so it is important to read the following information carefully in order to correctly model your metapopulation A global catastrophe will occur in the same years in all populations but the severity of effects can be entered as different or equal across populations Local catastrophes occur independently among the populations To cause a catastrophe to be regional in scope affecting only a subset of the populations you can specify that it is global but then set the frequency to 0 0 see
40. are diverse and not well defined the PHVA process contains a number of critical components First it is essential to gather an array of experts who have knowledge of the species or problem A PHVA is not required to bring together experts but it often facilitates such sharing of expertise because the collective knowledge of many is essential for a useful PVA in the narrow sense to be completed In addition to a diversity of people a PHVA workshop also requires and therefore facilitates the involvement of a number of agencies and other concerned organizations For example the PVA on the two endemic primates of the Tana River Primate Reserve in Kenya Seal et al 1991 was convened by the Kenya Wildlife Service facilitated by the IUCN SSC Captive Breeding Specialist Group benefited from the expertise contributed by members of the IUCN SSC Primate Specialist Group and was sponsored by the World Bank The involvement of many agencies and interested parties is critical to endangered species recovery An early requirement or prerequisite of a PHVA workshop is to determine the conservation problem to be addressed and to state the goals of the management plan Many endangered species programs have not clearly identified their goals For example at a PHVA and Conservation Assessment and Management Plan workshop on the forest birds of the Hawaiian islands Ellis et al 1992a 1992b it became apparent that the agencies responsible for the conservation o
41. as can the input file used for the Lineage pedigree program The fields in the studbook are not required to be in the order shown in the above header except that ID should always be the first field VORTEX will use the header to determine the order of data fields in the studbook The output file with extension all that is created when you choose the Special Option to produce a file of all individuals can also be used as the studbook input file for the starting population Therefore you can set this Special Option to produce the file from a single iteration and then use the results of that simulation as the starting population for a simulation further years This is one way to start a simulation with a population that already has a pedigree structure and history The only required data in the studbook file are ID dam sex and alive If Dam or Sire is blank WILD or UNK for an individual that individual is assumed to be a founder unrelated to all other founders Sex should normally be coded as Female or F or f or female and Male or male or M or m because different studbook programs use 0 and 1 for male and female respectively e g Lineage or the reverse female and male respectively e g Sparks so numeric coding of sex can easily lead to errors If Population is missing then all individuals are assumed to be in population 1 If either Selected or Alive is False or 0 then the individual i
42. available food supply for a detailed discussion of this technique see Hobbs and Swift 1985 For example Petit and Pors 1996 estimated population sizes flower availability and nectar output for each of three species of columnar cacti on Cura ao Carrying capacities for the two species of nectar feeding bats dependent on these cacti could then be estimated based on the daily availability of mature flowers and the field energy requirements of the bats with additional energy requirements associated with pregnancy and lactation taken into account If detailed data such as these are unavailable a rough estimate of habitat carrying capacity can be generated using long term data on population size If the size of the population of interest appears to be relatively constant over the period of observation and in the absence of significant human impact one can fairly safely assume that the population is at or near its carrying capacity If this equilibrium is observed in the presence of major human influences such as a strong hunting pressure then historical data could be consulted to determine if this stable size is indeed natural or purely artificial One could also calculate K for a given habitat using population density data from undisturbed habitats elsewhere in the species range Harvest In this section VORTEX gives you the option of removing individuals during a simulation Harvest can mimic hunting culling research related removal
43. banded birds 89 9 annual survival was observed in 386 bird years but band loss after several years could have accounted for some of the mortality recorded among banded individuals No variation was detectable statistically among mortality rates calculated separately for each age class beyond the first year The observed annual variation in survival rates from 1938 to 1990 was V 0 00255 the variation expected due to binomial sampling from a constant probability is V 0 00220 The difference can be attributed to environmental variation in the probability of surviving with V 0 00035 or SD 0 019 This value turned out to be very close to the intuitive estimate provided by workshop participants that annual fluctuations in mortality rates would be about 2 46 Catastrophes The input page for Catastrophes has been changed only slightly from version 9 The number of catastrophes is entered directly on this page and you move between catastrophes by selecting from a dropdown list rather than by clicking on a label File Salon Help fe Det D ST Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current New Scenario Default Scenario Default Scenario Copy Default Scenario Copy2 E Section Notes Scenario Settings Catastrophes Species Description aiai of catastrophes 2 State Variables s Select for which catastrophe you want to set
44. be something different from the options that were copied to all populations In this way if you are careful you can relatively quickly set the options that are to be the same for all populations do this first and then set some specific alternative options for each population After you set Genetic Management options for several populations it is a good idea to click through the dropdown list of populations to confirm that the options are correctly set to what you want for each one Optional criteria for Genetic Management of Population You can provide a function that will specify under what conditions the genetic management options will be applied When the function evaluates to True 1 the options are applied when it is False 0 they are not For example you can set a function of N gt 0 75 K to have the Genetic Management applied only 65 when the population is above 75 of K These criteria will not affect the option to set initial kinships to a value other than 0 Breed to maintain the population at K With this option the program will calculate each year the expected number of matings required to bring the population to but not beyond the carrying capacity Note that K may still not be reached if there are not enough adult females to fulfill the required number of matings When this option is selected the adult females breeding in Reproductive Rates has a somewhat different meaning than usual it will be the maximum
45. bit complex Because DS is usually quite small when the sample sizes n are at all large a quick somewhat generous estimate of EV is simply the total variation in rates observed across years treating DS as an insignificant contributor to the observed variation Finally keep in mind that the VORTEX simulation program generates DS automatically as it determines whether each individual lives whether it breeds and what sex it is Unlike some other PVA programs you do not specify that DS should be added into the model and you cannot exclude it from the model or from real life You do need to specify the magnitude of EV however as EV results from external processes rather than being an intrinsic and inevitable part of all population dynamics The size of DS is a consequence of the population size the size of EV depends on the constancy of the environment 29 State Variables Any number of state variables can be created to describe characteristics of the system global each population and each individual These can be useful if other input values will be specified as functions of such state variables or if a state variable tallies some metric of interest e g the number of 2 year old individuals as in PS2 below Vortex 10 MyProject CAVortex10Projects MyProject MyProjectxm PES File Simulation Help 4 ed amp det st Project Settings Simulation Input Text Output Tables and Graphs Projec
46. currently living still dependent offspring This means that you can specify for example that only females with no dependent young can breed each year Moreover if the dam dies then all currently dependent offspring are killed Annual sequence The sequence of events in the annual cycle can be specified to be something other than the default EV setting annual rates Breeding Mortality Aging Dispersal Harvest Supplementation Calculate Growth Carrying Capacity Update GSVars PSVars and ISVars Census Steps can be placed in any order and steps can be repeated e g there can be dispersal both before and after harvest Updating of state variables can be done as one operation with the order being GS then PS then IS or the three levels of state variables can be updated independently Age classes for which input values need to be specified will be determined by which steps are placed before Aging For example if Harvest occurs before Aging in each year then the 0 age class animals can be harvested If two breeding cycles occur without an Aging step intervening then 0 age class animals can breed State variables Any number of state variables can be created GSvars PSvars and ISvars can be referenced in functions by either the state variable number 1 e GS1 PS3 IS7 as before or can be referenced by their labels Be sure not to use a label that is the same as a built in function such as DAM SIRE PARITY with the
47. dies END IF END LOOP IF not yet dead GETDEATHRATE Set SurvivalRate 1 DeathRate IF Inbreeding gt 0 Set SurvivalRate exp 0 50 LethalEquivalents Inbreeding ENDIF IF RAND gt SurvivalRate Offspring dies END IF END IF IF not dead Calculate kinship to every living animal I See Ballou 1983 for the method of calculating inbreed ing and kinship coefficients END IF END offspring LOOP END breeding females LOOP END FUNCTION BREED BEGIN FUNCTION GETBREEDRATE Obtain BreedRate by evaluating fecundity function for population and individual parameters 11 Most often the fecundity function will simply return ProportionFemalesBreeding entered by the user VORTEX provides the option however of making breeding a func tion of PopulationSize GeneDiversity Inbreeding and other variables See Note 3 ADJUSTRATE BreedRate LocalBreedEV p LocalBreedEVRand LocalBreedEVNRana Adjust rate for local EV ADJUSTRATE BreedRate GlobalBreedEV p GlobalBreedEVRand GlobalBreedEVNRand 11 Adjust rate for global EV FOR each type of catastrophe c IF CatastropheFlag c TRUE Multiply BreedRate by Catastrophe BreedSeverity p c END IF END LOOP END FUNCTION GETBREEDRATE BEGIN FUNCTION MORTALITY for population p FOR each living animal in the population IF age gt 0 Infant mortality occurs within the BREED function not here 199 IF at maximum age Animal di
48. e g FemalesBreeding can be set to SV1 or can be used within a larger function so that a set of VORTEX input values are changed synchronously e g if SV2 is to be a multiplier for baseline mortality rates then each mortality rate might be specified with a function such as SV2 20 with 20 being the baseline rate for that age sex class a Give each SV a Description that is meaningful to you b The synonym is filled in automatically by VORTEX and it specifies to what new GSvar the SV will be assigned You can then use either SV1 or the synonymous GS1 in your inputs You cannot change either the SV or the GS synonym as these are automatically assigned by VORTEX c The Base Value will not impact the ST itself but it is useful because you can later run the ST scenario with the base values to provide a baseline set of results 95 d There are several methods for specifying the set of parameter values to be tested and they will be applied in the order specified below i Ifa Value List is provided then the values are sampled from that list This should be a list of values separated by semi colons not commas ii Ifno Value List is provided but a Minimum Maximum and Increment gt 0 are all provided then the values are sampled from the set of discrete values from the minimum to maximum inclusive at the specified intervals iii However with LHS the Increment is determined by the samples specified The Increment and th
49. each scenario READ_SPECIES_PARAMETERS IF NumberOfPopulations gt 1 READ_MIGRATION_PARAMETERSO 1 VORTEX describes dispersal between populations as migration END IF FOR each population p READ_POPULATION_PARAMETERS p END population LOOP FOR each population pSource II Calculate cumulative migration rates for each pairwise transition between populations Set CumMigrationProb pSource 1 MigrationProb pSource 1 FOR each destination population pDestination greater than 1 Set CumMigrationProb pSource p Destination CumMigrationProb pSource p Destination 1 MigrationProb pSource p Destination END pDestination LOOP END pSource LOOP Set NumberLethals InbreedingGeneticLoad ProportionLoadDue ToLethals Set LethalEquivalents InbreedingGeneticLoad 1 ProportionLoadDue ToLethals II See Note 2 FOR each population p Set GlobalBreedEV p BreedEV p EVConcordanceAmongPopulations Set LocalBreedEV p SQRT BreedEV p 2 GlobalBreedEV p 2 Partition Environmental Variation in breeding BreedEV into the component that is common to all populations GlobalBreedEV and the component that is specific to each population LocalBreedEV TotalEV 2 GlobalEV 2 LocalEV 2 1 Note EVs are given as standard deviations FOR each sex 5 FOR each age x up to age of breeding Set GlobalMortEV p 5 x MortEV p s x EVConcordanceAmongPopulations Set LocalMort
50. excluded from the data as spe cial cases the annual variation in adult mortality was only slightly greater than that expected due to random demo graphic stochasticity Mirande et al 1991 Figure 4 shows the population trends for the palila Loxioides bailleui a finch which is restricted to the ma mane forests on the slopes of the major volcanoes of the island of Hawaii Although some variation in population size may be caused by imprecise census estimates the spe cies clearly undergoes striking fluctuations in numbers even though the mean population size is ca 30 times great er than the current population of whooping cranes Palila must be sensitive to environmental variation probably Palila 1980 1993 1984 1986 1988 1990 1992 with respect to both breeding and survival In part because of the much higher sensitivity to environmental variation PVA modeling projected a higher probability of extinction for palila Ellis et al 1992 than for the much smaller pop ulation of whooping cranes Mirande et al 1991 The contribution of environmental variation to extinction vor tices is well recognized Belovsky 1987 Goodman 1987 Foley 1994 but as with demographic stochasticity we may not always recognize how large the effect can be Disrupted breeding systems There is another cause of demographic instability in small populations but it does not fit easily within the categories of Shaffer 1981 is rarely considered in PVA m
51. from the birth and death rates If you choose Use specified age distribution then you enter the number in each age sex class and VORTEX totals these to fill in the Initial Population Size table The initial age structure of the population can instead be specified by a proportional distribution with a total initial N With this option you need to enter both the total N and numbers for the age sex classes VORTEX will then allocate the initial N for you according to the specified proportional distribution The values you enter for the age sex classes do not need to total to 1 or to N or to any specific number VORTEX will use them as a relative distribution One way in which you can use a combination of these options is to first enter a specified age distribution Then change the option to a proportional distribution You can then create additional scenarios that keep that same proportional distribution even as you change the total N and other input values 50 Sometimes the stable age distribution cannot be calculated if you use functions for some of your demographic rates because in such cases the age distribution depends on the values of the variable parameters in your functions There are two ways in which you can get a reasonable starting age distribution in such cases You can create your scenario first with specified mean values for the demographic rates into which you will want to enter functions Then go to the Initial Populatio
52. impacts all individuals in the population simultaneously The sources of this environmental variation are outside the population examples include weather predator and prey population densities and parasite loads These factors can affect reproduction and survival independently or simultaneously Check this box if you think that good years for reproduction are also good years for survival Correlating environmental variation for reproduction and survival North America s whooping crane Grus americana shows a classic migratory pattern typical of many northern bird species The last remaining substantial population breeds in Alberta s Wood Buffalo National Park and spends the winter at Aransas National Wildlife Refuge along the Gulf Coast of Texas Because of this movement pattern the environmental conditions affecting chick production are quite different from those impacting mortality during the majority of the year Mirande et al 1991 Consequently we would expect EV affecting these processes to be uncorrelated when constructing a VORTEX model EV Correlation Among Populations You specify here the correlation of EV among populations applicable of course only when more than one population is modeled If this value is set to 0 0 then EV will be completely independent among populations If this value is set to 1 0 then EV in reproduction and in survival will be completely synchronized among populations As a result good years f
53. is provided for cases in which you want to tally disperse harvest or otherwise consider newborns before they are subjected to the 1 year mortality Note however that deaths due to inbreeding depression are imposed at birth regardless of this option e During harvest instead of killing individuals that are harvested set their ISx variable to 0 If x is not specified it is assumed to be IS1 This option can be used for example to contracept a specific number of animals each year assuming that you also set the probability of breeding to be a function of IS1 New Undocumented Options e P obtain the mate for each female from an Svar labeled MATE If MATE 1 then a mate is selected at random from the available males The Svar labeled MATE will be the index of the individual to be used as the mate if available e Q obtain mates from ISvar MATE as with option P but look for the male with ISvar name rather than ISvar index sequence in the list 149 e Ix read x ISvars from the studbook file specifying the starting population e Dx make offspring dependent on the dam for x years Thus a newborn is specified to be dependent on the dam until it becomes x years old This will use IS1 which you must create giving it appropriate Initialization Fn usually 0 Birth Fn 0 and Transition Fn IS1 as a place to store for each female the number of
54. lot of work The much easier method to determine probabilities of allele loss for alleles starting at various frequencies is to add one or more additional loci assign your desired allele frequencies to them and then track how they do For example if you want to know the probability of loss of rare alleles of initial frequency 0 05 use the methods above to assign 0 05 as the frequency to 20 alleles of a locus You can simultaneously test the rate of loss of alleles of various frequencies by assigning the frequencies to be tested to your additional loci For example giving initial allele frequencies of 0 05 0 05 0 10 0 10 0 20 0 50 will test the rate of loss of initially rare mid frequency and common alleles Genetic Management options Select a population to manage Genetic management options can be applied to all populations or to any subset of populations Different options can be specified for each population To specify a set of Genetic Management options for a population select that population from the dropdown list Be sure to select your population before changing the Genetic Management settings for that population After you set the Genetic Management options for a population you can copy those settings to all the other populations by hitting the Apply to All Populations button Even after copying settings to all populations you can select a specific population from the dropdown list and change one or more of its options to
55. of females that can breed but the option to breed to K may result in fewer females breeding The calculation of the numbers of matings to maintain the population at K takes into consideration the percent of breeding females that will produce each possible number of broods the mean brood size and the survival rates It does not adjust for possible inbreeding depression Pair according to mean kinships Managed breeding programs can retain maximal genetic diversity by selecting as breeders those individuals with the lowest mean kinship MK to the living population Ballou and Lacy 1995 If this option is selected then the user must also specify if the MK list for prioritizing breeders is to be updated as each pairing is selected dynamic MK list or left unchanged within each year as pairs are selected static MK list A dynamic list will preserve genetic diversity better if most males and females that are paired do produce offspring 1 e the females breeding is high A static list may provide better genetic management if many pairings fail because the dynamic list would incorrectly assume that many pairs do produce the expected offspring Note that selecting breeders to minimize MK will not usually be effective unless the Breed to maintain at K is also selected This is because all females and possibly most or all males will be used for breeding so selecting the lower MK individuals first for breeding still will not give th
56. of a small population will remove all sampling error in estimation of current parameter val ues but it will not necessarily provide sufficiently precise values for predicting future trends The entire existing population is still only a sample of the universe of all possi ble populations that could have resulted from the same processes Given that highly detailed models employing accurate estimates for a large number of parameters might be needed to project the dynamics of small populations well should PVA models be used to help guide conserva tion actions The alternative to using incomplete models with poorly estimated parameters that may overestimate population viability is to use even more general models that will omit many threatening processes and often more seriously underestimate risks or to rely on intuitive assess ments of complex probabilistic phenomena something that people are innately poor at doing Piattelli Palmarini 1994 Margolis 1996 When planning conservation ac tions for species that have already declined to near extinc tion we should use the best tools available but also recog Northern White Rhinoceros Observed Population Model Predictions ort 20 lt iad a Number in Garamba National Park 10 1985 1986 1987 1988 1989 1990 1991 48 1992 1993 1994 1995 1996 Fig 5 Observed number solid line of northern white rh
57. of inbreeding on demography Many conservation biologists assume that slow in breeding will not reduce fitness because selection can re move deleterious alleles during generations of inbreeding Charlesworth and Charlesworth 1987 Yet experimental evidence shows that such purging of the genetic load of deleterious alleles from a population often does not work many populations continue to decline in fitness as they become increasingly inbred Ballou 1997 Lacy and Ballou 1998 and may go extinct as a consequence Frankham 1995b Theoretical work indicates why selection is often ineffective in reducing inbreeding depression At the small population sizes at which inbreeding occurs random ge netic drift is a much larger force in determining which alle les increase or decrease in frequency than is all but the strongest selection random loss of adaptive alleles is al most as likely as loss of the deleterious alleles Except when inbreeding depression is due primarily to a few highly del eterious recessive alleles inbreeding is more likely to lead ECOLOGICAL BULLETINS 48 2000 to population extinction than to significant reduction of the genetic load Hedrick 1994 Some populations may be fortunate enough not to carry a genetic load of deleteri ous alleles which would be expressed under inbreeding but the evidence suggests that sensitivity to inbreeding may be determined by chance events such as founder ef fects as much as by any pr
58. of the simulations and the probability of persistence proportion of iterations in which the allele persisted Note that alleles are listed in the order in which they were assigned to initial animals Thus if your model had 3 populations each started from 10 individuals then the first 20 alleles descended from founders of population 1 the next 20 from population 2 founders and alleles 41 to 60 from population 3 founders Also any supplements added during the simulation would receive alleles starting with the 61 one in the list This allows you for example to determine how much genetic mixing occurs between populations during a simulation or to determine what percent of the gene pool descends from supplemented individuals Although you can analyze the optional Genetic Output files to obtain this information often it is easier to set Individual State variables to determine the source of each individual s alleles and then use Population State variables to tally these contributions from various founder sources VORTEX automatically tallies the mean SD and SE for each Population State variable in the model 69 Running your simulation Now that you have entered all the data for your scenario you can finally run your simulation Click on the Run icon the green triangle select Run from the Simulation menu or just hit F5 to open the Run Simulation window Select the scenarios that you want to be included in this simulation run B
59. only Population size 88 12 1 67 SE 16 61 SD Expected heterozygosity 0 8069 0 0049 SE 0 0486 SD Observed heterozygosity 0 8266 0 0070 SE 0 0696 SD Number of extant alleles 8 86 0 16 SE 1 64 SD Number of mt haplotypes 2 79 0 08 SE 0 84 SD Lethal alleles diploid 1 37 0 05 SE 0 47 SD In 100 simulations of Default Scenario for 100 years 1 went extinct and 99 survived This gives a probability of extinction of 0 01000 0 00995 SE or a probability of success of 0 99000 0 00995 SE 1 simulations went extinct at least once Of those going extinct mean time to first extinction was 53 00 years 0 00 SE 0 00 SD Means across all populations extant and extinct Mean final population was 87 24 1 87 SE 18 73 SD Age OQ 1 Adults Total 0 00 7 98 36 46 44 44 Males 0 00 8 00 34 80 42 80 Females Means across extant populations only Mean final N for extant populations was 88 12 1 67 SE 16 61 SD AgeQ 1 Adults Total 0 00 8 06 36 83 44 89 Males 0 00 8 08 35 15 43 23 Females Across all years prior to camying capacity truncation mean growth rate r was 0 0632 0 0013 SE 0 1251 SD Final expected heterozygosity was 0 8069 0 0049 SE 0 0486 SD Final observed heterozygosity was 0 8266 0 0070 SE 0 0696 SD Final number of alleles was 8 86 0 16 SE 1 64 SD Final number of mt haplotypes was 2 79 0 08 SE 0 84 SD Final lethal alleles diploid was 1 368 0 047 SE 0 468 SD Mean N
60. or it might have 2 lethal alleles and four 50 lethals or any other combination of deleterious alleles which have the same total effect VORTEX uses this concept of lethal equivalents to quantify the severity of depression of first year survival due to inbreeding Thus the user must specify how many lethal equivalents characterize the population under study For only a few species however has the number of lethal equivalents been measured in careful breeding studies Among those species that have been studied the number of lethal equivalents per diploid 2b ranges from 0 to more than 30 but it is usually in the range of 1 to 10 Isn t it depressing to know that you probably carry alleles which would be fatal genetic defects if you had two copies of any one of those alleles Aren t you glad that you are diploid To date no clear patterns 25 Juvenile Survival 0 2 0 3 Inbreeding Coefficient F have emerged to suggest that certain taxonomic ecological or other categories of species typically have high or low number of lethal equivalents it seems to be largely a matter of chance whether a population is severely affected by inbreeding or not How does VORTEX use lethal equivalents VORTEX simulates inbreeding depression in two ways because different genetic mechanisms of inbreeding depression can have different consequences for population viability Recessive lethal alleles are rather efficiently removed from a po
61. percentage of adult females breeding and survival The fecundity and survival rates for years in which a catastrophe occurs are obtained by multiplying those rates in a normal non catastrophe year by the specified factor These severity factors range from 0 0 to 1 0 Entering 0 0 indicates a total loss of reproduction or survival for the population and 1 0 means that the catastrophe when it occurs will have no effect For example entering 0 75 for the severity factor with respect to reproduction means that if 50 of adult females breed in a normal year then only 50 0 75 37 5 breed in a year with a catastrophe The frequency and severity of catastrophes are often difficult to estimate for the very reason that catastrophes are atypical events and therefore not often observed in relatively short periods of observation At the bottom of the input page is a reference that can be used to provide some guidance about typical rates of catastrophes in natural populations Catastrophe severity factors greater than 1 0 can be used in your model This would result in catastrophes having beneficial effects on reproduction and or survival 48 Mate Monopolization In some species some adult males are excluded from breeding because of a lack of a breeding territory subordinate status physiological limitations or otherwise VORTEX will randomly sample males from a breeding pool unless you otherwise constrain which males can
62. populations these commands are usually not worth using However if you have for example 40 populations you very well may want to use Excel to generate your dispersal rate matrix rather than typing in all 1560 pairwise dispersal rates Another command allows you to apply a multiplier to each non diagonal cell in the table By entering a value and hitting Apply Multiplier of you can shift all of the dispersal rates upwards or downwards This makes it much easier to test a range of dispersal rates across Scenarios of your Project For example you might enter an initial set of rates and then apply multipliers of 0 2 and 4 in order to test no dispersal and 2x and 4x increases in dispersal The fourth command Fill Matrix with in this section lets you quickly fill the non diagonal elements of the matrix with some constant dispersal rate This makes it easy to set up a meta population with a uniform rate of dispersal among all pairs of populations VORTEX provides you with significant flexibility in defining dispersal rates among populations For example rates may be inversely proportional to distance directly proportional to habitat area or they may be defined through a more complex determining function However you have the task of calculating these rates for each pair of populations VORTEX does not calculate them for you based on a set of internal rules 36 Reproductive System tc ew joer POEs POR lll SS File Simulati
63. populations generally result from sto chastic or random processes In any sampling process the predictability of an outcome decreases as the sample size is reduced Many aspects of population dynamics are inher 39 ently sampling processes rather than completely deter mined events including mate acquisition breeding suc cess sex determination transmission of genetic alleles sur vival and dispersal The uncertainty in such processes can lead to instability in population dynamics Moreover fluc tuations in demographic and genetic processes cause de pression in long term rates because the geometric means and other appropriate compound measures of population performance are less than the arithmetic means Finally reductions in growth rates and fluctuations in rates can in teract synergistically causing increasing instability and more rapid decline until the ultimate stability is reached when the population becomes extinct These processes were termed extinction vortices by Gilpin and Soul 1986 and their examination constitutes the core of most population viability analyses PVA Soul 1987 Boyce 1992 Lacy 1993 1994 Caughley 1994 argued that there is a dichotomy in conservation biology between those who follow a declin ing population paradigm examining deterministic causes of population decline and those who follow a small pop ulation paradigm examining the processes that further imperil pop
64. probabilities rather than with absolute certainty at any given time The consequences of factors influencing population dynamics are often delayed for years or even generations With a long lived species a population might persist for 20 to 40 years beyond the emergence of factors that ultimately cause extinction Humans can synthesize mentally only a few factors at a time most people have difficulty assessing probabilities intuitively and it is difficult to consider delayed effects Moreover the data needed for models of population dynamics are often very uncertain Optimal decision making when data are uncertain is difficult as it involves correct assessment of probabilities that the true values fall within certain ranges adding yet another probabilistic or chance component to the evaluation of the situation The difficulty of incorporating multiple interacting probabilistic processes into a model that can utilize uncertain data has prevented to date development of analytical models mathematical equations developed from theory which encompass more than a small subset of the processes known to affect wildlife population dynamics It is possible that the mental models of some biologists are sufficiently complex to predict accurately population vulnerabilities to extinction under a range of conditions but it is not possible to assess objectively the precision of such intuitive assessments and it is difficult to transfer that knowledge to others
65. processes usually have little impact on long term population dynamics as long as the population is abundant and spread over a wide geographic range and a number of habitats Deterministic processes such as those listed above predominate in widespread still common species while local chance events impacting subsets of the population will average out across the broader diverse range When a population becomes small isolated and localized however chance events can become important even dominating the long term dynamics and fate of a population Many stages in the life history of an organism and the processes that define the history of a biological population are essentially stochastic sampling phenomena Births deaths dispersal disease sex determination and transmission of genes between generations all are largely probabilistic phenomena Small samples intrinsically have greater variance around the probabilistic mean or expectation than do large samples and therefore small populations will experience greater fluctuations in births deaths sex ratio and genetic variation than will larger populations The fundamental problem facing small populations is that the fluctuations they experience due to the multiple stages of sampling each generation make it increasingly likely that the populations will unpredictably decline to zero Once populations are small the probability that they will become extinct can become more strongly determined by th
66. rates Dispersal Catastrophe1 y Reproductive System Reproductive Rates Catastrophe Label Catastrophel Mortality Rates Catastrophes Frequency and extent of occurrence Mate Monopolization Population 1 Population 2 Initial Population Size Local El EA Carrying Capacity Frequency 1 1 Harvest Supplementation Genetics Severity proportion of normal values Population 1 Population 2 Reproduction 1 1 Survival 1 1 H Copy input values from Population1 z this section z to subsequent populations The frequency and severity of catastrophes can be difficult to estimate The review by Reed et al 2003 The frequency and severity of catastrophic die offs in vertebrates Animal Conservation 6 109 114 indicates that severe die offs 50 or greater decrease in population size of vertebrate populations occur at a frequency of approximately 14 per generation Number of Types of Catastrophes Catastrophes are extremes of environmental variation that strongly impact reproduction and or survival Types of catastrophes might include sudden habitat destruction floods forest fire epidemic disease outbreaks etc Catastrophes can be significant threats to small isolated populations For example disease decimated the last population of black footed ferrets and a hurricane killed half of remaining wild Puerto Rican parrots It is up to you to determine what types of catastrophe if
67. rather than from within the user interface The most common need for this is when someone writes an external shell program usually in R to generate a large number of scenarios for testing for 8 example to run sensitivity tests that use a different sampling scheme than the ones available within the ST module of the interface To run VORTEX from a command line instead of starting Vortex10 exe use the program Vortex 10Command exe that is included in the installation Then to run a VORTEX model from an OS command use syntax as in C Program Files Vortex10 Vortex10Command exe C Vortex10Projects ZPG xml 1 2 You would need to specify whatever paths contain your program and project files and it is safest to fully specify paths rather than assuming that a default location will work The additional and optional parameter 1 2 in the example above specifies that the 1 and 2 scenarios in the project file are to be run Enclose the string of scenario numbers within quotes so that it is read as a single commend line parameter rather than as a series of parameters The quotes around the program and project file names avoid problems with vs in the paths But if the above syntax does not work for you try it with symbols instead If you do not provide on the command line a list of the scenarios to be run then all scenarios in the project will run except for suites of ST samples which are not stored with
68. simulations The statistics reported in this file saved with extension out for each Scenario and each Population are The cumulative number of iterations in which the population is extinct or remains extant The probability of population extinction PE or survival equivalent to the proportion of iterations that the population is extinct or remains extant The mean population size reported separately for all populations N all and only for those remaining extant N extant with standard error SE and standard deviation SD across iterations The mean expected heterozygosity or gene diversity remaining in the extant populations with standard error and standard deviation across iterations The mean observed heterozygosity equal to 1 mean inbreeding coefficient remaining in the extant populations with standard error and standard deviation across iterations The mean number of alleles remaining within extant populations from an original number equal to twice the number of founder individuals with standard error and standard deviation The mean number of mitochondrial haplotypes remaining within extant populations from an original number equal to the number of founder individuals with standard error and standard deviation If the inbreeding depression option is included in the simulation the number of lethal alleles remaining per diploid individual with standard error and standard deviation determi
69. so you do not select which Sampled Scenarios and Populations to include 7 Sensitivity Test Tables amp Graphs c ES Plot Table ST Analysis MyST3 y Spider plot of N y SV1 PBreed SV2 JMort SV3 AFMort SV4 AMMort Baseline Erorbars None SE SD Spider Plot Options 250 X axis 0 Standarized Not standardized 240 Relativeto Base Midpoint 220 N all 20 40 50 60 0 Value of tested ST variable relative to Base Send to Report Save As Print Edit Line Labels Update Plot j f Spider plots show for the discrete values of each variable tested the mean value of the output variable averaged across all combinations of values for the other tested variables A steep slope as for the PBreed variable at least at the lower range of values in the above graph indicates that the test variable has a large impact on the results A flat or very shallow slope as for the AMMort variable adult male mortality in the above graph indicates that the variation in that variable had little or no impact on results Note that the lines may not be straight because decreases and increases in a variable may not have symmetrical effects on population dynamics Also the lines often will not cross at the value for the base scenario shown on the graphs as a blue diamond because of interactions among variables asymmetrical ranges of values tested or the base values not nece
70. still read VORTEX 9 vpj project files However because the syntax of some variables used in functions has been changed see below some editing of input values may be necessary to get a VORTEX 9 project to run correctly in VORTEX 10 Files saved in VORTEX 10 format cannot be read subsequently by VORTEX 9 After reading any VORTEX 9 vpj files into VORTEX 10 go through all input sections to be certain that values were translated correctly between versions and correct any that were not Although it is easiest to enter input values from the user interface the project files that specify input values can be edited directly in a browser or text editor Early alpha test versions of VORTEX 10 could save projects in version 10 vpj files that had a somewhat different format than do the VORTEX 9 vpj files VORTEX 10 no longer will save a project in any vpj format although it can still read vpj files created by either VORTEX 9 or test versions of VORTEX 10 However during the revisions of VORTEX 10 to create the official released version changes were occasionally made to the vpj file format to allow new features to be added If you had created projects in an early pre release VORTEX 10 and saved them as VORTEX 10 vpj files then the best way to now load and further work with those projects is to first use your alpha test version of VORTEX 10 to save the projects in the xml format This will happen automatically if you save as a VORTEX 10 project
71. that access alleles and that locus 1 is always the default infinite alleles neutral locus and you cannot specify the genotypes for that locus Thus to read in genotypes for 3 loci plus the mtDNA your header might be ID Sire Dam Sex Selected Alive Population VV2 ZZ2 VV3 ZZ3 VV4 ZZ4 MT ISvars You do not need to provide mtDNA haplotypes just leave MT out of the header if you do not The ISvars if any need to be after the genotypic information in each line of data 61 You also must specify that the number of neutral loci to be modeled see below is at least the number of loci with specified genotypes plus one more for the default first locus If you ask for more loci to be modeled than are included in the studbook file the additional loci will be modeled with alleles assigned by VORTEX just as normally happens If you ask for fewer loci to be modeled than for which genotypes are provided the extra genotypes in the studbook file will be ignored When coding the alleles in your studbook file it is best if you use sequential numbers starting with 1 although you can use other positive integers if you wish Any numbers skipped in your coding sequence will be considered by VORTEX to be additional alleles that are not present in any individuals Entering an allele code O for a non founder in the studbook will signify that the individual had not been genotyped and that VORTEX should assign alleles inherited from the parents at random Found
72. that year updated after each population is supplemented 112 Valid Function Variables Individual descriptors Age Inbreeding coefficient a number from 0 to 1 Population Sex 0 or F for female 1 or M for male Paternal allele identifier Maternal allele identifier Note that has a different meaning when applied to individuals the individual s inbreeding vs populations population mean homozygosity The meaning will depend on where the function is used VV i and ZZ i the paternal and maternal alleles at the i th modeled locus Can also be written as VV1 VV2 andZZ1 ZZ2 etc 1S1 152 153 1510 Individual State Variables DAM1 DAM2 DAM3 etc Individual State Variables of the Dam only available when offspring are being created SIRE1 SIRE2 SIRE3 etc Individual State Variables of the Sire only available when offspring are being created X1 X2 X3 etc Individual State Variables of an animal when setting initial kinships Y2 Y3 etc Individual State Variables of the other animal when setting initial kinships Population of an animal when setting initial kinships Population of the other animal when setting initial kinships numerical code for an individual set sequentially as individuals are created 1 based index of an individual number in the sequence of current individuals mtDNA haplotype mean kinship ID of dam ID of sire kinship between parents LOCUS locus for mu
73. the dispersal rates after the first Dispersal event and use that PSvar to specify rates in the second Dispersal event Harvest and Supplementation tallies HARVESTS and SUPPLEMENTS are updated before each population is subjected to each annual event Therefore it is possible to modify the harvest or supplementation of 2 and later populations based the harvests and supplementations already imposed on prior populations that year Finally note that the various tallies of activity within each year PAI RS BROODS PROGENY MMI GRANTS EMI GRANTS HARVESTS and SUPPLEMENTS are reset at the beginning of each year Thus if you want to use the tally from the prior year you must set a Population State variable to the value at the end of the year and then use that PSvar in your function in the next annual cycle Valid Function Variables Scenario descriptors Run simulation iteration Year 1TOT1 ITOT2 etc Total across living individuals ofi th individual state variable MEAN1 MEAN2 etc Mean across individuals ofi th individual state variable IMI N1 1MIN2 etc Minimun across individuals ofi th individual state variable MAX1 1MAX2 etc Maximum across individuals of th individual state variable Note when the above four kinds of variables are used in definitions of Global State Variables the calculations are done over the metapopulation Otherwise they apply to the specific population Miscellaneous other
74. the subsequent populations You choose if to copy only for the current page or also for all pages of input 18 Quick view of Deterministic Rates When entering input values hitting ctrl D or clicking on the Det icon will pop up a window that gives the deterministic rates r lambda RO and generation time for each of the populations of the current Scenario This is a quick way to check to see if your input values will produce a positive population growth in the absence of any stochastic variation Female Generation Time Male Generation Time Mean Generation Time To calculate these statistics on the deterministic population growth rates VORTEX uses the same approach as the one described in Ricklefs 1982 and many other population ecology texts As a very brief summary of the methods RO the net reproductive rate is first calculated as Sum LxMx in which Lx is the age specific survival and Mx denoted Bx by Ricklefs but Mx by some other authors is the fecundity and the summation is over all age classes x An approximate and usually pretty good estimate of T generation time can be obtained by Sum x Lx Mx Sum Lx Mx And an approximate value for r exponential growth rate can then be obtained as In RO T VORTEX however goes to the trouble to get a more accurate estimate by determining the value of r that solves the Euler equation 1 Sum exp rx Lx Mx T is then obtai
75. the top with left to right evaluation for sets of operators on the same line is di exponentiation negation logical NOT multiplication divide and modulus remainder from integer division ee lt gt lt gt 15 and EQUALS are all equivalent and is the same as AND OR NAND NOR and amp amp and AND are all equivalent and and OR are all equivalent NAND can be coded as and NOR can be coded as Syntax for using GSvars PSvars ISvars and related functions has changed as follows GS1 rather than GS 1 PS1 rather than PS 1 PPS1 p rather than PPS 1 p IS1 rather than IS 1 ITOTI1 rather than ITOT 1 ISUM1 rather than ISUM 1 IMEAN rather than IMEAN 1 IMAX1 rather than IMAX 1 IMIN 1 rather than IMIN 1 No longer available as built in variables but available via PSvars set to these values FF MM JJ UU WW XX NN is still available but now with syntax NNx e g NN1 rather than NN 1 Parentheses In VORTEX 9 the number of closing parentheses at the end of a function were automatically adjusted to make them match the opening parentheses However this is a dangerous thing for VORTEX to do because the error in parentheses may not actually have been at the end of the function Therefore in Vortex10 an error will occur if parentheses do not match i
76. there is a 20 chance that an individual will die during the process of moving from population A to population B Dispersal Modifier Function Dispersal patterns can be very complex and determined by many factors VORTEX does not provide a full model of dispersal across complex landscapes but instead models movements among discrete populations with the user specifying the rate of movement between each pair of populations However this box provides you with the opportunity to customize dispersal in perhaps very complex ways Any function entered here will be used as a modifier of the rates to be entered later For example you could cause dispersal of males to be twice as high as the specified rate and twice as high as for females by entering D 1 S M The parameter D in the equation stands for the specified dispersal rate between any two populations Such dispersal modifier functions can be used to cause dispersal to be dependent on sex age inbreeding population density and many other characteristics of the individuals and populations With respect to dispersal or other aspects of population dynamics the standard VORTEX model may not match precisely the behavior of your species However VORTEX does provide the capability to create models that are more complex sometimes much more complex than the standard VORTEX model These more complex population models are built by using functions rather than constants for input va
77. this little Box The advantage of doing this is over just using the Specified Exact Distribution is that you can then make that distribution be a function of other variables such as age You can also enter a function for the mean and then also enter an SD gt 0 This will generate the mean from the function and then will add normally distributed variation with the specified SD around that mean Copy input values from When modeling a metapopulation you often will want to use the same values for most input parameters across all of the populations On the left side of the Input pages is a tool that allows you to copy input values from any one population to all subsequent populations You can copy only those values in the current Section of input or copy values in all the input Sections A reminder Throughout the process of data entry you should be adding notes to the Section Notes on input pages Otherwise there is little chance that you will later remember where you got all the input values and there is no chance that anyone else looking at your project will know when you had solid data and when you were just playing with plausible guesses Using good notes can also free you up to experiment with various possible values and to move ahead with constructing a model even when you don t yet have a solidly justified number to enter for some input variable After you get your model running then you can go back to reexamine those input va
78. valid and returns the answer 3 116 Valid Vortex Operators Function Description Example Operations to create or modify Lists FILE PLIST SEQUENCE SORT SORTREV REVERSE SUBSET SAMPLE SSAMPLE APPEND PREPEND NSERT REMOVE REMOVEALL REMOVEAT Creates a list from the values in a text file Creates a list from the values in PPSx Creates a list with values froma tob inclusive by increments of Sorts from low to high Sorts from high to low Reverses the order creates a list fromc d starting with the a position and ending at b position Creates a new list of x items randomly chosen from a b c etc Creates a new list of x items randomly chosen with seed s Appends x to the list Inserts x at the beginning Inserts x at the nth position Removes first item equal to x Removes all items equal to x Removes the nth item State Variable Histories GSHI ST PSHI ST SHI ST GSLI ST PSLIST SL eS Gets a value from the history of the GSvar Gets a value from the history of the PSvar Gets a value from the history of the Svar List of GSvar history List of PSvar history List of Svar history 117 FILE C Temp MyFile txt PLIST1 PPS1 2 PPS1 3 etc 1 3 5 SORT 1 7 3 5 8 1 3 5 7 8 SORTREV 1 7 3 5 8 8 7 5 3 1 REVERSE 1 7 3 5 8 8 5 3 7 1 SUBSET 2 4 6 7 5 8 9 7 5 8 SAMPLE 3 1 7 3 5 8 1 5 7 or 8 1 3 or 3 1 5 or SSAMPLE 1
79. well as the actual expression 1 Continuous linear decline over time RATE 50 0 2 Y This function specifies a starting rate 50 0 perhaps for adult female breeding success or 45 0 for carrying capacity equal to 50 in year 0 o 40 07 with a decline of 0 2 per year resulting in a 350 rate equal to 30 after 100 years 2 30 0 o 2501 3 200 5 450l a 10 0 5 0 0 0 cr 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 2 Linear decline limited to a period of years RATE 50 0 2 MIN Y 1 50 In this case the decline occurs only through 50 0 eS ae ey ee the first 50 years of the simulation Note that 45 0 L Sy the decline is specified to start in year 2 so o 400l that year 1 still has a rate of 50 This is the ol form of the function used by VORTEX if the 2 300 user specifies a linear trend in carrying amp 25 0 capacity S 200 5 15 0 10 0 f 5 0 F 0 0 cannes 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 122 3 Linear decrease during intervals of years RATE 50 5 MIN 5 Y Y 25 Y gt 25 The rate starts at 45 in year 1 declines to 25 by year 5 and again resumes the decline at a rate of 5 per year after year 25 50 0 f 45 0 40 0 35 0 30 0 f 25 0 20 0 15 0 f 10 0 5 0 F 0 0 0 Demographic Rate 10 20 30 40 50 60 70 80 90 100 Year of Simulation 4 Exponential decline RATE 50 0 98 Y The rate declin
80. 025 NK 2 NAN Basic Variables State Variables Special Variables Synonyms 50 50 25 N K 2 N A N Variable Value a Variable Value Variable Value Synonym MapTo Variable A SCENE F o M 1 FEMALE 0 MALE 1 TRUE 1 FALSE 0 E 2 718281828 Pl 3 141592653 BROODS T TARGET T PP T MATE Q NMATES L EXTINCT DAM SIRE PARITY BROOD NN1 NN2 wi zz1 MT CAT CAT2 Evaluate 24 7524752475248 Accept Cancel BoSBeceo8BSoo4c mM 4 m z x zlo 7 ooe Yy Vars used N K A _ Save Graph Print Graph If you are on a data entry box that will accept a function when you enter the Function Evaluator the function perhaps just a number from that input data will be transferred to the top left Enter Function box If you are not on a valid data entry box for a function then the Function Editor will start with a simple default function A 3 RAND In either case you can type or edit any function into the top left box The Insert Series File button allows you to browse to find a file that you want to insert into a FILE filename within your function In the Function Editor it is optional to precede your function with an sign The Check Syntax button can be used to test if the function is considered valid by VORTEX all variables recognizable parentheses matched and required number of values passed to built in f
81. 1 p But note that since the kinship between any two individuals is the probability that two alleles sampled from them are ibd and thus the mean of all pairwise kinships within the population which can be symbolized as MKw is the probability that two randomly sampled homologous alleles will be ibd i e MKw J Moreover for comparisons between two populations x and y the mean across all kinships of an individual in population x to an individual in population y symbolized MKb for the mean kinship between the populations will be the probability that homologous alleles sampled one from x and one from y are ibd thus MKb gt pxi pyi Jxy Similarly Jr is the mean of all pairwise kinships in the metapopulation Therefore all the gene identity components that are needed for calculating the standard measures of genetic distance among subpopulations can be derived from the matrix of pairwise kinships defining the relationships among all individuals in the metapopulation and its submatrices extracted for each subpopulation A convenient aspect of using the kinship matrix to calculate the measures of genetic differentiation in a metapopulation is that since the kinship of each individual to every other individual in the metapopulation is known it is a simple matter to determine how the diversity within each population and between populations would change if any individuals were moved into other populations This can provide a po
82. 10 The Dynamics of Small Populations Many wildlife populations that were once widespread numerous and occupying contiguous habitat have been reduced to one or more small isolated populations The primary causes of the decline of many species are obvious and deterministic Populations are over harvested natural habitat is converted and lost to the species often involving the replacement of diverse ecological communities with monocultures environments are polluted with the dumping of toxins into the air water and soil local and now even global climates are modified by the actions of humans and numerous exotic competitors predators parasites and diseases are introduced into communities that have never evolved defenses to the new invaders The primary causes of species decline are usually easy to understand and often easy to study and model but usually though not always difficult to reverse Even if the original causes of decline are removed a small isolated population is vulnerable to additional forces intrinsic to the dynamics of small populations which may drive the population to extinction Shaffer 1981 Soul 1987 Clark and Seebeck 1990 Of particular impact on small populations are stochastic or random or probabilistic processes Indeed the final extinction of most populations often occurs not so much because of a continuation of the pressures that led to the initial decline but because of bad luck Chance or stochastic
83. 2373 1 7 33538 or 8 1 3 or 3 1 5 or same list returned every time APPEND 2 1 7 3 5 1 7 3 5 2 PREPEND 2 1 7 3 5 2 1 7 3 5 I NSERT 6 2 1 7 3 5 1 6 7 3 5 REMOVE 3 7 3 5 3 8 7 5 3 8 REMOVEALL 3 7 3 5 3 8 7 5 8 REMOVEAT 3 7 3 5 8 7 3 8 1 5 7 with the GSHIST1 3 3 value assigned to GS1 by GSHIST1 0 Init value 2 value assigned to PS3 Initialization value 5th value assigned to IS2 Initialization value GSHI ST1 0 GSHIST2 1 PSHIST3 0 PSHIST3 1 SHIST1 0 1SHIST2 1 its Transition fn PSHI ST3 2 PSHI ST3 0 I SHI ST2 5 SHI ST2 0 GSLIST1 PSLIST3 ISLIST2 FILE filename creates a list from the values in a text file E g LOOKUP 3 FILE myfile txt will look up the third value in the list provided in myfile txt and MEAN FILE myfile2 txt will calculate the mean of the values in myfile2 txt This can be useful if you want to specify a series of values in a file that will be read into VORTEX Note that it is safer to use rather than Y in filenames they mean essentially the same thing to Windows because the character has a special meaning in the C programming language Accessing histories of State Variables The operations GSHI ST PSHI ST and SHI ST can be used to access the prior values assigned to State Variables For example GSHI ST1 3 gets the third value assigned to GS1 by its Transition function during the iteration GSHI
84. 50 Use Normal distribution approximation Specify exact distribution Previously on the Reproductive System input page you defined the maximum number of offspring produced per brood Now you must specify the percentage of litters clutches broods produced by the breeding adult females that are of a given size You have two options for specifying the distribution of numbers of progeny You can use a Normal distribution approximation or you can fully specify the probabilities of each number of progeny When you use the Normal approximation VORTEX will randomly select a number of progeny for each breeding female by sampling from a normal distribution with the specified mean and standard deviation To convert the random normal number to an integer because real offspring don t come in fractional pieces unlike the ones in the matrix models of population ecology VORTEX uses probabilistic rounding The brood size is rounded up with a probability equal to the fractional part of the number and rounded down otherwise This preserves the mean of the distribution at the value you specified The distribution will be symmetrically truncated if necessary in order to prevent the specification of negative brood sizes and to prevent bias in the sampling of the distribution If you have data on the percents of females producing each possible number of progeny and if the maximum number produced is not very large then it is more accurate to enter that exact
85. 83 Calculating inbreeding coefficients from pedigrees Pages 509 520 in Schonewald Cox C M S M Chambers B MacBryde and W L Thomas eds Genetics and Conservation A Reference for Managing Wild Animal and Plant Populations Menlo Park California Benjamin Cummings Ballou J D 1997 Ancestral inbreeding only minimally affects inbreeding depression in mammalian populations Journal of Heredity 88 169 178 Ballou J D and R C Lacy 1995 Identifying genetically important individuals for management of genetic diversity in pedigreed populations Pages 76 111 in J D Ballou M Gilpin and T J Foose eds Population Management for Survival amp Recovery Analytical Methods and Strategies in Small Population Conservation New York Columbia University Press Ballou J D R C Lacy D Kleiman A Rylands and S Ellis eds 1997 Leontopithecus I The Second Population and Habitat Viability Assessment for Lion Tamarins Leontopithecus Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Belovsky G E 1987 Extinction models and mammalian persistence Pages 35 57 in Soul M E ed Viable Populations for Conservation Cambridge Cambridge University Press Berger J 1990 Persistence of different sized populations an empirical assessment of rapid extinctions in bighorn sheep Conservation Biology 4 91 98 Bonaccorso F P Clark P S Miller and O Byers eds 1999 Conservation Assessment and Manageme
86. 88 Estimates of lethal equivalents and the cost of inbreeding in mammals Conserv Biol 2 185 193 Ronce O Perret F and Olivieri L 2000 Evolutionarily stable dispersal rates do not always increase with local extinction rates Am Nat 155 485 496 Ryan K K 2000 Causes and consequences of male mate choice in a monogamous oldfield mouse Peromyscus polionotus Ph D thesis Univ of Chicago Saccheri I et al 1998 Inbreeding and extinction in a butterfly metapopulation Nature 392 491 494 ECOLOGICAL BULLETINS 48 2000 Schonewald Cox C M et al eds 1983 Genetics and conser vation A reference for managing wild animal and plant pop ulations Benjamin Cummings Menlo Park California Seal U S and Lacy R C 1989 Florida panther population viability analysis Report to the U S Fish and Wildlife Service IUCN SSC Captive Breeding Specialist Group Ap ple Valley Minnesota Seal U S et al 1992 Genetic management strategies and popu lation viability of the Florida panther Felis concolor coryi Report to the U S Fish and Wildlife Service IUCN SSC Captive Breeding Specialist Group Apple Valley Minnesota Shaffer M L 1981 Minimum population sizes for species con servation BioScience 31 131 134 Shaffer M 1987 Minimum viable populations coping with uncertainty In Soul M E ed Viable populations for conservation Cambridge Univ Press pp 69 86 Sjo
87. 97 Effects of social structure and prey dynamics on extinction risk in gray wolves Conserv Biol 11 957 965 Westemeier R L et al 1998 Tracking the long term decline and recovery of an isolated population Science 282 1695 1698 51
88. EVl p s x SQRT MortEVIp s x 2 GlobalMortEV p s x 02 1 Partition EV in mortality MortEV into the compo nent that is common to all populations GlobalMortEV and the component that is specific to each population LocalMortEV END age LOOP END sex LOOP 194 Set GlobalKEV p KEV p EVConcordanceAmongPopulations Set LocalKEV p SQRT KEV p 2 GlobalKEV p 2 Partition EV in carrying capacity KEV into the com ponent that is common to all populations GlobalKEV and the component that is specific to each population LocalKEV END population LOOP FOR each iteration FOR each population Create initial individuals assigning population sex age alive dead status inbreeding coefficient and kinships initially 0 and alleles at six loci FOR each of five non neutral loci FOR each founder allele 2 The probability that a given founder allele is a lethal is NumberLethals 10 because there are 10 alleles across the five diploid loci IF RAND lt NumberLethals 10 Set Lethal l a TRUE Allele a of locus J is a recessive lethal ELSE Set Lethalfl a FALSE END IF ELSE END founder allele LOOP END locus LOOP Display initial population sizes on screen and write to output files END population LOOP FOR each year IF NumberPopulations gt 1 GLOBAL_EV_RANDS Generate random numbers for specifying environmen tal variation concordant across pop
89. In polygamous models there only needs to be at least one male for all females to have an opportunity to breed However in a later section Mate Monopolization you can specify that only a subset of males have opportunities to breed For example you can create a polygynous system in which some males control harems of typically 5 females while the remaining males are excluded from breeding If you do not choose a Long term option then VORTEX will assume that mates are randomly reshuffled each year or each Breed event if there are multiple Breed events per year but not between broods in a single Breed event If you do specify one of the Long term models then once pairs are formed those pairs will remain together across years of the simulation until either the male or the female dies or disperses to a different population Note that in Genetics you can specify conditions for separating a long term pair Demographically 1t will not matter whether you choose long term pairings or re arrangement of pairs each year Genetically there may be a small effect on the rate of loss of genetic diversity from the population In a hermaphroditic species every individual is both a male and female although VORTEX will label them all as females With Hermaphroditic species an individual can potentially mate with 37 any other individual including itself On a later input page Mate Monopolization you can specify the probability of selfin
90. K N Stochastically kill excess above K Animal dies END IF END each animal LOOP END N gt A IF Tally PopulationSize p IF population is extinct Decrement NumberExtantPopulations p IF population was not extinct in prior year Set YearExtinct p Current Year IF population has not been recolonized First extinction Set Time ToExtinction p Current Year Increment NumberOfExtinctions p ELSE Re extinction of population Set Time ToReextinction p Current Year YearOfRecolonization p END recolonized IF ELSE END was not extinct IF ELSE Not extinct ECOLOGICAL BULLETINS 48 2000 IF population was extinct in prior year Recolonization Set YearRecolonized p Current Year Set Time ToRecolonization p Current Year YearExtinct p Increment NumberOfRecolonizations p END was extinct 1F Set YearExtinct p 0 Flag for not extinct END extinct IF ELSE Display PopulationSize p on screen graph END population LOOP FOR each population p CALC_GENETIC_METRICS p END population LOOP END year LOOP END iteration LOOP 11 At this point the simulation is complete and summary statistics can be calculated FOR each population p Calculate and report means SDs and SEs across iterations for Population growth rate r p N Current Year N Previous Year TimeToExtinction p TimeToRecolonization p TimeToReextinction p FOR each year Calculate and out
91. Lethals F ASi Median TE GS1 lations to be ine 32 Baseline Pop1 90 You can plot from Year 0 up to any year of the simulations although the default will be that you see the full span of years You also specify if you want a plot of the Mean the default selection or Standard Deviation or Standard Error If you choose Mean then you can add SD or SE bars to the data points See next figure You also need to specify for which variable you want to see the results plotted Some of the arrangements of graphs that were available in Vortex9 such as graphing Populations or Variables across the x axis are no longer available Those graphs were difficult to interpret and not very useful and very few people ever used them For all of the graphs and almost all graphs displayed in any part of VORTEX you have the options to Send to Report which also leaves an image of the graph in the Windows clipboard available for pasting into Word PowerPoint or other documents Save As which opens a dialog box to let you select the image format in which you want the graph saved or Print You can also hit Edit Line Labels to open up a list of the labels for editing The default labels that VORTEX creates are combinations of Scenario and Population names and can be rather long and cumbersome Z Vortex 10 Bi CAVortex10ProjectsiSal v 5 e So File Simulation Help O amp Det
92. LocalMortE VNRand NRANDO Select random normal deviate for specifying EV in mor tality Set LocalMortEVN Rand to same sign as LocalMortEVRand Set LocalKEVN Rand NRAND Select random normal deviate for specifying EV in K ELSE EV in breeding is correlated with EV in mortality Set LocalMortEVRand LocalBreedEVRand Set LocalMortEVNRand LocalBreedEVNRand Set LocalKEVNRand LocalBreedEVN Rand END EV correlation IF ELSE END FUNCTION LOCAL_EV_RANDS BEGIN FUNCTION CATASTROPHES for popula tion p FOR each type of catastrophe c IF Catastrophe is local in effect IF RAND lt CatastropheFrequency p c 11 See Note 5 Set CatastropheFlag c TRUE Catastrophe has occurred ELSE Set CatastropheFlag c FALSE END catastrophe IF ELSE ELSE IF GlobalCatastropheRand lt CatastropheFrequency p c Set CatastropheFlag c TRUE ELSE Set CatastropheFlag c FALSE END catastrophe IF ELSE END Local Global catastrophe IF ELSE END catastrophe LOOP 198 END FUNCTION CATASTROPHES BEGIN FUNCTION BREED for population p Find breeders for the year FOR each living animal in the population IF sex female AND age gt FemaleBreedingAge Add female to breeding pool END IF IF not hermaphroditic IF sex male AND age gt MaleBreedingAge IF RANDO lt ProportionMalesInBreedingPool p Add male to breeding pool END IF END IF END IF END animal LOOP IF no males
93. M E ed Conservation biology the science of scarcity and diver sity Sinauer pp 13 34 Goodman D 1987 The demography of chance extinction In Soul M E ed Viable populations for conservation Cambridge Univ Press pp 11 34 Gyllenberg M and Hanski I 1992 Single species metapopula tion dynamics a structured model Theor Popul Biol 42 35 61 50 Hedrick P W 1994 Purging inbreeding depression and the probability of extinction full sib mating Heredity 73 363 372 Hedrick P W and Miller P S 1992 Conservation genetics techniques and fundamentals Ecol Appl 2 30 46 Hedrick P W et al 1996 Directions in conservation biology comments on Caughley Conserv Biol 10 1312 1320 Jim nez J A et al 1994 An experimental study of inbreeding depression in a natural habitat Science 266 271 273 Keane B 1990 The effect of relatedness on reproductive success and mate choice in the white footed mouse Peromyscus leu copus Anim Behav 39 264 273 Keller L E et al 1994 Selection against inbred song sparrows during a natural population bottleneck Nature 372 356 357 Kindvall O 1996 Habitat heterogeneity and survival of the bush cricket Metrioptera bicolor Ecology 77 207 214 Lacy R C 1987 Loss of genetic diversity from managed popula tions interacting effects of drift mutation immigration se lection and population subdivision
94. ND determine when new random numbers are selected Repeated calls to the random number return the same value if the same seed is specified Random numbers produced with different even sequential seeds will not be correlated The unseeded forms RAND and NRAND set their own unique or nearly so seed each time they are called The very first use of a random number generator in VORTEX uses a seed based on the number of seconds elapsed since the turn of the century Each call to an unseeded random number generator also sets a new seed for the next call for an unseeded random number Thus identically configured computers starting the same simulation at exactly the same second on their clocks would produce identical results for an analysis This synchrony may require however that all memory storage locations including hard disk caches and even the hard disk contents are identical on the systems because they will affect the time required for each read or write to the disk 118 The specification of random number seeds allows synchronization of sequences of random numbers This can be used to create synchrony of events such as catastrophes or environmental variation across populations or autocorrelations among years time lags or cycles If several different demographic rates are specified by functions containing random number generators perhaps to trigger separate catastrophes impacting survival and fecundity care must be taken to create
95. New Project New Project I es File Simulation Help 0 B amp Det st Project Settings Simulation Input Text Output Tables and Graphs Project Report Project Name New Project Special Options Project Notes and Users Do not show graphs during iterations These are my project notes 7 Do not show messages during run E Do not include last population in metapopulation tally Produce a file with the census for the first 0 iterations E Produce a file of all living animals at the end of the first 1 iterations Produce a file of all animals created in each of the first 1 iterations E Produce a file with Gene Diversity by year and iteration E Produce files with the first 0 GSvars by year and iteration E Produce files with the first 0 PSvars by year and iteration E Delay 1st year mortality until all annual mortality is done rather than in Breed E Use Harvest to set to 0 Svar 1 E Prioritize breeding based on Svar 1 use negative for dynamic E Include extinct and extant runs in Genetic summary statistics E Include extinct and extant runs in GSvar and PSvar summary statistics Y Use undocumented options MKD GDM2 12 Special Options Special Options available on the Project Settings page e Do not show graphs during iterations It is fun to watch the simulations proceed but if you won t be watching then the simulations will run a little bit fa
96. ORTEX from a Command prompt c cccccecccessceseeeeeeeseeeseeeseecsaecnsecesecnseeneeseeeseaeeses 8 OPUESTA AA A A AA A ee aha A A oh eevee 9 Output Al A A A A A 10 Navigating around VORTEX it died 10 GSM Updates sy dt A A A EE was TA A RA ats ee each 11 Creating your Vortex Project Entering data ccceccccsscsssceseceseceeecseeeseeeeeeeeeseeeseecseeeseecaeenteenseeeaeen 12 Project AUN i 12 Special OPIO E AA A AAA Ai 13 Simulation OU A O ads 18 COTO AO it a ai 20 Species DeSeriptOM ii veces vo lbevaddece dd bien eigen E E E N E E 24 State Variables tt td oler ados dain to ett a 30 Di o aid ea 34 Reproductive System iii a A a A dee Mas AAA AA di 37 Reproductive Rates AA da 41 Mortality Rates s 0 is 45 CatastrophS lA A A EA LADA Ad 47 Mate MonopoliZation customs aro 49 Initial Population Size is A A E as 50 Carrying Capacity inorena aaa a aa a a a aa a a aoaaa aSa 52 a EET B YA SA1 PEE E PA ENEE E A a td 55 SUPplementat Onsite chia a a Sate ae ted E A E E deste 57 Genet Saregune a as AA 60 Running YQUE SI ath OFF seey cev ve cevae ve cakawhades ess a sucehs e i E R EE E i 70 Text U ei 72 OPUS ati 72 Deterministic RESUIES zaini edron tard id AA ca 73 CUT UE SUT ary A vie Pas AS N 76 ST TADS s s NE NN 83 Other Output Piles aii AS A Fe Sos Se ea A AA ee ec ERP Relea 83 Pabl svand Graphs iii inst 84 Standard Graphs omai ai a ao ae aa O aN a Aaaa aA a a NEE ENAA Ea 85 Custom Plot Ad 90 Project RePOrt
97. RTEX will fill in the remaining alleles with frequencies of 0 that you did provide Note that if there are not enough frequencies specified for the numbers of alleles specified on line 2 then VORTEX will fill in the remaining alleles with frequencies of 0 64 How can I project how well rare and common alleles will be retained in my population Because VORTEX starts each founder with two unique alleles the alleles persisting over time can be difficult to interpret Most alleles in real populations don t start out being present in just one copy except right at the point that they arise by mutation and such singleton alleles are lost with very high probability even in large populations Therefore the number of such alleles reported by VORTEX makes it look like diversity is being lost fast and it is for any initially singleton alleles even while the population is rather healthy genetically overall To determine the loss of alleles that start at higher frequencies you could add together a number of founder alleles in the optional genetic output file that reports allele frequencies and persistence see below to get the frequencies and probabilities of loss of aggregate sets of founder alleles But this is a really hard way to estimate loss of alleles you would need to determine how many founder alleles to combine the probability of cumulative loss is a complicated function of the losses of individual alleles and the calculations are a
98. Rate END LOOP FOR each litter size n in decreasing order IF BreedRand gt CumulativeProbLitterSize n 1 Ser LitterSize n BREAK from Litter Size LOOP END IF END LOOP ELSE 11 MaximumLitterSize 0 is a code for using normal distri bution of litter sizes Set LitterSize MeanLitrerSize p SDLitterSize p NRANDO Set LitterSize max 0 LitterSize Set LitterSize min 2 MeanLitterSizelp LitterSize Truncates symmetrically to avoid creating bias Set IntegerLitter Largest integer less than LitterSize Set Remainder LitterSize IntegerLitter IF RAND lt Remainder 1 Round off litter size probabilistically Set LitterSize IntegerLitter 1 ELSE Set LitterSize IntegerLitter END IF ELSE END IF ELSE 1 Create the offspring Set Inbreeding Kinship between Sire and Dam FOR Offspring from 1 to LitterSize Assign ID age 0 population alive TRUE FOR each of six loci 11 First locus is neutral others can have lethals Pick at random an allele from Dam Pick at random an allele from Sire END LOOP IF not hermaphroditic AND RANDO lt SexRatio Assign sex as male ELSE Assign sex as female ECOLOGICAL BULLETINS 48 2000 END IF ELSE JI Does offspring live Offspring mortality is placed here in the code rather than in the MORTALITY function for better speed and lower memory requirements FOR each non neutral locus IF homozygous AND allele is a lethal Offspring
99. T1 0 gets the value assigned to GS1 by its Initialization function Similarly comparable P SHI ST and SHI ST expressions get the values assigned to PSvars and ISvars These can be useful for determining for example what was the value of a PSvar three years earlier with a function such as GSHI ST4 Y 3 The functions GSLIST PSLIST and SLI ST will create lists from the history of the State Variables For example GSL ST1 creates a list of all values that have been assigned to GS1 starting with the Initialization value These lists can be used to determine for example if a state variable has ever been 0 with FI ND 0 GSLI ST1 gt 0 Or the lists can be used to determine the maximum value that a State Variable has had for example with HI GH I SLI ST3 Do not use any of these operations in an Initialization fn for a state variable because the State Variable histories will not yet exist If an element in a history is requested that does not exist e g GSHI ST1 3 when GS1 has had assigned only two values or GSHI T4 1 when there are only 3 GSvars then the operation will return 0 Using Random Numbers in Functions Random number generators can be used to create a wide variety of stochastic events for example a 5 year drought that occurs on average once every 30 years but the proper use of these functions requires careful consideration of how the seed values implicit as in RAND and NRAND or explicit as in SRAND and SNRA
100. Then install the newest VORTEX 10 and use it to open and then save those xml project files Opening and saving an xml file in VORTEX 10 will usually make for you any adjustments to the input file format that are necessary due to changes that have been made in VORTEX 10 If you have been using the test version of VORTEX 10 and you have trouble converting important projects for use in the full release version contact Lacy for assistance The input values that are most likely to cause problems as you move up to the latest version are the specifications for automated sensitivity testing because that is a part of the program where substantial changes were made to the available options Population based modeling The simulation can be run as a population based model rather than as an individual based model In a population based simulation all genetic options and modeling are disabled as is 148 individual variation demographic stochasticity Population based models will run much faster than do individual based models VORTEX 10 has no hard coded limit on population size Computer RAM might limit population size if inbreeding depression is modeled As with VORTEX 9 inbreeding calculations will be very slow if N gt 10 000 If N typically stays above about 1000 throughout the simulation it might be more efficient much faster with no detectable change in results to run the scenario as a population based simulation Note that inbreeding calculat
101. VConcordanceAmongPoulations END IF Read in Number TypesOfCatastrophes Read in Monogamous Polygynous Hermaphroditic Read in FemaleBreedingAge Read in MaleBreedingAge Read in MaximumAge Read in SexRatio at birth Read in Maximum LitterSize Read in DensityDependentBreeding The pseudocode for modeling density dependent breed ing is not given below END FUNCTION READ_SPECIES_PARAMETERS BEGIN FUNCTION READ _ MIGRATION_PARAMETERS Get input population structure and migration patterns Read in MigrationAges Read in MigrationSexes Read in MigrationSurvival Read in MigrationDensity FOR each population pSource FOR each other population pDestination Read in MigrationProb pSource p Destination END LOOP END LOOP END FUNCTION READ_MIGRATION_PARAMETERS BEGIN FUNCTION READ_POPULATION_PARAMETERS for popula tion p Read in ProportionFemalesBreeding p Read in BreedEV p Environmental variation is specified as a standard deviation 196 Read in Litter size distribution either as MeanLitterSize p and SDLitterSize p or as the fully specified distribution of ProbLitterSize p n FOR each age x up to FemaleBreedingAge Read in FemaleMortality p x Read in FemaleMortalityEV p x END age LOOP FOR each age x up to MaleBreedingAge Read in MaleMortality p x Read in MaleMortalityEV p x END age LOOP FOR each type of catastrophe IF NumberPopulations gt 1
102. Y R 100 lt 0 Oe The background rate of 50 drops to 30 on 50 0 average once every 20 years A seeded 45 0 random number is needed otherwise the o 400l years in which the rate drops would be E gol independent among individuals effectively 30 0 the rate would continuously be 49 The seed S 25 0 of Y R 100 causes a different seed to be S 20 0 used for each year of each iteration if there E 150 ee a are 100 or fewer years The above function is 10 0 equivalent to specifying a catastrophe with 5 0 frequency 5 and severity 0 60 0 0 4 A 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation Random pulses independent among populations RATE 50 20 SRAND Y R 100 100 SRAND P lt 0 05 The catastrophes are independent among populations because each population P sets a new and random seed for the random number generator which tests whether the catastrophe occurs Careful use of parentheses or brackets is critical in this function in order to ensure that the random number seeds work as intended Catastrophes affecting only selected age class es RATE 50 A lt 3 20 SRAND Y R 100 lt 0 05 The catastrophe affects only individuals of ages 1 and 2 The 2 D graphs of this function do not illustrate the age dependent relationship The graphs against Y and R set A 1 and show the catastrophes affecting young individuals while the graph against A happens to displa
103. a few iterations so that it will create valid output files Otherwise when you go to look at tables and graphs VORTEX might crash because of trying to access corrupted files 71 Text Output The Text Output provides five tabs for viewing text and tables with data The text and tables that can be viewed in the Text Output tab are all saved as text files in the VOutput subfolder of the Project folder There are other output files both standard and optional that are also placed into the VOutput folder for possible later viewing and analysis but the user interface does not display them For each of the tabbed sections of text displays you can send the text to the Project Report save a copy of it under a new file name or print the text file Input Summary The first tab shows a text file saved with extension inp in the project folder that has all of the input values for each scenario You can move between scenarios with the Scenario dropdown list Within a scenario you can jump to the beginning of the text for a population by selecting it from the Population dropdown list You can also scroll to any place within the input text SS Z Vortex 10 New Project CAVorte File Simulation Help amp Det ST Project Settings Simulation Input Text Output Tables and Graphs Project Report fi Y Deterministic Results Output Summary Output Tables ST Tables
104. a format of the computer e g a period in the USA but a comma in most of Europe 3 0 5 0 0 0 1 1 0 2 9 0 0 0 55 0 1 0 1 0 0 110 1 0 1 0 50 0 22 0 1 16 Joe 1 0 1 0 22 0 5625 0 0 A value of 1 is a code for a missing kinship A2 0 2 0 0 0 1 0 0 0 5 Only the lower left side of this symmetrical matrix needs to be provided but it does not hurt to include the full matrix An alternative format for entering kinships is a file with pairwise kinships listed one per line rather than as a matrix The line after the list of IDs must then contain the label PAIRWISE somewhere in the line An example with the same kinships as above Comments to be ignored by the program are preceded with 3 9 11 Joe A2 PAIRWISE data entry This file format would be more convenient than the matrix when there are only a few kinships 3 3 0 5 3 9 0 0 3 11 0 1 3 Joe 0 2 Note that missing values could be entered as 1 but the lines can also just be omitted 9 9 0 55 9 11 0 1 9 Joe 0 1 9 A2 0 0 11 11 0 50 11 Joe 0 22 11 A2 0 1 Joe Joe 0 5625 Joe A2 0 0 A2 A2 0 5 Any kinships between initial individuals that are not assigned in this matrix will be set to 0 if the individuals are founders with Unknown or Wild parents or set to the kinship that would normally be calculated from the pedigree for descendants Any kinships that are provided in the matrix will replace the values that othe
105. ables that seem most important Finally the graphs available in VORTEX for displaying ST results can be quick and effective ways to visualize which uncertain variables are primary determinants of population dynamics but they are not full replacements for detailed statistical analysis of ST results For example complex interactions possibly involving more than 2 variables cannot be seen on the graphs and the graphs do not allow you to select the set of possibly interacting variables that together have largest impact The results provided in the stsum file can be fed into statistical packages for regression or other analyses to more fully analyze the determinants of population results 104 Using Functions in VORTEX A cautionary note The use of functions rather than specific values for input into Vortex is both very powerful and often difficult to use wisely For many users there will never be a reason to use functions in the input For those who do need greater flexibility to build more complex models Vortex allows you to set most of the input variables almost all of the ones that would normally accept a number to be functions of properties of the system the populations or individuals VORTEX provides the option of modeling demographic rates as functions of population or individual parameters The population descriptors that can be used as variables in the functions include time year in the simulation iteration population popu
106. about a number of the intricacies of population structure For example social groupings or preferences are often assumed to be invariant or lacking resulting in random mating and dispersal is usually assumed to be random between all sites the island model or only to occur between adjacent sites the stepping stone model Much more work is needed either to develop more complex and flexible models or to demonstrate that the simple models are sufficient to provide guidance for conservation A third method of conducting a PVA is the use of computer simulation modeling to project the probability distribution of possible fates of a population Simulation models can incorporate a very large number of threatening processes and their interactions if the processes can be described in terms of quantitative algorithms and parameterized Although many processes affecting small populations are intrinsically indeterminate the average long term fate of a population and the variance around the expectation can be studied with computer simulation models The focus is on detailed and explicit modeling of the forces impinging on a given population place and time of interest rather than on delineation of rules which may not exist that apply generally to most wildlife populations Modeling and Population Viability Analysis A model is any simplified representation of a real system We use models in all aspects of our lives in order to 1 extract the importan
107. ale and test its suitability before giving up and leaving the female without a mate for that year A default value of 10 is used if this input box is left empty or is set to 0 Optional criteria for separating a long term pair Although Long term Monogamy and Long term Polygyny specified on the Reproductive System input page normally leave a pair together until one of the mates either dies or disperses to another population you can specify that pairs remain together only for set tenure A function or number entered for this option will be used as the probability each year that a long term pair will be separated For example if a function evaluates to 0 25 then with 25 probability each year the pair will be separated and new mates assigned 68 Genetic Output Two options exit for producing more detailed genetic output for analysis Produce a file in GenePop format at the end of each iteration Checking this box will generate at the end of each iteration of the simulation a file with extension gp listing all living individuals and their genotypes at those loci for which summary statistics are requested The file is in the format required for analysis with the GENEPOP software http wbiomed curtin edu au genepop Produce a file of allele frequencies and probabilities of persistence If this option is checked then VORTEX will create an output file with extension gen that lists for each founder allele the mean frequency at the end
108. an and standard deviation for the distribution of offspring numbers rather than specifying the percentage of females producing each possible number of young see below This removes the limitation on the size of offspring numbers that can be 38 modeled and therefore makes it much easier to model species with high fecundities If you will being choosing this option then you can enter 0 or anything at all on this page for the maximum number of progeny per brood Sex Ratio at Birth Enter here a number between 0 0 and 100 0 to represent the average percentage of newborn offspring that are male This number is typically very near 50 signifying a roughly equal male female sex ratio at birth If relatively more or fewer males are born to a given female per year enter the appropriate percentage e g 55 for 55 males Density Dependent Reproduction Does the reproductive rate of your species change with changing population size That is is reproduction low when the population is small due to a difficulty in finding mates or conversely does reproduction drop off when the population is large more specifically at high density due to limited resources or territories intraspecific competition crowding stress etc If so check the box and then enter the subsequent parameters defining the nature of the density dependence If your population s reproduction is density dependent you will need to model this relationship VORTEX models densit
109. ant job of using science to safeguard the future of wildlife populations In summary Population Viability Analysis PVA and Population and Habitat Viability Analysis PHVA refer to an array of interrelated and evolving techniques for assessing the survival probability of a population and possible conservation actions It might be useful to restrict the term PVA to its original meaning the use of quantitative techniques to estimate the probability of population persistence under a chosen model of population dynamics a specified set of biological and environmental parameters and enumerated assumptions about human activities and impacts on the system PHVA refers to a workshop approach to conservation planning which elicits and encourages contributions from an array of experts 138 and stakeholders uses PVA and other quantitative and non quantitative techniques to assess possible conservation actions and strives to achieve consensus on the best course of action from competing interests and perspectives incomplete knowledge and an uncertain future Many of the components of PVAs and PHVAs even when used in isolation can be effective educational and research tools To be a useful framework for advancing the conservation of biodiversity however PHVA must incorporate all of 1 collection of data on the biology of the taxon status of its habitat and threats to its persistence 2 quantitative analysis of available data 3 input of populatio
110. arameter value and the interactions among parameters but the total number of tests can become very very large with even a moderate number of parameters to be tested d With the Single Factor option each parameter is varied across its range while holding all the other parameters at the base values This option provides a way to test each parameter independently usually with far fewer samples than is required 94 for testing the combinations of parameters using one of the first three methods but it does not allow for testing interactions among parameters It might be a good option for initial sensitivity tests to determine which factors have a large enough impact to be worth exploring in more detail 4 For either Sampled or LHS the number of samples to be taken of the parameter space is specified For initial tests either to see if the ST is working or to begin to determine which parameters have large impact and are worth further study 100 samples might be adequate For good statistical results however often many more should be used perhaps 1000 or more if there 4 or more parameters being varied Note however that there will be a trade off with respect to the time it takes to complete the analysis The total time will be approximately proportional to the samples in the ST x iterations in each scenario Some good statistician can probably provide guidance on whether it is better to increase samples or increase iterations although th
111. arge to allow scientifically accurate and reliable projections of population dynamics Therefore the predictions made from PVA models should be considered to be projections about what would most likely happen to the population if various hypotheses about the status of the populations and the threats are true Conservation and management decisions must be made based on the most plausible hypotheses about the population status before sufficient data could be collected to test those hypotheses scientifically An important advantage of PVA models is that they forced systematic consideration and specification of the assumptions and hypotheses that must be made in the absence of adequate data This facilitates careful reassessment and improvement in the analyses as better data become available Questions that can be explored with PVA models Below are some of the conservation and management questions that can be explored by Population Viability Analysis modeling References describing uses of VORTEX give many examples of these and other applications of PVA techniques to guide conservation Using the best current information on the biology of the taxon and its habitat are the populations projected to persist if conditions remain as they are now Beyond just the persistence of the population what is the most likely average population size range of population sizes across years and rate of loss of genetic variation If the population is at risk of extinction
112. aseline Check the Scenarios that you want to run and then hit the Run button During the simulation VORTEX will display a graph of the changing size unless you had selected the Special Option to not show graphs during iterations VORTEX erases the lines after each 100 iterations and starts again because drawing the lines can be the slowest part of the simulation when there are many lines on the graph and because the graph usually becomes unreadable with more than 100 lines The Stepwise buttons allow you to run the simulation either one year at a time or one iteration at a time with the program pausing in between until you tell it to proceed by hitting OK At each paused step VORTEX writes a list of all individuals in each population to a text file These stepwise runs can be useful for teaching or for confirming that at each step of the simulation things are proceeding as you expect If you hit Cancel when the program has paused then VORTEX will no longer pause the simulations and will proceed with all the iterations 70 280 260 240 220 o 200 l a 180 S 160 E amp 140 So 120 100 80 60 Vortex has paused at iteration 8 with the Animal List sent to 40 C WortexL0Projects Samples VOutput BigCat v10_Baseline txt file s 20 0 Iteration 9 After the simulation has completed
113. ases in demographic fluctuations of small popula tions are considered rates of loss of genetic variation and accumulation of inbreeding can be much faster than has been suggested before These processes can be examined in detailed individual based PVA models Accurate data to parameterize these models however are often not available Thus we need to interpret cautiously PVA conclusions for populations that are small highly fragmented or projected for many generations R C Lacy rlacy ix netcom com Dept of Conservation Biology Daniel E e Ada L Rice Center Chicago Zoological Society Brookfield IL 60513 USA There are many kinds of threats to the viability of populations of wildlife The processes which have driven many once abundant populations down to one or few small populations in scattered remnants of habitat include direct exploitation over harvest habitat destruction and fragmentation degradation of habitat quality introduc tion of exotic species and chains of extinction Caughley 1994 Often after precipitous declines occur conserva tion biologists and governmental agencies establish recov ECOLOGICAL BULLETINS 48 2000 ery actions to try to prevent local extirpation of populations or the ultimate extinction of the taxon As wildlife populations become smaller additional threats to stability and persistence arise which can exacer bate the difficulty of stopping or reversing a decline These problems of small
114. at brings to bear the knowledge of many people on species conservation eliciting and assessing multiple options for conservation action principally by using the tool of PVA as a way evaluate present threats to population persistence and likely fates under various possible scenarios Population Viability Analysis PVA Two defining characteristics of a PVA are an explicit model of the extinction process and the quantification of threats to extinction These features set PVA apart from many other analyses of the threats facing species including for example the IUCN Red Books of Threatened Species As a methodology to estimate the probability of extinction of a taxon PVA necessarily must start with an understanding or model of the extinction process Clark et al 1990 Generally the model of extinction underlying a PVA considers two categories of factors deterministic and stochastic Deterministic factors those that can shift species from long term average population growth to population decline include the well known threats of over harvest habitat destruction pollution or other degradation of environmental quality and the introduction of exotic predators competitors and diseases Singly or combined these forces have driven many wildlife populations to low numbers and for some to extinction Once a population becomes small and isolated from conspecific populations that might serve as sources for immigrants that could stabilize demograp
115. at the percents add to 100 That last row cannot be edited If you do use a function in this table it is then your responsibility to be sure that the rows will sum to 100 If the values sum to more than 100 the excess will be taken from the last value s If the rows sum to less than 100 the missing percents will be add to the last value 42 A Quick and Easy Way to Estimate a Standard Deviation from Scant Data Ideally to estimate the standard deviation of a demographic rate across years we would want to have many years perhaps 10 or more of field data However we often have information on just a few years and often only the best and worst years in recent times Fortunately the expected range observed in a sample of n values from a normal distribution can be specified see below and Rohlf and Sokal 1981 To estimate the standard deviation of a distribution the observed range best worst years can be divided by the expected range For example across 15 years of observations on Sonoran pronghorn antelope Hosack 1998 the mortality rate of fawns was 85 in the worst year and 55 in the best year Dividing the observed range 30 by the expected range for a normal distribution 3 47 SD units provides us with an estimate of the SD of 30 3 47 8 64 Mean ranges in SD units for samples of a normal distribution Number of Range observations 1 13 1 69 2 06 2 33 2 53 2 70 2 85 2 97 3 08 3 47 3 74 3 93 4 09 4 32 4
116. ate all population statistic output files Note Before you run any ST scenarios be sure that you have edited the ST scenario input to specify where the SVs or GS synonyms are to be used Save all sampled ST scenarios as an additional project file Much of the mechanics and values of the ST module are more easily explained by stepping through the use of the tool The screen shot below shows the STsetup window The steps in using it are as follows Creating ST scenarios l Ze The first step to run sensitivity tests on parameters in a VORTEX project is to provide a name for the ST in the ST analysis text box at the top of the window Do not use the default label New ST i e change it to something else so as to not confuse an existing ST with a request for creation a new one A Template scenario is then chosen from the existing scenarios in the project This template defines all the parameters that will not be varied in the ST The template scenario as a fully functional VORTEX scenario defines also values for those parameters that will be varied but those values will be over written by the values tested within the ST The template will be copied to a new scenario which becomes the STbase that has the same name as given in step 1 to the ST analysis The ST module provides four options for how the ranges of parameter values will be explored Sampled Latin Hypercube Sampling Factorial or Si
117. ather than ITOT 1 ISUM1 rather than ISUM 1 IMEAN rather than IMEAN 1 IMAX1 rather than IMAX 1 IMIN 1 rather than IMIN 1 A number of new built in variables and functions are available for use See the manual section on Functions for a complete list No longer available as built in variables but available via PSvars set to these values FF MM JJ UU WW XX NN is still available but now with syntax NNx e g NN1 rather than NN 1 Quick view of Deterministic Rates When entering input values hitting ctrl D or clicking on the Det icon will pop up a window that gives the deterministic rates r lambda RO and generation time for each of the populations of the current scenario This is a quick way to check to see if your input values will produce a positive population growth in the absence of any stochastic variation 153 Literature Cited still to be edited and updated for version 10 Akcakaya H R 1997 RAMAS Metapop Viability Analysis for Stage Structured Metapopulations Version 2 0 Setauket NY Applied Biomathematics Altmann J D Schoeller S A Altmann P Muruthi and R M Sapolsky 1993 Body size and fatness of free living baboons reflect food availability and activity levels American Journal of Primatology 30 149 161 Alvarez K 1993 Twilight of the Panther Biology Bureaucracy and Failure in an Endangered Species Program Myakka River Publ Sarasota Florida Ballou J D 19
118. ation of Small Populations Brookfield Illinois Chicago Zoological Society Clark T W G N Backhouse and R C Lacy 1991 The population viability assessment workshop A tool for threatened species management Endangered Species Update 8 1 5 Clark T W and Seebeck J H eds 1990 Management and Conservation of Small Populations Brookfield Illinois Chicago Zoological Society Clarke G M 1995 Relationships between developmental stability and fitness Application for conservation biology Conservation Biology 9 18 24 Crow J F and Kimura M 1970 Introduction to Population Genetics Theory New York Harper and Row Doughty R W 1989 Return of the Whooping Crane Austin University of Texas Press Edroma E L N Rosen and P S Miller eds 1997 Conserving the Chimpanzees of Uganda Population and Habitat Viability Assessment for Pan troglodytes schweinfurthii Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Ellis S K Hughes C Kuehler R C Lacy and U S Seal eds 1992a Alala Akohekohe and Palila Population and Habitat Viability Assessment Reports Apple Valley MN Captive Breeding Specialist Group SSC IUCN Ellis S C Kuehler R C Lacy K Hughes and U S Seal eds 1992b Hawai ian Forest Birds Conservation Assessment and Management Plan Apple Valley MN Captive Breeding Specialist Group SSC IUCN Falconer D S 1981 Introduction to Quantitative Genetics 2 ed Ne
119. ation of what proportion of this genetic load is due to recessive lethal alleles vs other genetic effects such as overdominance Recessive lethal alleles are modeled such that the death of animals homozygous for lethal alleles will reduce the frequency of the lethals and thereby reduce the average effects of future inbreeding The proportion of inbreeding depression not due to lethal alleles is modeled as an impact on fitness that follows a negative exponential equation Morton et al 1956 and is not reduced during generations of inbreeding Note 3 For rates which can be specified as functions of age sex inbreeding population size gene diversity year and population the rate to be used is determined by evalu ating the function specified by the user If the user enters a fixed constant for the rate as is usually the case then the function simply returns that constant However the user can specify a mathematical formula that defines a demo graphic rate as being density dependent or a function of other population parameters For example fecundity could be specified to decline in older age classes adult mortality could be specified to increase with inbreeding or habitat carrying capacity could be specified to decrease over time The algorithms for parsing and evaluating user defined rate functions e g the first step of functions GETBREEDRATE and GETDEATHRATEQ are not given in the pseudo code Note 4 The proportion of mal
120. ations will be most applicable to mam mal and bird species and the bias toward these groups in examples below reflect my greater experience with PVA of these taxa Processes destabilizing small populations Shaffer 1981 categorized the stochastic threats to small populations demographic stochasticity environmental stochasticity natural catastrophes and genetic stochasticity These causes of uncertainty and fluctuation in population size interact but they are conceptually distinct Demographic stochasticity Demographic stochasticity is the random variation in the numbers of births number of deaths and sex ratio in a population that results from the fates of individuals being independent outcomes of probabilistic events of reproduc tion mortality and sex determination Shaffer 1981 The observed variation across years or across populations with constant probabilities would be distributed as binomial distributions If fates of individuals are independent then demographic stochasticity is intrinsic to the population and is a simple consequence of the sampling that occurs as individuals are subjected to the population rates Figure 1 shows the percent of whooping cranes Grus americana each year from 1938 to 1994 that failed to return the following year to the wintering grounds in Texas Al though some variation in mortality was due to environmen tal variation and likely catastrophes see below most of the variation in survi
121. babilities and times to extinction and recolonization R C Lacy rlacy ix netcom com Dept of Conservation Biology Daniel E amp Ada L Rice Center Chicago Zoological Society Brookfield IL 60513 USA VORTEX and like programs do exactly what they are told to do as constrained by the static single species mod els that provide their structure They can be useful for vari ous purposes so long as the user understands what the pro grams are doing Caughley and Gunn 1996 p 208 The complexity and multiplicity of processes influenc ing the dynamics of natural populations of animals and plants means that population viability analysis PVA models are also frequently complex Different models in corporate different population processes Individual popu lation processes can be modeled in various ways requiring different sets of driving variables using different equations to define the processes and providing different output to describe the population dynamics Users of PVA models should understand the basic structure of the models they use and it is important that models used for scientific studies and conservation efforts can be examined and rep licated Yet often the details of PVA computer programs ECOLOGICAL BULLETINS 48 2000 are not available to the users because the code is proprie tary information or otherwise not provided to users or simply because the task of reading and understanding the source code fo
122. bad practice because it can deviate far from actual observed heterozygosity and because the concept can be defined even for species that are not diploid and therefore for which the term heterozygosity is meaningless A more appropriate term is gene diversity often symbolized G or H with its converse 1 G being gene identity often symbolized J When calculated from allele frequencies p at a locus J Y p and G 1 Y p with the summation across all alleles at the locus Across loci G and J are simply averaged Averaged across subpopulations the average gene identity within s subpopulations is Js Jx For two populations the gene identity between them is Jxy pxi pyi The total gene identity for a metapopulation Jr can be calculated from overall allele frequencies and it is also given by Jp O YS yy in which the first summation is over all subpopulations x and the second summation is over all pairs of subpopulations in which x y Converting gene identities to gene diversities for which I will use the symbol H because it is more common even if misleading in the literature Hr 1 Jr and Hs Js The gene diversity between populations often symbolized Dgr is Dst Hr Hs Js Jr With the above background the most common measures of genetic distance between 2 populations can be defined as follows As noted above Jxy is termed the gene identity between two populations Genetic Identi
123. be specified to change over time to model losses or gains in the amount or quality of habitat 146 Density dependence in reproduction is modeled by specifying the proportion of adult females breeding each year as a function of the population size The default functional relationship between breeding and density allows entry of Allee effects reduction in breeding at low density and or reduced breeding at high densities Populations can be supplemented or harvested for any number of years in each simulation Harvest may be culling or removal of animals for translocation to another unmodeled population The numbers of additions and removals are specified according to the age and sex of animals Migration among populations VORTEX can model up to 50 populations with possibly distinct population parameters Each pairwise migration rate is specified as the probability of an individual moving from one population to another Migration among populations can be restricted to one sex and or a limited age cohort Emigration from a population can be restricted to occur only when the number of animals in the population exceeds a specified proportion of the carrying capacity Dispersal mortality can be specified as a probability of death for any migrating animal which is in addition to age sex specific mortality Because of between population migration and managed supplementation populations can be recolonized VORTEX tracks the dynamics of local extincti
124. become divergent without also losing gene diversity becoming more homozygous as they drift to fixation for the alternate alleles Thus in this special case within population gene identity becomes highly correlated with and thus an acceptable indirect measure of divergence How can pedigree kinships be used to calculate genetic distance between populations measured The methods described in the above box are used to quantify the genetic similarity or divergence between populations Analogous methods can be used to estimate the same quantities from the kinship coefficients that can be calculated from any pedigree First note that the coefficient of kinship also termed the coefficient of consanguinity is defined as the probability that two homologous alleles are identical by descent ibd By definition the alleles in the founders of a pedigree are not identical by descent so analysis of probabilities of alleles being shared ibd is the same as an analysis of an infinite alleles model of genetic loci in which each founder contributes initially two unique alleles to the population This is why VORTEX uses just such an infinite alleles model of transmission of founder alleles as its default for the simulation Thus the initial allele frequencies are all p 1 2N in which N is the number of founders In subsequent generations descended from these founders gene identity within the population is J p and gene diversity is G
125. below for those populations which are not affected by that regional catastrophe You may also specify that a catastrophe is global for some populations but local for others In that case the catastrophe happens concurrently across the populations for which it is global but occurs independently in those populations for which it is local Normally the frequency of a global catastrophe would be set to be the same in each population affected by that global catastrophe However you can specify different frequencies for a global catastrophe among the populations When the catastrophe hits a population it will also hit all other populations in which that catastrophe has at least as high a frequency of occurrence The catastrophe will sometimes occur in the populations that have higher frequencies while not occurring in populations with lower frequencies Frequency Once the scope of the catastrophe is identified you need to define the probability that a given catastrophe will occur in a particular year Enter this as a percent from 0 0 to 100 0 For example a value of 1 0 means that there is a 1 chance that this particular event will occur in any one year Thus a catastrophe given a frequency of occurrence of 1 means that in a simulation lasting 100 years this event is expected to occur one time on average per iteration Severity proportion of normal values For each catastrophe you need to define the severity with respect to reproduction
126. breed via a function here or in Genetics You enter here the probability that a male can compete for mates Vortex 10 New Project CA File Simulation Help D ist Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current New Scenario Default Scenario Default Scenario Copy Default Scenario Copy2 s Scenario Settings Mate Monopolization Section Notes Species Description State Variables Dispersal Reproductive System PO O A Reproductive Rates Males in breeding pool 50 50 Mortality Rates Catastrophes Mate Monopolization Initial Population Size Degree of monopolization of breeding opportunities Population 1 Population 2 m Calculate from males siring offspring Calculate from mates successful sie The percent of adult males in the pool of potential breeders can be entered directly or you can use the buttons Carrying Capacity below the table to have Vortex calculate it for you from either the of males that successfully sire offspring Harwext which will generally be greater than the percent in the breeding pool because some are unlucky or from the average number of females with which successful males are mated Vortex makes these calculations based on J Supplementation the assumption that mating success by males is distributed according to a Poisson distribution The Mate Mon
127. ccurate predictions for a number of spe cies The species for which historic population trajectories were modeled in the above studies had been reduced to single populations rather than existing within metapopu lations and most had relatively simple breeding systems rather than complex social structures Also PVA models may be more reliable when habitat is not limiting popula tion growth than when dynamics near carrying capacity are modeled Mills et al 1996 Brook et al 1997 How small is small The processes and cases described in this paper suggest that when it comes to assessing whether wildlife populations have declined to dangerously small sizes small may be bigger than we usually think it is Isolated populations with fewer than ca 50 breeding adults may suffer from inbreeding depression within a few genera tions Larger populations that are fragmented into partially isolated subunits of fewer than ca 50 breeding animals in each may lose variability much faster than would be esti mated from the total metapopulation size Lacy and Lindenmayer 1995 Genetic decay in populations with fewer than ca 500 breeding adults or even 5000 adults Lande 1995 may eventually reduce adaptability and po tential for recovery Lacy 1997 Monogamous species and species with complex social systems may have reduced breeding if numbers fall below several hundred adults Each of these factors tends to be a greater threat in those species su
128. ce the individuals may all have gen otypes that otherwise would confer high fitness and indi viduals may not be inbred in fact it is the avoidance of inbreeding that causes the depression of fitness Genetic homogeneity leads to an epiphenomenon with frequency dependent selection causing the inbreeding depression at the population level Some long isolated populations of beach mice such as Peromyscus polionotus leucocephalus have low genetic diversity low frequencies of breeding when mice are paired in captive colonies and the poor breeding is increasingly exacerbated when experimental populations are further inbred Brewer et al 1990 Lacy and Ballou 1998 It is possible that mate choice behavior that evolved to prevent inbreeding is now often preventing breeding as the mice breed readily when paired with mice from other subspecies Lacy unpubl Inbreeding interacts with other threats to population viability For example Keller et al 1994 found that in bred song sparrows Melospiza melodia were less likely to survive a severe winter and inbred animals have occasion ally been observed to be more vulnerable to other environ mental stresses Miller 1994 Not only does demographic decline increase inbreed ing which can in turn further depress mean demographic rates but smaller populations undergo greater relative de mographic fluctuations The increased fluctuations in numbers depress the genetically effective populat
129. ch as many mammals and birds that have low fecundity and only slow population growth under optimal conditions Finally it may be difficult to know when a population is so small that additional stochastic factors must be included in a PVA to obtain an accurate projection of its dynamics Therefore it is often useful to test several models to deter ECOLOGICAL BULLETINS 48 2000 mine if added complexity substantially alters PVA predic tions and provides a better fit to observed population trends A good example of this type of exploration is pro vided by the ongoing work of Lindenmayer and his col leagues on the fauna of fragmented forests in Australia Lindenmayer et al 1999 2000 PVA models should be no more complex than necessary but to be useful for con servation they must also be detailed enough to model the real population dynamics accurately Starfield and Bleloch 1986 Starfield 1997 Akcakaya and Sj gren Gulve 2000 Lacy and Miller 2001 Acknowledgements 1 thank the editors for their many construc tive comments References Akcakaya H R 2000 Population viability analyses with demo graphically and spatially structured models Ecol Bull 48 23 38 Ak akaya H R and Ferson S 1992 RAMAS Space Spatially structured population models for conservation biology Appl Biomath New York Ak akaya H R and Sj gren Gulve P 2000 Population viabili ty analyses in conservation planning an overvie
130. colonization Pages 247 265 in Hanski I A and M E Gilpin eds Metapopulation Biology Ecology Genetics and Evolution London Academic Press IUCN Species Survival Commission 1994 IUCN Red List Categories IUCN Gland Switzerland Kjos C O Byers P S Miller J Borovansky and U S Seal eds 1998 Population and Habitat Viability Assessment Workshop for the Winged Mapleleaf Mussel Quadrula fragosa Final Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Krebs C J 1994 Ecology The Experimental Analysis of Distribution and Abundance 4 ed New York Harper Collins Lacy R C 1993a VORTEX A computer simulation model for Population Viability Analysis Wildlife Research 20 45 65 Lacy R C 1993b Impacts of inbreeding in natural and captive populations of vertebrates Implications for conservation Perspectives in Biology and Medicine 36 480 496 Lacy R C 1993 1994 What is Population and Habitat Viability Analysis Primate Conservation 14 15 27 33 Lacy R C 1997 Importance of genetic variation to the viability of mammalian populations Journal of Mammalogy 78 320 335 Lacy R C G Alaks and A Walsh 1996 Hierarchical analysis of inbreeding depression in Peromyscus polionotus Evolution 50 2187 2200 156 Lacy R C and J D Ballou 1998 Effectiveness of selection in reducing the genetic load in populations of Peromyscus polionotus during generations of inbreeding Ev
131. conservation has expanded considerably beyond the quantitative analysis of extinction probabilities as advanced by Shaffer 1981 1990 Soul 1987 Gilpin 1989 Clark et al 1991 Boyce 1992 and others PVA workshops have incorporated consideration of resource use and needs by local human populations Seal et al 1991 Bonaccorso et al 1999 education programs for the local human populations Odum et al 1993 trade issues Foose et al 1993 and trends in human demographics and land use patterns Walker and Molur 1994 Herrero and Seal 2000 Recognizing that the conservation assessment workshops increasingly incorporated more than just the population biology modeling which still formed a core organizing and analysis framework for the workshop the CBSG has termed their workshops Population and Habitat Viability Analyses PHVA We would recommend that the term Population and Habitat Viability Analysis PHVA be used to describe the collaborative workshop approach to species conservation that centers on but encompasses more than a Population Viability Analysis in the narrow sense The concept of a PHVA continues to expand and evolve as it should considering the need for more holistic and flexible approaches to conservation e g Ruggiero et al 1994 Thus in the usage I recommend PVA is a quantitative analysis of the probability of population persistence under defined sets of assumptions and circumstances PHVA is a workshop process th
132. ction of Text Output provides two summary tables One table provides a line of basic summary statistics for each Population of each Scenario that has been run The summary statistics tabulated are the number of iterations Runs the deterministic growth rate det r the mean stochastic growth rate stoch r experienced in the simulations the SD of the stochastic population growth SD r and final values at the end of the simulation for many of the descriptive statistics listed above in the Output Summary The Scenario Summaries tables also list the mean and SD at the end of the simulation for any Global State variables and Population State variables The means of Population State variables listed for a metapopulation when there is more than population will be the mean across the populations of their PS variable means File Simulation Help BF ed amp det p st a On Input Summary Deterministic Results Output Summary Scenario Summaries Iteration Summaries Runs Population detr SDi PE N extant SD Next N all SD Nall iv MedianTE MeanTE Population 0 0 086 0 63 0 125 95 643 13 168 24 0 0 Population 0 0 0 152 70 Population2 0 y 0 124 0 E 1 y 0 Meta y 0 107 0 Y 5 y I j 0 Population 0 y 0 126 0 Population2 0 y 0 125 0 Meta 0 098 0 The other table in Output Tables provides Iteration Summaries a tabula
133. ctuaries Foose et al 1993 suggested that periodic movement of rhinos between fenced sanctuaries to reduce inbreeding and demographic fluctuations would be necessary to stabilize the populations in the smaller parks Moreover the modeling provided estimates of the rate at which the larger populations would be able to provide surplus animals for translocation It would be an error to assume that any PVA model incorporates everything of interest A PVA simulation program can only include those processes that are known to the programmer This will likely be a subset of what might be known to the field biologists which in turn will definitely be a subset of 137 those processes that impact natural populations A number of variables affecting population dynamics and viability are not yet commonly examined in PVA models These include social and ecological determinants of dispersal complex social processes such as the role of non breeders in group stability and the impacts of other aspects of the social environment on reproductive success and survival competitive exploitative or mutualistic interactions with other species experiencing their own population dynamics and the effects of changes in the global environment To date most PVA models treat organisms as independent actors in spatially homogeneous physical biotic and social environments There is tremendous opportunity and need for elaboration of PVA models and it is likely that increasingl
134. d 001 Y Current BNNR r 0 10 2 _Sendto Repot Save As _ Print Edit Line Labels Update Pla The same Frequency Distribution of TE but with Bin Width set to 5 years 86 Frequency Distribution of N by Year Proportion of iterations having each population size as of the specified year default is the last year You can set the bin to a value greater than 1 so as to smooth the frequency distribution This type of graph and Quasi Extinction graph see below also provide an option to specify that the year for which the results are displayed is sometime before the final year of the simulation which is the default year for these graphs This can be useful when for example you run a simulation for 200 years but you want to examine the distribution of N or the extinction or quasi extinction probabilities also at perhaps year 50 year 100 and year 150 File Simulation Help HB e amp de st Project Settings Simulation Input Text Output Tables and Graphs Frequency Distribution of N by Year Ft Plot Options Bin width 0 Use 0 for automatic binning For which year do you want the graph displayed 0 Use Ofor final year Scenarios to include y R AbundantPrey a LowEV 2Pops 3Pops 10Pops MyST1 MyST3 MyST2 Populations to be included Y Baseline Pop1 Frequ
135. d 65536 Non integer seeds will be truncated hence SRAND 35 23 SRAND 35 89 and values above 64K will be wrapped the modulus taken so that SRAND 65636 SRAND 100 J Notes Regarding Function Syntax and Use e Variables of trigonometric functions are assumed to be in radians except for the function RADI ANS which returns a value in radians e The operator NEG is the same as using a minus sign before a number By the context VORTEX will interpret whether a minus sign signifies subtraction a binary operation or the negative a unary operation CEI L FLOOR andROUND convert rational numbers to integer values but all expressions are evaluated as rational numbers For example FLOOR 3 7 FLOOR 4 p CEIL 2 1 CEIL 3 7 ROUND 3 1 ROUND 3 6 0 75 e Numbers may be written with or without leading and trailing zeroes Decimal points for integral values are optional For example all of the following are valid expressions in the USA see the next point 3 3 00 0 03 03 0 30 5 e Note however that the decimal delimiter point or comma used by Vortex will be the appropriate one for the regional data format set in Windows on the computer running VORTEX Thus Y4 would be written as 0 25 in most of Europe but as 0 25 in the USA e Functions containing invalid mathematical expressions are prohibited such as SQR 10 Square root of a negative number LN 10 Natural log of a negative number or zero 119
136. d J R Squires 1994 Viability analysis in biological evaluations Concepts of population viability analysis biological population and ecological scale Conservation Biology 8 364 372 Rylands A B 1993 1994 Population viability analyses and the conservation of the lion tamarins Leontopithecus of south east Brazil Primate Conservation 14 15 34 42 158 Samuels A and J Altmann 1991 Baboons of the Amboseli basin Demographic stability and change International Journal of Primatology 12 1 19 Sapolsky R M 1982 The endocrine stress response and social status in the wild baboon Hormones and Behavior 15 279 292 Sapolsky R M 1986 Endocrine and behavioral correlates of drought in the wild baboon American Journal of Primatology 11 217 227 Seal U S ed 1992 Genetic Management Strategies and Population Viability of the Florida Panther Felis concolor coryi Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S ed 1994 Attwater s Prairie Chicken Population and Habitat Viability Assessment Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S and R C Lacy eds 1989 Florida Panther Population Viability Analysis Report to the U S Fish and Wildlife Service Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S J D Ballou and C V Padua eds 1990 Leontopithecus Population Viability Analysis Workshop Report Apple Valley MN Captive Breeding Sp
137. d areas throughout the island of Sumatra and collation and integration with a Geographic Information System GIS map of habitats and human pressures on those habitats The PHVA on the Grizzly Bear in the Central Canadian Rockies Ecosystem provided the opportunity for detailed habitat mapping data to be integrated with population biology data on the bears resulting in the development of models which would allow projection of the impacts of habitat changes on the bear populations 136 It is important to specify the assumptions that underlay a PHVA and any consequent management recommendation For example the Hawaiian bird conservation efforts are constrained by a belief that no birds bred outside of the islands should ever be brought back to the islands for release While this position derives from a reasonable concern for disease transmission much of the decline of Hawaii s native birds is thought to be due to introduced avian diseases as much as from any political or philosophical stand any justification for the restriction must be questioned in light of the fact that wildlife agencies import and release without quarantine 1000s of exotic game birds onto the islands annually Once experts are assembled problems stated and goals set data gathered and assumptions specified then the PHVA process can proceed with what I describe as PVA in the narrow sense estimation of the probability of population persistence The available data are used to e
138. d ferret Mustela nigripes was being eliminated by an outbreak of distemper when the last 18 ferrets were captured Clark 1989 Genetic drift is the cumulative and non adaptive fluctuation in allele frequencies resulting from the random sampling of genes in each generation This can impede the recovery or accelerate the decline of wildlife populations for several reasons Lacy 1993b Inbreeding not strictly a component of genetic drift but correlated with it in small populations has been documented to cause loss of fitness in a wide variety of species including virtually all sexually reproducing animals in which the effects of inbreeding have been carefully studied Wright 1977 Falconer 1981 O Brien and Evermann 1988 Ralls et al 1988 Lacy et al 1993 Lacy 1997 Even if the immediate loss of fitness of inbred individuals is not large the loss of genetic variation that results from genetic drift may reduce the ability of a population to adapt to future changes in the environment Fisher 1958 Robertson 1960 Selander 1983 Thus the effects of genetic drift and consequent loss of genetic variation in individuals and populations negatively impact on demographic rates and increase susceptibility to environmental perturbations and catastrophes Reduced population growth and greater fluctuations in numbers in turn accelerates genetic drift Crow and Kimura 1970 These synergistic destabilizing effects of stochastic process on small populations of
139. d or males that you will add at each time interval defined for each age class through adults Enter 0 for no individuals to be supplemented in a given age class These parameters differ slightly from the parameters defining harvesting in that the last age class corresponds to the first year of adulthood instead of the aggregate adult stage This difference results from the fact that while harvesting selects any adult individual regardless of age VORTEX must assign a specific age class to each adult that is being added to the recipient population The age of adults added to the population is always equal to the age at which breeding commences Note that for both Harvest and Supplementation the number of individuals harvested or supplemented can be specified to be a function e g of Year or N or some Population State variable rather than a fixed number If the function results in a non integral number VORTEX will use probabilistic rounding see PROUND in the section on Functions so that the mean number harvested or supplemented is not biased 58 59 Genetics VORTEX provides a variety of options to specify the initial genetic conditions genetic management that might be applied by either human managers or by the breeding behavior of the animals themselves and more extensive genetic output The default genetics model in VORTEX will simulate allele transmission at one neutral locus and at a number of additional loci that are used to model th
140. demographic stochasticity to make a significant contribution to the total observed variance the number of individuals sampled for a given rate n would have to be quite small on the order of a few tens The right panel of the Figure also shows the frequency distribution obtained by including the catastrophe outlier in the calculation of overall mean and variance The inclusion of this single observation results in a significantly poorer fit to the data as the overall distribution of values the mean of all values in the left panel does not look much like a normal distribution This helps in part to illustrate why catastrophes events that are infrequent in occurrence yet severe in population impact are treated separately from more typical annual or seasonal fluctuations Finally it is instructive to note that each of the distributions in the right panel extend beyond 0 0 and or 1 0 As this is biologically implausible we need to truncate these distributions in order to allow their proper use in defining probabilities Partly for this reason VORTEX uSually uses a binomial distribution which does not extend beyond 0 and 100 but which otherwise looks much like a normal distribution to represent EV For ease of calculation VORTEX sometimes does use a normal distribution when it is a very close approximation to the binomial but it then truncates the normal curve symmetrically about the mean to avoid creating any bias The above methods are a
141. deviate far from the means Environmental variation is the fluctuation in the probabilities of birth and death that results from fluctuations in the environment Weather the prevalence of enzootic disease the abundances of prey and predators and the availability of nest sites or other required microhabitats can all vary randomly or cyclically over time The fluctuations in demographic rates caused by environmental variation is additive to the random fluctuations due to demographic stochasticity Thus the difference between the observed variation in a demographic rate over time and the distribution describing demographic variation must be accounted for by environmental variation Catastrophic variation is the extreme of environmental variation but for both methodological and conceptual reasons rare catastrophic events are analyzed separately from the more typical annual or seasonal fluctuations Catastrophes such as epidemic disease hurricanes large scale fires and floods are outliers in the distributions of environmental variation As a result they have quantitatively and sometimes qualitatively different impacts on wildlife populations A forest fire is not just a very hot day Such events often precipitate the final decline to extinction Simberloff 1986 1988 For example one of two populations of whooping crane was decimated by a hurricane in 1940 and soon after went extinct Doughty 1989 The only remaining population of the black foote
142. ding with stochastic simulations so that you will know whether the rates of reproduction and survival are at least minimally adequate to allow for population growth in the absence of random fluctuations and other destabilizing processes such as inbreeding and harvest Remember that you can also see a shorter version of the Deterministic Results while you are entering input values by hitting ctrl D 73 It is important to look at the deterministic projections of population growth for any analysis If ris EF negative the population is in deterministic decline the number of deaths outpace the number of births and will become extinct even in the absence of any stochastic fluctuations The difference between the deterministic population growth rate and the growth rate resulting from the simulation can give an indication of the importance of stochastic factors as threats to population persistence Deterministic Calculations in VORTEX Before the actual stochastic simulation begins VORTEX performs a standard life table analysis to calculate the deterministic mean population growth rate r the exponential growth rate or 4 lambda the annual multiplicative growth rate the mean generation time for males and females and the stable age distribution used optionally to initialize the starting population These calculations will provide accurate long term averages if stochastic variation due to demographic stochasticity environmental variatio
143. duals harvested from other populations are moved into that holding population Any individuals harvested from the holding population are killed During the movement of individuals into the holding population a survival rate can be entered to model the loss of individuals during the translocation This survival rate imposes an additional mortality on top of the normal annual mortality for each age class If the option to Implement as a Translocation is set on either the Harvest or the Supplementation page it will be set automatically to be the same on the other one of these two pages Check the Population Harvested box to request a regular harvest of individuals The harvest can begin and end at any time during the stipulated length of the simulation Enter the First Year of Harvest and the Last Year of Harvest For example if you wish to begin harvesting in year 10 and end in year 25 enter 10 and 25 for these two questions respectively If you wish to harvest every year within the specified time frame enter 1 for the Interval Between 55 Harvests If you wish to harvest animals every other year enter 2 As another example if the first year of harvest is 10 the final year is 50 and the interval is 10 years then harvesting will take place in years 10 20 30 40 and 50 Optional Criterion for Harvest You can specify here some criterion that will restrict harvesting to occur only if the population status meets certain conditions You en
144. e Value List will be calculated and filled in automatically and they cannot be edited by the user If you change the Minimum Maximum or samples then the Increment and Value List will be automatically updated iv Ifno Value List is provided and Increment 0 then the values for the ST are sampled from a uniform distribution across the minimum to maximum interval If this option is used in an ST that is Factorial the default Increment will be set to 1 Beware that this could create a huge number of ST scenarios so you should almost always change the Increment to some larger number for a Factorial ST 6 After an ST is fully specified as above hit the Accept ST scenario button to save that ST This saves that ST within your project Until the ST is accepted you cannot run that ST You can discard an ST that you were building by hitting the Cancel button When you save an ST VORTEX saves the specifications for creating all the sampled scenarios in that ST but does not normally actually save the full scenario information as separate scenarios in the xml Project file This is because there might be many maybe 1000s of scenarios created by an ST However if you do want to save a Project File that has each of the ST sampled scenarios you can hit the button at the lower right to do so 7 You can save an ST and exit the ST module without yet running anything by hitting the Accept and Close button In fact almost always afte
145. e amount of fluctuations in population size than in the mean deterministic population growth rate Thus extinction 131 can be viewed as a process in which once common and widespread populations become reduced to small isolated fragments due to extrinsic factors the small remnant populations then become subjected to large fluctuations due to intrinsic processes the local populations occasionally and unpredictably go extinct and the cumulative result of local extinctions is the eventual extinction of the taxon over much or all of its original range Gilpin and Soul 1986 Clark et al 1990 The stochastic processes impacting on populations have been usefully categorized into demographic stochasticity environmental variation catastrophic events and genetic drift Shaffer 1981 Demographic stochasticity is the random fluctuation in the observed birth rate death rate and sex ratio of a population even if the probabilities of birth and death remain constant Assuming that births and deaths and sex determination are stochastic sampling processes the annual variations in numbers that are born die and are of each sex can be specified from statistical theory and would follow binomial distributions Such demographic stochasticity will be most important to population viability perhaps only in populations that are smaller than a few tens of animals Goodman 1987 in which cases the annual frequencies of birth and death events and the sex ratios can
146. e answer likely depends on the output measure that is being assessed e g Prob Extinction requires many iterations to be estimated adequately while mean N usually requires fewer and mean GD yet fewer as the latter measures often vary less among iterations a With the Factorial option the samples created in the factorial ST is the product of the number of levels to be tested for each parameter and the box for the samples is disabled b The samples has a slightly different meaning for Single Factor analyses First if you specify a discrete set of parameter values to be tested either with an Increment or by providing a Value List see below then the samples doesn t do anything in a Single Factor analysis because the number of samples for each factor will just be the number of values in the list However if you just give a Minimum and Maximum with no Increment to define a discrete list then the samples for a single factor analysis will be the number of samples to be taken within that range for each factor Thus the samples applies to each variable that does not have a discrete list rather than as in Sampled and LHS methods the total number of samples tested in the analysis 5 In the Variables to be tested you specify a SV which will be made as a synonym for a newly created GSvar for each parameter that you wish to vary Note that these SVs will later need to be directly inserted into a VORTEX input parameter
147. e calculated from loss of heterozygosity in extant populations 49 79 Sendto Report Save As Print e The mean effective population size in extant populations calculated from the loss of gene diversity from year 1 to the last year Note that this Ne is the size of a randomly breeding population each generation i e tallying only the adults not the juveniles that constitute the next generation across the generations This will be approximately the harmonic mean of Ne at each generation and will be less than an arithmetic mean Ne across generations if the populations are growing declining or fluctuating in size over time The standard deviations reported for summary statistics give an indication of the variation that occurred among iterations of the simulation The standard errors reported for each summary statistic will indicate whether the number of iterations was large enough to give mean results that are sufficiently stable precise for your purposes Additional summary information will be provided when you have built a metapopulation model If any recolonization events occurred during the simulation VORTEX will report the frequency of recolonization the mean time to recolonization and the frequency and mean time to population re extinction if appropriate Also given for metapopulations will be some tables of genetic distances and identities with standard deviations to show the amount of gen
148. e can actually calculate the relative contributions that demographic stochasticity DS and environmental variability EV make to the total observed variance Consider the example presented in the figure the mean mortality rate calculated from these annual data is 0 387 with a standard deviation combining effects of DS and EV of 0 148 Note however that the catastrophe shown as the outlier in the dataset was not included in this calculation if it were the mean and standard deviation would change to 0 435 and 0 204 respectively 28 If we consider the data with the outlier absent we can calculate the standard deviation due to EV ey O ee CEV Y Ev YTOT ps where soe is the total variance across the data and one is the mean sampling binomial variance across the individual rates see Box B for how to calculate a binomial variance In the example above the mean binomial variance turns out to 0 0022 Therefore ogy oe V0 0219 0 0022 0 140 which is the variation across years of the mean peak values for each curve in the left panel of the figure This calculation tells us that the contribution of demographic stochasticity to the total variance observed in our nine years of mortality data remember we removed the outlier from the analysis is quite small the variance attributable to environmental variability is almost 90 of the total variance in mortality This is shown graphically in the right panel In order for
149. e effects of lethal recessive alleles in inbred individuals The maternally inherited mtDNA haplotype is also modeled A a File Simulation Help B amp Det D st Project Settings Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current Default Scenario x Scenario Settings Genetics Section Notes Species Description Genetic Input State Variables E Read initial population s from studbook file Dispersal E Append studbook to initial population rather than replacing initial N Reproductive System Number of neutral locito be modeled 5 Reproductive Rates Loci included in summary statistics Locus 1 only Additional loci only Allloci Mortality Rates Catastrophes Number of loci to be subject to mutation 2 with a rate of 0 0001 Mate Monopolization E Read initial allele frequencies from file Initial Population Size Gros Contr Select a population to manage Population C Apto Al Populations Harvest EIE Optional Criteria for Genetic Management of population upplementation E PP E Breed to maintain the population at K 7 Genetics E Pair according to mean kinships Use a dynamic MK list Use a static MK list Copy input values from The following options can model either management by humans or natural breeding constraints Population 1 X 7 Prevent matings with kinships inbreeding greater than 0 249 Start population with al
150. e that is consistent with data on Drosophila and a few other species that have been studied well would be 50 However cases have been reported in which nearly all of the genetic load is due to lethals while in other populations virtually none of the effects of inbreeding appears consistent with the action of recessive lethal alleles Lacy et al 1996 You may wish to test low and high values to see if it affects your simulations of population dynamics It probably won t because it is difficult to maintain a population for long at the very small population sizes at which effective purging of recessive lethal alleles would occur 24 Quantification of Inbreeding Depression Inbreeding depression is the reduction in fitness commonly observed when individuals are produced by matings between genetic relatives Inbreeding depression seems to affect most perhaps even all species of sexually reproducing organisms and can cause reduction in survival of infants juveniles and adults mate acquisition fertility fecundity number of progeny per litter or brood and a variety of physiological measures related to fitness such as growth rate disease resistance stress resistance metabolic efficiency sensory acuity and behavioral dominance see Lacy 1997 update and references therein Although inbreeding depression can affect many components of fitness often the overall effect can be reasonably well summarized by or combined into an eff
151. e typically described on an annual or per generation basis must be redefined in terms of the new definition of year For example consider a major catastrophic flood that is thought to occur on average once every 100 years The annual probability of occurrence then is 0 01 Because of the altered definition of year the rodent model must define the probability that this flood will occur in any given 90 day interval The number of 90 day time cycles in a calendar year is T 365 90 4 06 Therefore Pr flood 365 _ 0 010 T 4 06 Pr flood 99 0 0025 The same considerations must be applied to all other demographic rates such as mortality age of first and last breeding etc In addition appropriate migration harvesting and supplementation rates must be established relative to the revised time cycle 21 Population based modeling The simulation can be run as a population based model rather than as an individual based model In a population based simulation all genetic options and modeling e g of inbreeding depression are disabled as is individual variation demographic stochasticity Population based models will run much faster than do individual based models VORTEX 10 has no hard coded limit on population size Computer RAM might limit population size if inbreeding depression is modeled Inbreeding calculations will be very slow if N gt 10 000 If N typically stays above about 1000 throughout the simulatio
152. ea of the normal distribution outside of the 0 1 range is lt 0 000001 When modelling EV as a normal distribution the distribution must be truncated at O and 1 To avoid creating any bias in the mean demographic rate as a result of this truncation VORTEX always truncates the distribution symmetrically ECOLOGICAL BULLETINS 48 2000 For example if the mean is p 0 3 VORTEX truncates the distribution at 0 0 and 0 6 This truncation will cause the SD of the distribution to be very slightly less than that entered by the user Some PVA models use continuous distributions such as the normal or log normal to represent EV even when EV is large In such cases the necessary truncations can cause EV to be substantially less than intended by the user Moreover if the truncation is not symmetric then the mean demographic rate generated by the model can be strongly biased away from the input parameter References Ballou J D 1983 Calculating inbreeding coefficients from ped igrees In Schonewald Cox C M et al eds Genetics and conservation a reference for managing wild animal and plant populations Benjamin Cummings Menlo Park Cali fornia pp 509 520 Burgman M A Ferson S and Ak akaya H R 1993 Risk assessment in conservation biology Chapman and Hall Caswell H 1989 Matrix population models construction anal ysis and interpretation Sinauer Caughley G and Gunn A 1996 Conservation biology
153. eaning but are rather the result of few letters remaining available for denoting additional parameters for functions By specifying that demographic rates are functions of the alleles carried by an individual it is possible to model a wide variety of genetic processes impacting population dynamics including the effect and fate of alleles that confer alternative life history strategies e g lower fecundity but higher survival balancing disruptive or directional selection for alleles impacting demography hybrid vigor or outbreeding depression caused by introgression of alleles from a distinct taxon or geographic population and genetically based individual variation in demographic rates When the initial population is created and when the population is supplemented with any new individuals the founders are assigned unique alleles sequentially Hence the first individual of the Population 1 is assigned alleles 1 and 2 the second individual is assigned alleles 3 and 4 and so on Final frequencies of all founder alleles in each population averaged across all iterations can be outputted to a file if that option is selected on the Genetics input page The allele frequencies are placed into a file with extension gen 121 Examples of Rate Functions The easiest way to demonstrate the formats in which functions can be entered into VORTEX is with a series of examples The examples shown below include a plot of the function where appropriate as
154. eatening factors that were considered However the term implied to some people that there was a well defined number below which extinction was certain and above which persistence was assured Re emphasizing the probabilistic nature of the extinction process a number of conservation biologists have focused on methods for estimating the probability of extinction over defined time periods for a designated population exposed to a specific scenario of environmental conditions threats to persistence and future management actions and other foreseeable events Brussard 1985 Starfield and Bleloch 1986 Soul 1987 Simberloff 1988 Gilpin 1989 Shaffer 1990 Boyce 1992 Burgman et al 1993 Thus Population Viability Analysis or the synonymous Population Viability Assessment and Population Vulnerability Analysis came to describe any of the array of methods for quantifying the probability of extinction of a population Although PVA has been extended by some to encompass a broader approach to conservation see below the term Population Viability Analysis or PVA should perhaps be reserved for its original yet still rather broad meaning Beginning in about 1989 Lacy et al 1989 Seal and Lacy 1989 Seal et al 1990 it became increasingly recognized that PVA can often be most usefully incorporated into a strategy for the conservation of a taxon if it is part of and often central to a conservation workshop that mobilizes collaborat
155. ecialist Group SSC IUCN Hanski LA and M E Gilpin 1991 Metapopulation dynamics A brief history and conceptual domain Biological Journal of the Linnean Society 42 3 16 Hanski I A and M E Gilpin eds 1997 Metapopulation Biology Ecology Genetics and Evolution London Academic Press Hedrick P W 1994 Purging inbreeding depression and the probability of extinction full sib mating Heredity 73 363 372 Hedrick P W 2000 Genetics of Populations 2 Ed Jones Barlett Publishers Sudbury Massachusetts Herrero S P S Miller and U S Seal eds 2000 Population and Habitat Viability Assessment Workshop for the Grizzly Bear of the Central Rockies Ecosystem Ursus arctos horribilis Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Hobbs N T and D M Swift 1985 Estimates of habitat carrying capacity incorporating explicit nutritional constraints Journal of Wildlife Management 49 814 822 Holling C S ed 1978 Adaptive Environmental Assessment and Management International Series on Applied Systems Analysis 3 International Institute for applied systems analysis Toronto John Wiley and Sons Hosack D A 1998 Population Viability Analysis Workshop for the Endangered Sonoran Pronghorn Antilocapra americana sonoriensis in the United States Washington DC Defenders of Wildlife Ims R A and N G Yoccoz 1997 Studying transfer processes in metapopulations Emigration migration and
156. ecialist Group SSC IUCN Seal U S R C Lacy K Medley R Seal and T J Foose eds 1991 Tana River Primate Reserve Conservation Assessment Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Selander R K 1983 Evolutionary consequences of inbreeding Pages 201 215 in Schonewald Cox C M S M Chambers B MacBryde and W L Thomas eds Genetics and Conservation A Reference for Managing Wild Animal and Plant Populations Menlo Park CA Benjamin Cummings Shaffer M L 1981 Minimum population sizes for species conservation Bioscience 1 131 134 Shaffer M L 1987 Minimum viable populations Coping with uncertainty Pages 69 86 in Soul M E ed Viable Populations for Conservation Cambridge Cambridge University Press Shaffer M L 1990 Population viability analysis Conservation Biology 4 39 40 Simberloff D A 1986 The proximate causes of extinction Pages 259 276 in Raup D M and D Jablonski eds Patterns and Processes in the History of Life Berlin Springer Verlag Simberloff D A 1988 The contribution of population and community biology to conservation science Annual Review of Ecology and Systematics 19 473 511 Simmons M J and J F Crow 1977 Mutations affecting fitness in Drosophila populations Annual Review of Genetics 11 49 78 Sokal R R and F J Rohlf 1994 Biometry 3 ed New York W H Freeman and Company Soul M E ed 1987 Viable Populati
157. ect on infant survival For example if inbreeding causes a 10 reduction in litter size and then a 10 reduction in survival of those individuals born the cumulative effect would be the same as a 19 reduction in infant survival resulting in 81 of the yearlings which would have been produced if no inbreeding had occurred Therefore the primary way in which inbreeding depression is incorporated into VORTEX is through a reduction in first year survival of inbred individuals If desired inbreeding effects on later survival reproduction carrying capacity and even dispersal can be modeled using functions of inbreeding to specify demographic rates While inbreeding depression is widely known and has been for centuries understanding the various possible underlying mechanisms the ways of quantifying it and the consequences for population survival and viability is not at all simple Inbreeding depression may result from recessive deleterious alleles which are exposed more frequently in homozygous inbred individuals or from a general disadvantage of homozygotes relative to heterozygotes or from other genetic mechanisms see Charlesworth and Charlesworth 1987 Lacy 1993b In studies of Drosophila flies it has been observed that about half of the effect of inbreeding depression on survival is due to recessive lethal alleles Simmons and Crow 1977 The relationship between survival and inbreeding caused by the presence of recessive lethal alleles
158. ed 100s or more of samples it might be wise to first select only 5 or 10 to be graphed until you know that you are getting the results that you want Also a graph with 100s or 100s of lines is rarely clear enough to be useful and may take a long time for the program to create After selecting sampled scenarios to be included the list below it will automatically show the populations for those scenarios You can leave them all checked or you could uncheck some For example you might want to see only the results for the Metapopulations when your scenarios each have many populations 100 From the dropdown below the ST Analysis in the upper left you can select which graph you wish to see displayed The Table tab will then also show you the data that generated the graph The top three graphs N GD and P survive are the same as the first three default graphs in the main Tables amp Graphs tab Similarly the Custom Plot option takes you to the settings for specifying any of the standard graphs available in VORTEX The graphs that are unique to ST are four spider plots and four Max Min graphs These graphs are available only if the ST Analysis used a sampling scheme that generates a discrete set of values for the sampled variable with an Increment or Value List for every variable to be tested Also these specialized graphs always use the full set of samples created by the ST Analysis and only show results for the metapopulations
159. ed PVA model incorporated the reduction in breeding as shown in Fig 2 for monoga mous species that would be expected due to sex ratio fluc tuations Many population models ignore sex ratio and breeding system entirely projecting numbers of females 41 Effect of random fluctuations in sex ratio on reproduction in monogamous species 1 0 10 c 2 0 9 0 9 o 3 3 5 0 8 0 8 EN e T S 0 7 0 7 E Q a 0 6 06 0 5 0 5 0 100 200 300 400 500 Size of breeding population Fig 2 Mean proportion of monogamous pairs that could be formed relative to the case of a constant 50 50 sex ratio as a con sequence of random fluctuations in the sex ratio in breeding pop ulations of varying size under the assumption that there are always males available for mating Individual based models are well suited for cas es in which sex ratio biases can disrupt breeding because they automatically generate stochastic variation in the sex ratio Rules defining the breeding system can then be built into the model Thus if there is not promiscuous breeding random fluctuations in the sex ratio can depress population growth in even moderate sized populations Similarly random de mographic stochasticity in the numbers of births and deaths per year can depress mean population growth be cause of variation in the age distribution and other disrup tions of optimal breeding For example managers of zoo populations are often distressed to find that r
160. ed by recessive lethal alleles and by additional loci internal to the model other than those discussed above that are used to model the effects of recessive lethal alleles The inbreeding of the population for example if you use T as a variable in some population state variable is calculated as the homozygosity at the modeled neutral loci so it is influenced by which loci you ask to have included in summary statistics Mutation Mutation rates can be specified for modeled loci The default is no mutation The mutation rate per individual per allele is specified The user can also specify which loci are subjected to mutation If no allele frequency file has been provided see below an infinite allele model of mutation is used If an allele frequency file is provided then a finite allele mutation model is used with the mutation being sampled at random from the other alleles at the locus as specified for the supplementation or last population By using functions for the mutation rate you can specify different rates for different loci or different rates for the maternally vs paternally derived alleles In the function for mutation rates LOCUS indicates the affected locus and the variable MALLELE is 1 for the maternal allele and 0 for the paternal allele Thus a mutation rate of LOCUS 1 0 0001 LOCUS 2 0 0005 will apply a per generation mutation rate of m 0 0001 for locus 1 and m 0 0005 for the 2 locus Mutat
161. edictable factors Ralls et al 1988 Barrett and Kohn 1991 Lacy et al 1996 The rate of adaptive evolution of any population is ex pected to be proportional to its additive genetic variation and heritability for the traits under selection Fisher 1958 and the limited evolutionary potential of domesti cated animals with depleted genetic variation has been shown repeatedly It would be difficult to know whether limited response to selection in rapidly changing habitats is a contributing threat to the persistence of natural popula tions Some populations have persisted at small numbers for many generations e g the Javan rhinoceros Rhinoceros sondaicus and until 1986 the black footed ferret Mustela nigripes but other populations have rapidly gone extinct when an unusual stress appeared in the environment e g the golden toad Bufo periglenes Pounds and Crump 1994 and the black footed ferret in 1986 Clark 1989 Given the current situation of unprecedented environ mental change and an accelerating extinction rate perhaps more PVA models should consider the maintenance of suf ficient genetic variability to ensure ecological and evolu tionary flexibility rather than solely immediate fitness ef fects and short term population persistence One way to accommodate long term viability into conservation plan ning would be to use the potential for rapid recovery as the primary measure of population viability rather than mere popula
162. eding for that year Set Global BreedE VNRand NRAND 11 Select random normal deviate for specifying EV in breeding for year Whether EVRand or EVNRand will be used depends on the magnitude of EV See Note 6 Set GlobalBreedEVNRand to same sign as GlobalBreedE VRand IF E VCorrelation Between ReproductionAndSurvival No Set GlobalMortEVRand RAND I Select random 0 1 number for specifying EV mortality for that year Set GlobalMortEVNRand NRANDO 11 Select random normal deviate for specifying EV in mor tality for that year Whether EVRand or E VNRand will be used depends on the magnitude of EV Ser GlobalMortE VN Rand to same sign as GlobalMortEVRand Set GlobalKEVNRand NRAND 197 11 Select random normal deviate for specifying EV in K for year ELSE EV in breeding is correlated with EV in mortality Set GlobalMortEVRand GlobalBreedEVRand Set GlobalMortEVNRand GlobalBreedEVNRand Set GlobalKEVN Rand GlobalBreedEVNRand END EV correlation IF ELSE END FUNCTION GLOBAL_EV_RANDS BEGIN FUNCTION LOCAL_EV_RANDS Set LocalBreedEVRand RAND Select random number for specifying EV in breeding for year Set LocalBreedEVNRand NRAND Select a random normal deviate for specifying EV in breeding Set LocalBreedEVN Rand to same sign as LocalBreedEVRand IF EVCorrelationBetweenReproductionAndSurvival FALSE Set LocalMortE VRand RAND Select random number for specifying EV in mortality Set
163. eeding which is always set at the mean homozygosity of modeled loci but it will affect the inbreeding of individuals The mean inbreeding can be determined by setting IS1 I and then setting PS1 IMEANI1 A new option is available for Criteria for separating a long term pair A function or number entered for this option will be used as the probability each year that a long term pair will be separated For example if a function evaluates to 0 25 then with 25 probability the pair will be separated and new mates assigned 151 Section Notes Notes about input values are now entered within a text box for each input section These notes are inserted into the file with inp extension that lists all the input values for a scenario Output files All output files created by VORTEX 9 are still available in VORTEX 10 However there have been some minor changes to the dat files that are used for graphing Sometimes but not always you can open data that were created in VORTEX 10 for graphing in VORTEX 9 It is better to stick with VORTEX 10 once a project has been run in the new version VORTEX 10 places all output files and a copy of the input file into a subfolder labeled VOutput New standard output file N a tally by year and iteration of the population size the data that are used to create the run time display of N New optional output files See Special Options above Sensitivity Tests Sensitivity Tests a
164. eens you had the option to send text tables and graphs to your Project Report This is where you were sending them It is always a good idea to liberally send information to your Project Report whenever you think that it may be information that you will want to capture for inclusion in project reports of any sort It is always easy later to edit or delete sections of your Project Report but it may be difficult to later resurrect information that you neglected to send to the report File Simulation Help B amp Det p ST Project Settings Simulation Input Text Output Tables and Graphs Deterministic projections assume no stochastic fluctuations no inbreeding depression no limitation of mates no harvest and no supplementation Scenario AbundantPrey Population 1 Population 1 Deterministic population growth rate Caution Deterministic growth rate may not be meaningful if functions were used for some demographic rates r 99 9900 lambda 0 0000 RO 0 0000 Generation time for females 0 00 males 0 00 Stable age distribution Age class females males 0 000 0 000 0 1 2 3 4 5 6 7 8 4 The Project Report will automatically be saved as an rtf file in the Project Folder when you save your Project and it will automatically re load the Project Report when you open a project You also have the option to save a copy of it as an rtf or txt file in any folder with any fil
165. eeseeeeceaeeaeeeeaecaeeeeeeaecaeeeees 148 Heateratune Cites sete i Merete OSA 154 REDDS ose resets ov NR ONO 161 Getting Started Installation Download the Vortex10Installation msi from www vortex10 org Vortex10 aspx and run the msi to install the program The program and your projects folder can be installed anywhere although your projects will need to be installed in a folder where you have full read write access On many systems especially if managed by an IT department users are not authorized to access files in folders such as Program Files or sometimes in any folder except those within MyDocuments On some old Windows systems the Vortex 10 Installation msi file cannot be started by just double clicking on that installation file In that case the user can install VORTEX by running the Setup exe that is included with the msi file in a zip file available on the website The two files should first be extracted from the zip file A QuietInstallation is available www vortex10 orge Downloads Vortex 10QuietInstallation msi for users primarily system administrators who wish to install VORTEX into default directories without any need for user interaction during the installation This can be useful if you are installing on a 100 computers for a classroom A Note about Cost VORTEX is provided free of charge because of the commitment of the Chicago Zoological Society to making it widely available to further biodi
166. eing plotted in the middle of that scale 102 ST Analysis MyST4 Spider plot of N Erorbars None Spider Plot Options 9 Standarized Not standardized SE SD X axis Relative to Base Midpoint If scaled relative to the Base see above then the base value is placed at the x 50 location and the x 0 or the x 100 point or both will be the most extreme tested value s for each variable If the base is not at the midpoint of the tested range for a variable then the line for that variable Table Plot SV1 PBreed SV2 JMort SV3 AFMort SV4 AMMort Baseline Sendto Report Save As Prnt 30 40 50 60 7 Value of tested ST variable relative to Base will not extend equally far to the right and left of the Base The different options for the spider plots give different views of the data Which view is best depends on your preference and the distributions of values sampled in your Sensitivity Test Max Min plots are a little easier to understand although they don t provide any information about the range of values that were tested to generate the graphs 103 ST Analysis MyST4 Min Max N zj Plot Table N all fh e H N N 5 amp PBreed JMort AF Mort AMMort Sendto Report Save As Print A Ma
167. eles as each subpopulation becomes fixed for a random subset of the diversity of the original metapopulation This second process can be a benefit of ECOLOGICAL BULLETINS 48 2000 population subdivision but it becomes significant only af ter populations lose most of their gene diversity and be come highly inbred and it depends on no populations be coming extinct as a result of that inbreeding or other fac tors In individual based PVA models that model genetic changes the effects of subdivision on gene diversity are quite different because the PVA models do not unrealisti cally constrain the populations to be constant in size Smaller populations undergo greater fluctuations in number and therefore lose gene diversity much faster than if they were part of a larger breeding population As a con sequence of this greater demographic instability fragment ed metapopulations will usually lose genetic variation both heterozygosity and number of alleles per locus more rapidly than does a single more panmictic large popula tion This trend occurs even when the effects of fragmenta tion are partly offset by dispersal among partly isolated populations In models of populations of mountain brush tail possums Trichosurus caninus Lacy and Lindenmayer 1995 found that both heterozygosity and number of alle les were reduced more quickly when metapopulations of 100 or 200 possums were fragmented into 2 5 or 10 sub populations that excha
168. ell as total numbers of individuals within a population VORTEX assumes that the individuals that are being added to the recipient population are Vortex 10 BigCat v10 CAVortex10Projecta Test BigCat v10 xm Simulation B A amp De st Project Settings Simulation Input Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current 3Pops Baseline Baseline PBM AbundantPrey LowEV 2Pops 3Pops 10Pops MyST1 E PESTE Supplementation eae E Pee F Implement as Translocation if Y gt 10 aimee Species Description State Variables Percent survival during Translocation 50 Di Optional criteria for individuals to be released 1 lt 0 10 ispersal Reproductive System Population2 Population3 Reproductive Rates Population supplemented E El F Mortality Rates First year of supplement 0 0 0 Last year of supplement 100 100 0 Catastrophes E Interval between supplements 2 4 1 Al Optional criteria for supplements 1 Initial Population Size Carrying Capaci yes Capacity Number of females of each age to be supplemented Harvest 7 z ae Sopena Supplement from age 1 to 2 2 3 0 Sa Supplement from after age 2 2 3 0 s Copy input values from to subsequent populations Number of males of each age to be supplemented Population2 Population3 Supplement from age 1 to 2 1 Supplement from age 2 to 3 1 i e Supplement from after age 3 1 2 0
169. em more mating opportunities There is a Special Option that can be used to prioritize breeding on traits other than MK Prevent matings with kinships inbreeding greater than F x xxx With this option females will not be paired with a male that is more closely related than the specified maximal allowable inbreeding If a male initially chosen is too closely related a different male will be picked instead See the option four down to see what happens if repeated males are unsuitable Start population with all inbreeding and kinships set to This option allows initial inbreeding coefficients and pairwise kinships among founders to be set to a value greater than 0 With this option you can start with a population that is already inbred and low in gene diversity This will cause inbreeding depression to be imposed immediately on their offspring if inbreeding depression is chosen and if not all of the inbreeding depression is due to recessive lethal alleles Note that the higher inbreeding that occurs when this option is chosen will not affect the model of inbreeding depression due to recessive lethal alleles because that part of the inbreeding depression is not calculated based on inbreeding coefficients but rather is a consequence of the simulated transmission of recessive alleles Note also that this option will also not affect the mean expected and observed heterozygosity or any calculations on the population mean inbreeding which is always
170. ename Such files can be imported directly into MS Word and most other word processors where you can use their more powerful editing capabilities to further refine your report You can also Print the Report 92 Sensitivity Tests ST Sensitivity Tests are handled in a very different way in VORTEX 10 than in VORTEX 9 so that they are both more flexible and powerful but also easier to use Therefore and STs defined in a VORTEX 9 project file will be ignored when the old vpj file is loaded into VORTEX 10 VORTEX provides a module that facilitates the creation and running of sensitivity tests on parameters that are uncertain or subject to management The method used by VORTEX for ST is to create a series of scenarios that explore the uncertain parameter space These scenarios all have the same values for the input but the parameters to be tested will be defined to be functions of Scenario number variable SCENE in the VORTEX functions so that they take on alternative values when evaluated in the cloned scenarios VORTEX first makes a base scenario STbase by making a copy of a template that is one of the scenarios already existing in the project The STbase is then cloned to create the series of scenarios that are run to complete the ST The STbase scenario can be and usually must be edited to make it properly represent the sensitivity tests to be conducted see below After selecting the template and creating the STbase fro
171. ency 160 180 200 220 240 N Sendto Report Save As Print 87 Quasi extinction QE Prob vs Threshold The probability that the population size was below each possible N If the Terminal option is chosen then the graph shows the probability of N being below each threshold at the end year for this graph which can be set to a year prior to the final year of the simulation If the Interval option is chosen then the graph shows the probability that N dropped below each threshold at any time before the end year of the graph File Simulation Help el amp Det ST Project Settings Simulation Input Text Output Tables and Graphs Project Report Plot Table Quasi extinction QE Prob vs Threshol y Plot Options 2Pops Pop 2Pops Population2 2Pops Metapopulation 9 Terminal Interval For which year do you want the graph displayed 0 Use O for final year Scenarios to include E AbundantPrey E LowEV 4 2Pops A 3Pops 10Pops MyST1 MyST3 E MyST2 z opulations to be included 2Pops Pop1 2Pops Population2 2Pops Metapopulation The quasi extinction graphs can be used to determine the likelihood of extinction for any population size that is chosen as the defini
172. eproduction is kept well below optimal levels because of temporary im balances in the sex ratio or the age distribution Following the advice of conservation biologists zoo managers have assumed that a population of 50 or more is safe from the threat of demographic stochasticity but random fluctua tions are causing problems for maintaining stable popula tions of rhinoceroses spectacled bears lions and other species for which there is limited flexibility to accommo date changes in numbers Environmental variation Environmental variation or stochasticity is the variation in demographic rates or probabilities that results from fluc tuations in the environment Shaffer 1981 Thus local environmental variation causes temporal clustering of births and deaths which would increase uncertainty and variability in population size and thereby make a small population more vulnerable to extinction The kinds of perturbations of the environment which cause variation in birth and death rates include disease sporadic predation 42 irregular food availability and variable weather Natural catastrophes are the extreme of environmental variation in which droughts floods fires disease epidemics and other local disasters can decimate a population Although both demographic stochasticity and environ mental variation cause fluctuations in the number of births and deaths in a population the processes are conceptually distinct and statistical
173. er a function in place of a constant number in VORTEX preface your function with the sign as in 40 10 A gt 3 to set a rate to be 40 for individuals up through 3 years of age and a rate of 50 thereafter 10 A caution about models with long run time If an analysis requires a very long time to complete it is possible that Windows will enter a sleep suspend mode when it does not detect any activity from the user MS Windows is sometimes too stupid to detect that a program is busy working You can prevent this by setting Windows power management settings to not enter sleep mode when it does not detect user activity Screen saver mode is OK as it will not stop VORTEX from working and screen saver mode or otherwise disabling the screen display may actually allow VORTEX to run a little faster Just do not let Windows enter Sleep or Suspend mode when VORTEX is running otherwise VORTEX will indeed suspend its work Getting updates In the Help menu is an option to Check for Updates This will go to the VORTEX website and compare the most recently released version against the version that you are using If a more recent version is available then a window will open that provides the links to get the latest installation It is recommended that you check for updates occasionally especially if you encounter a problem that you think may be a bug That bug might already have been fixed The installation of VORTEX will place in
174. ers should never be given the missing allele code of 0 because VORTEX will have no way to assign alleles to those individuals Any supplemented individuals in the population will be assigned new unique alleles unless you specify the allele frequencies for the loci see below Append studbook to initial population rather than replacing initial N By default VORTEX will replace any individuals specified in the starting population s with those in a provided studbook However with this option you can add the studbook population to the default population specified in the Initial Population Size section One way that this option can be used is to read one population for example a captive or otherwise intensively managed one from a studbook while letting other populations be started from default unrelated individuals If you use this option in this way just be sure to set the initial N for the studbook population to 0 unless you do want that population to start with a combination of studbook individuals and new individuals Number of neutral loci to be modeled VORTEX normally simulates Mendelian transmission of alleles at one neutral locus at which every founder is assigned two unique alleles 1 e it uses an infinite alleles model Any number of additional loci can be simulated by specifying the number here This will produce more precise estimates of genetic variation within and genetic distances among populations and can be useful for
175. es ELSE GETDEATHRATE IF RANDO lt DeathRate Animal dies END IF END IF ELSE END age gt 0 IF END animal LOOP END FUNCTION MORTALITY BEGIN FUNCTION GETDEATHRATE Obtain DeathRate by evaluating mortality function for population and individual parameters Most often the mortality function will simply return the mortality rate entered by the user for the age and sex of the current animal VORTEX provides the option however of making mortality a function of PopulationSize GeneDiversity Inbreeding and other variables ADJUSTRATE DeathRate LocalMortEV p LocalMortEVRand LocalMortEVNRana 11 Adjust rate for local EV ADJUSTRATE DeathRate GlobalMortEV p GlobalMortEVRand GlobalMortEVNRand Adjust rate for global EV FOR each type of catastrophe c IF CatastropheFlag c TRUE Let DeathRate CatastropheSurvivalSeverity p c 1 DeathRate END IF END LOOP END FUNCTION GETDEATHRATE BEGIN FUNCTION ADJUSTRATE Rate EV EVRand EVNRana Determine binomial parameter 7 for modeling EV 11 See Note 6 IF n lt 26 I Find the adjusted Rate from binomial EV FOR each BinomialOutcome 0 through n Add BinomialOutcome n to BinomialProportion Calculate BinomialProbability for BinomialProportion Add BinomialProbability to CumulativeBinomial IF EVRand lt CumulativeBinomial Set Rate Binomial Proportion BREAK from LOOP END IF END LOOP ELSE Use Normal distribution for EV
176. es END WHILE END IF ELSE END LOOP FOR each age x IF VumberFemales p x lt NumberFemales ToBeHarvested p x All females age x die ELSE WHILE number harvested lt NumberFemales ToBeHarvested p x from age class Choose at random a living female in age class x Female dies END WHILE ECOLOGICAL BULLETINS 48 2000 END IF ELSE END LOOP Adjust tallies of population size END FUNCTION HARVEST BEGIN FUNCTION SUPPLEMENT for population p FOR each age x up to MaleBreedingAge WHILE number males created lt NumberMales ToBeSupplemented p x Create a male assigning ID age sex alleles population Set kinships to all other animals 0 Set Inbreeding 0 END WHILE END LOOP FOR each age x up to FemaleBreedingAge WHILE number females created lt NumberFemales ToBeSupplemented p x Create a female assigning ID age sex alleles population Set kinships to all other animals 0 Set Inbreeding 0 END WHILE END LOOP END FUNCTION SUPPLEMENT BEGIN FUNCTION CALC_GENETIC_METRICS for population p FOR each living animal in the population Increment NumberAlleleCopies a for each of the two alleles a at a neutral locus IF allele 1 is same as allele 2 Increment NumberHomozygotes END IF END LOOP FOR each allele 2 of the neutral locus IF NumberAlleleCopies a gt 0 Increment NumberExtantAlleles Add 0 25 NumberAlleleCopies a PopulationSize p NumberAlleleCopi
177. es a PopulationSize p to ExpectedHomozygosityp END IF END LOOP Set GeneDiversity p 1 ExpectedHomozygosity p Set ObservedHeterozygosity p 1 NumberHomozygotes PopulationSize p FOR each living animal in the population FOR each non neutral locus IF allele 1 at the locus is a lethal Increment NumberLethals END IF IF allele 2 at the locus is a lethal Increment NumberLethals END IF END locus LOOP END animal LOOP 201 Set LethalFrequency p NumberLethals PopulationSize p END FUNCTION CALC_GENETIC_METRICS Note 1 Random integers from 0 to 64K are generated by the algorithm given by Kirkpatrick and Stoll 1981 The C code was modified from Maier 1991 Random real numbers between 0 and 1 are produced by first generating a random integer berween 0 and 64K and then dividing that integer by 64K Random numbers from a normal dis tribution with mean 0 and SD 1 are generated by the polar algorithm supplied by Latour 1986 Binomially distributed numbers are generated by first calculating the cumulative probability distribution for the discrete out comes of the desired distribution then generating a ran dom real number and then assessing which binomial out come covers the portion of the distribution encompassing the random real number Note 2 VORTEX asks for the effects of inbreeding to be entered as a number of lethal equivalents per diploid ani mal with further specific
178. es by 2 each year 50 0 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 5 0 0 0 0 Demographic Rate 10 20 30 40 50 60 70 80 90 100 Year of Simulation 5 Exponential decline with inbreeding RATE 50 EXP 2 0 1 The rate declines from 50 in non inbred 50 0 animals down to 6 7 in fully inbred animals I 45 0 1 An equation like this might be used to 40 0 specify a decline in fecundity due to 35 0 inbreeding 30 0 f 25 0 E 20 0 15 0 10 0 5 0 0 0 0 Demographic Rate 10 20 30 40 50 60 70 80 90 100 Inbreeding Coefficient 6 Age dependent fecundity with linear decline after the onset of breeding RATE A gt 5 50 A 5 2 Breeding begins with a rate of 50 at age 5 but then declines by 2 each year thereafter Demographic Rate 0 10 20 30 40 50 60 70 80 90 100 Age Years 7 Age dependent fecundity with a symmetrical peak at age 15 RATE A gt 5 50 ABS A 15 2 50 0 45 0 F 40 0 35 0 30 0 25 0 20 0 15 0 10 0 5 0 F 0 0 Demographic Rate 0 10 20 30 40 50 60 70 80 90 100 Age Years 8 Age dependent fecundity with an asymmetrical peak at age 10 RATE A gt 5 A lt 10 A 5 10 Pee ae 60 ja de Different trends are specified for age intervals 50 0 E 0 4 5 9 and 10 Note the use of 45 0 L parentheses brackets and braces to improve readability 40 0 35 0 F
179. es in the breeding pool can be entered directly or indirectly in the form of the propor tion of males that breed or as the average number of litters per breeding male If the proportion in the breeding pool is given indirectly VORTEX will assume that the distribu tion of male reproductive success follows a Poisson distri bution The proportion of males in the breeding pool is 202 then calculated by solving the following equations for the unknowns LittersPerMale ProportionFemalesProducingLitters id NumberAdultFemales NumberAdultMales Note Adult sex ratio is deter mined from stable age distribution LittersPerMale ProportionMalesInBreedingPool Lit tersPerMaleInBreedingPool ProportionMalesBreeding ProportionMalesInBreeding Pool 1 exp LittersPerMaleInBreedingPool This last equation adjusts for the fact that in any given year some males in the breeding pool will not happen to be successful breeders the zero class of the Poisson distribu tion Note 5 The occurrence of probabilistic events is deter mined by a random number generator The event is deemed to occur if a random number between 0 and 1 is less than the probability of occurrence for that event Note 6 Environmental variacion EV in breeding and in each mortality rate is modeled as a binomial distribution or as a normal distribution depending on whether the magnitude of EV is large The user specifies a mean and standard deviation for each ra
180. es of wildlife populations have provided empirical data on the relationship between population size and probability of extinction e g Belovsky 1987 Thomas 1990 but presently only order of magnitude estimates can be provided for MVPs of vertebrates Shaffer 1987 More empirical studies are needed but the time and numbers of populations required for such studies are precluded in the cases of most species threatened with extinction exactly those for which estimates of population vulnerability are most urgently needed A more elegant and general approach to PVA is to develop analytical models of the extinction process that will allow calculation of the probability of extinction from a small number of measurable parameters 139 Goodman s 1987 model of demographic fluctuations and applications to conservation of the classic population genetic models of loss of genetic diversity by genetic drift Franklin 1980 Soul et al 1986 Lande and Barrowclough 1987 are valuable efforts in this direction Unfortunately our understanding of population biology is not yet sufficient to provide fully adequate analytical models of the extinction process For example none of the existing analytical models incorporate all three of demographic environmental and genetic fluctuations and thus they do not begin to model the array of extinction vortices described by Gilpin and Soul 1986 Moreover the analytical models make extremely simplifying assumptions
181. es vs other genetic mechanisms As mentioned above for Drosophila flies it has been reported that about half of the lethal equivalents are due to actual lethal alleles Almost no other species have been studied in sufficient detail to quantify the contributions of different types of alleles to inbreeding depression but the scant data available are not inconsistent with about half of the inbreeding effects being due to lethals in other species as well The initial default value for Lethal Equivalents in VORTEX 9 was 3 14 based on the mean reported for 40 captive populations of mammals However several authors have argued persuasively that 3 14 would under estimate the impact of inbreeding in most wild populations both because wild populations are subjected to stresses from which captive populations are sheltered and because the value of 3 14 was based only on effects on juvenile mortality while inbreeding impacts many other aspects of reproduction and survival as well Some authors have argued that realistic effects of inbreeding on total fitness are modeled better with LE 12 or even higher Of course you can set the value to whatever you think is appropriate for your species and it is useful to add notes to explain your choice 26 EV Concordance of Reproduction amp Survival Environmental variation EV is the annual variation in the probabilities of reproduction and survival that arise from random variation in environmental conditions EV
182. et a different value of a demographic rate for each age class or at each year or in each population Some of these functions are used by the automated Sensitivity Testing module to sample from the lists of values to be tested Valid Vortex Operators Function Description Example Operations on Lists LOW Lowest value LOW 3 5 7 1 8 HI GH Highest value HI GH 3 5 7 1 8 MEDI AN Median value MEDI AN 3 5 7 1 8 MEAN Mean value MEAN 3 5 7 1 8 4 SUM Sum SUM 3 5 7 1 8 24 0 PRODUCT Product PRODUCT 3 5 7 1 8 960 0 LOOKUP Value at the x location in the LOOKUP 3 5 7 1 8 1 0 subsequent list CHOOSE Randomly chosen value from CHOOSE 3 5 7 1 8 3 0or5 or7 orl or8 the list COUNT Number of values COUNT 33 557 158 5 0 FIND Location of value X in the FIND 1 5 7 1 8 3 0 subsequent list 0 if not found PERCENTILE Value in the subsequent list PERCENTILE 40 5 7 1 8 that is at the X percentile PRANK Percentile of value X in the PRANK 3 5 7 1 8 5 0 subsequent list TI MESERI ES The list item that is at the TI MESERI ES 3 5 7 1 8 5 0 in year 2 location given by the current year Y Note that the following operations to create or modify lists can t stand alone in a function because they do not return a single value Instead they must be used within one of the above functions that operate on a list For example a function of SORT 1 3 5 is not valid but FIND 3 SORT 1 3 5 4 2 is
183. etic Management Genetic management options can be applied to all populations or to any subset of populations Different options can be specified for each population The maternally inherited mtDNA haplotype is now modeled Mutation rates can be specified for modeled loci The mutation rate per individual per allele is specified The user can also specify which loci are subjected to mutation If no allele frequency file has been provided an infinite allele model of mutation is used If an allele frequency file is provided then a finite allele mutation model is used with the mutation being sampled at random from the other alleles at the locus as specified for the supplementation or last population A new option is available to allow specification of initial inbreeding coefficients and pairwise kinships among founders to be set to a value greater than 0 With this option you can start with a population that is already inbred and low in gene diversity This will cause inbreeding depression to be imposed immediately on their offspring if inbreeding depression is chosen and if not all of the inbreeding depression is due to recessive lethal alleles Note that the higher inbreeding that occurs when this option is chosen will not affect the model of inbreeding depression due to recessive lethal alleles Note also that this option will also not affect the mean expected and observed heterozygosity or any calculations on the population mean inbr
184. etic differentiation that existed between populations at the end of the simulations The measures of genetic distance that are displayed are Nei s standard genetic distance D genetic identity I gene identity J and Gst Note that genetic distance D is undefined and will be displayed in the output file as 0 with a sample size of 0 if the populations have no shared alleles because of no dispersal between them The output also provides the overall Gst among populations both unweighted and weighted by population size See Nei 1987 and the box below for more details about these measures of genetic distance Z Vortex 10 New Project CAVisual Studio 2010 Vortex Vortex10 bin Release New Project New Proj mt File Simulation Help B eh amp Det st Project Settings Simulation Input Text Output Tables and Graphs Project Repor Input Summary Deterministic Results Output Summary Output Tables ST Tables Scenario Default Scenario x Population Population X Genetic distances among populations calculated from 1 loci mean D below diagonal mean above diagonal mean G on diagonal Population 1Population2 Population 0 8066 0 0000 Population2 0 0000 0 8069 Standard deviations across iterations D below diagonal above diagonal G on diagonal Population 1Population2 Population 1 0 0562 0 0000 Population2 0 0000 0 0486 Sample sizes Note f n D
185. ex 10 New Project C Vortex10Projects New Project New Project xml ex pS File Simulation Help z i OQ amp Eh amp Det sT Project Settings Simulation Input Text Output Tables and Graphs Project Report Gaa Plot Table Default Scenario Population1 Default Scenario Population2 Default Scenario Metapopulation Quasi extinction QE Prob vs Threshold 20000 Custom Plot 18000 16000 14000 Scenarios to include check all uncheck all 12000 Y 0 10 20 20 40 50 60 70 80 90 100 Populations to be included Y Default Scenario Population1 Default Scenario Population2 Default Scenario Metapopulation Sendto Report Save As Pont Edit Line Labels _ Update Plot daa GD vs Year same as the Gene Div graph in the custom graphs PE vs Year same as the P survive graph in custom graphs the probability that a population will be extant at each year Frequency Distribution of TE proportion of iterations becoming extinct at each year This graph will be blank if there have been no extinctions The bin width determines how smooth the graph will be If a lot of iterations were run and many resulted in extinction then a narrow bin width even 1 will show the frequency distribution in the finest detail Wider bins combine counts across years
186. examples presented above more proc esses threaten the viability of small populations than are commonly addressed in PVA models Analytical models and simple population projection models can therefore overestimate population growth underestimate popula tion fluctuations and seriously underestimate probabili ties of extinction More accurate PVA of small populations may often require individual based models that simulate interactions among threatening processes rather than rely ing on theoretical equations derived under assumptions of simplified population processes acting in isolation Lindenmayer et al 2000 found that PVA model predic tions matched the observed dynamics of populations of three species of marsupials in a highly fragmented land scape only when the models incorporated distance dependent and density dependent dispersal high mortal ity during dispersal and spatial variation in habitat quality Knowledge of times since isolation of each habitat frag ment was also critical as the metapopulations were pro jected to lose more component subpopulations before reaching extinction recolonization equilibria In an alter native approach Sj gren Gulve 1994 Sj gren Gulve and Ray 1996 used a logistic regression model to incorporate similarly detailed information about the habitat character istics spatial arrangement and surrounding forestry prac tices on the extinction recolonization dynamics of pool 47 frog Rana les
187. exception of a special use of MATE see below Dispersal New options in the Dispersal input section include Prevent individuals from dispersing into saturated populations This option will stop individuals from entering a population if it is already at its carrying capacity thereby preventing that immigration from immediately causing the population to exceed K and be truncated Ifa dispersing individual had been scheduled to be moved into a population that is already at K then the individual will move to a different population instead During dispersal use the dispersal rates to specify a fixed N of individuals that will disperse rather than a percent 150 Reproductive System Maximum ages of breeding for males and for females can be set to be less than the maximum age This allows modeling of species that can have post reproductive life spans Specified Initial Age Structure An option was added so that the initial age structure of the population can be specified by a proportional distribution with a total initial N VORTEX will then allocate the initial N for you according to the specified distribution Carrying Capacity K can be specified to be a criterion other than a limiting N E g K can be a limiting number of females or of adults or of individuals with IS1 1 The proportion by which K exceeds the limiting value will determine the proportion of individuals across all age and sex classes that will be removed Gen
188. f Hawaii s bird fauna had not determined whether their goal was to prevent species extinctions prevent taxa species or subspecies from becoming extirpated on any of the islands they presently inhabit preserve species in sufficient numbers and distribution to allow them to continue to fill ecological roles in the biological communities or the restoration of taxa to most or all parts of the original ranges The management actions required to achieve these various levels of conservation are quite different In contrast a PHVA on the Grizzly Bear in the Central Rockies of Canada Herrero and Seal 2000 clearly identified that provincial policy called for maintenance of stable or growing populations of the species Thus the criterion against which alternative management scenarios were judged was whether the PVA projections indicated that the populations would not decline PHVA workshops facilitate the assembly of all available data Often important information is found in the field notes of researchers or managers in the heads of those who have worked with and thought about the problems of the species and in unpublished agency reports as well as in the published scientific literature A pending PHVA can be the impetus that encourages the collection of data in anticipation of presentation review and analysis at the workshop For example a Sumatran Tiger PHVA helped stimulate the systematic collection of data on sightings and signs of tigers in protecte
189. f each year in days 365 Sa E Run as population based model Mate Monopolization Initial Population Size Extinction definition 9 Only 1 sex remains Carrying Capacity Total N lt critical size Harvest Number of populations 2 X Supplementation Genetics Population 1 Population 2 Name Population1 Population2 Copy input values from Order of events in a Vortex year this section A EV Changing the sequence of events in the simulated year can Breed have complex implications for your model It is recommended to subsequent populations Mortality that you become familiar with the standard Vortex model Age before you try changing the sequence Disperse Harvest Supplement Calc Ktruncation UpdateVars Census Add J _Delete Up Down Reset Event Sequence to the Default Number of Iterations How many times you wish to repeat the simulation given the data that you provide in the subsequent steps Each repetition is generally defined as a run or iteration Because VORTEX uses a random number generator to simulate random events in the life cycle no two iterations will be identical Thus to obtain a more complete picture of your simulated population you will want to generate multiple iterations of your model As a first step you may want to make sure that the simulated population is behaving in a manner that is similar to your expectations To check this you can limit the number of iterations to just 10 o
190. f no longer filling its original role in nature even as it is praised as a conservation success story and would be considered safe from extinction and viable The use of the PHVA process to help guide conservation decisions is not a singular event in which an analysis can be completed management actions recommended and implemented and conservation thereby assured The many uncertainties in the process mandate that PVA be used as a tool in an adaptive management framework and a PHVA workshop is just one stage of an effective conservation strategy In adaptive management the lack of knowledge adequate to predict with certainty the best course of action is recognized management actions are designed in such a way that monitoring will allow testing of the adequacy of our model and understanding and corrective adjustments to management plans are made whenever the accumulating data suggest that the present course is inadequate to achieve the goals and that a better strategy exists Holling 1978 The urgency of the biodiversity crisis will not permit us ethically to refrain from aggressive conservation action until we have scientifically sound understanding of all the factors that drive population community and ecosystem dynamics PHVA provides a forum for making use of the information we do have in a well documented process that is open to challenge and improvement PHVA workshops can therefore assist wildlife managers in the very difficult and import
191. f number of offspring per female per brood Copy input values from Use normal distribution Specify exact distribution enter as percents Population 1 Z gt 5 Population 1 Population 2 Population 1 Population 2 Mean l 1 Offspring 0 to subsequent populations Standard Dev 2 Offspring 100 100 Copy Adult Females Breeding Here you specify the mean percentage of adult females that breed in a given year or stated another way the probability that a given adult female will successfully produce offspring in a given year Data on the interbirth interval or the time span between successive birth events for a given female can be useful for estimating the percentage of adult females breeding annually A simple example if the average length of time between successive births for adult females is 2 years then 50 of all adult females are expected to breed in a given year this assumes of course that animals can breed throughout their normal lifespan Be 41 careful however because this estimate will be biased because you don t have data on inter birth intervals for females that have not bred multiple times Yet those poorly reproducing females need to be considered when you estimate the proportion of all adult females that breed in an average year EV in Breeding Environmental variation EV in reproduction is modeled by the user entering a standard deviation SD for the percent females producing litters of offsprin
192. f the all file will likely be required to prepare it as an input file for PMx or other pedigree analyses The file of all individuals from a simulation can also be used as the input population for starting another Vortex simulation See the Genetics input section for information about using a studbook file to specify the starting population e Create an output a file of gene diversity heterozygosity each year of each iteration This file with extension Het is useful for more detailed analysis of genetics Note that an output file of N for each year of each iteration is always produced e Output a file of the value of GS1 through GSx with the x being a number each year of each iteration e Output a file of the value of PS1 through PSx with the x being a number for each population each year of each iteration 13 Delay 1 year mortality until Mortality is imposed on all age classes Normally VORTEX imposes the 1 year mortality immediately after a brood is produced This avoids having the population grow to very large size during the Breed step when a species has high fecundity and high 1 year mortality This immediate imposition of 1 year mortality allows these early deaths to be removed before the kinship calculations are done often thereby allowing VORTEX to run much more quickly because large numbers of kinships don t need to be calculated for newborns that immediately die The option to delay 1 year
193. female is assigned a mate from the pool of available males using the normal breeding system in VORTEX Users must be careful about interactions between mate assignments and the probability of breeding Assignment of a mate does not guarantee that a female will breed and produce offspring Instead her probability of breeding each year is determined by the breeding input parameter Note that an easy way to enable breeding success for females assigned mates and prevent any female from breeding if she does not have a pre assigned MATE would be to set the breeding to be the function 1S1 100 in which IS1 is the Svar labeled MATE If females assigned mates should have a breeding rate lt 100 this can be modeled by setting the breeding to be IS1 gt 0 x in which x is replaced by the breeding desired for those females To set different breeding rates for females already assigned mates say 55 and females not yet assigned mates say 45 the breeding can be set to IS1 0 45 IS1 gt 0 55 Q obtain mates from ISvar MATE as with option P but look for the male with ISvar name rather than Svar index sequence in the list Ix read x ISvars from the studbook file specifying the starting population Replace x with a number Dx make offspring dependent on the dam for x years Thus a newborn is specified to be dependent on the dam until it becomes x years old This will use IS1 which you must 15 create
194. g VORTEX does not fully customize the details of mating systems because of the complexities of considering a wide variety of species and their particular characteristics More complex breeding systems can substantially impact genetic variation but are less likely to seriously alter the demographic performance of a population Age of First Reproduction for Females and Males VORTEX defines breeding as the time when the first offspring are born not the age of onset of sexual maturity or the age of first conception The program also assumes that breeding and for that matter all other events occurs at discrete intervals usually years but this can be described in terms of whatever you have defined as a suitable time cycle Thus breeding age must be entered as an integer you cannot enter 2 5 years as the first age of breeding but must enter either 2 or 3 years In addition you should enter the median age of first breeding not the earliest age ever observed since the earliest observed age may not be typical of the normal population behavior Maximum Age of Reproduction Maximum ages of breeding for males and for females can be set to be less than the maximum age This allows modeling of species that can have post reproductive life spans Maximum lifespan VORTEX will terminate the life of any individual that reaches this age Usually however the annual mortality rates prevent more than a small number of individuals from ever reaching the
195. g Mortality Aging Dispersal Harvest Supplementation Calculate Growth Carrying Capacity Update GSVars PSVars and ISVars Census Steps can be placed in any order and steps can be repeated e g there can be dispersal both before and after harvest Updating of state variables can be done as one operation with the order being GS then PS then IS or the three levels of state variables can be updated independently Age classes for which input values need to be specified will be determined by which steps are placed before Aging For example if Harvest occurs before Aging in each year then the 0 age class animals can be harvested If two breeding cycles occur without an Aging step intervening then 0 age class individuals can breed VORTEX automatically adjusts input page displays to accommodate breeding initial N harvest etc of age 0 animals if the specified sequence of events makes it possible for age 0 individuals to experience those events A few examples of the use of alternative order of events are Harvest can be moved before Mortality if you want to be able to harvest some newborn animals Note however that for this sequence to work you will also need to select the Special Option to Delay 1 year mortality see above Harvest can be moved before Age but after Mortality if you want to harvest the newborns but only after initial mortality occurs Updating of state variables can be moved up if you need the curren
196. g VORTEX then determines the percent breeding for a given year by sampling from a binomial distribution with the specified mean and standard deviation Although environmental variation in birth and death rates can have a substantial impact on the viability of a population it is often difficult to obtain the data needed to estimate EV Long term field studies are needed in order to determine the amount of fluctuation that occurs in the demographic rates of your population If these data are available the standard deviation in mean birth rate can be simply calculated using standard statistical methods If your dataset is small but you are comfortable with making a rough quantitative estimate of the variability you can use the technique presented below A common problem in estimating annual fluctuations in demographic rates is that the data might be so sparse that it is difficult or impossible to estimate the parameters on an annual basis If this is the case you might be forced to admit that the data are not sufficient to allow estimation of the variability around the mean values The only alternatives are to guess at the fluctuations in reproductive and mortality rates based on a general understanding of the natural history of the species or to omit environmental variability from the model altogether by entering 0 when each standard deviation is requested In this case you must recognize that a potentially important component of population variabili
197. giving it appropriate Initialization Fn usually 0 Birth Fn 0 and Transition Fn IS1 as a place to store for each female the number of currently living still dependent offspring This means that you can specify for example that only females with no dependent young can breed each year Moreover if the dam dies then all currently dependent offspring are killed RT during supplementation of individuals with the Translocation option populations are chosen in a random order to receive translocated released individuals so that if there are not enough individuals in the last population to fulfill the supplements across years and iterations each population will have an equal chance of receiving its specified supplements However new supplements to the last population or the holding population see next option are always added after the supplements translocations into the prior populations HPx in the Translocation option use population x rather than the last population as the holding population MKD For scenarios with more than 1 population include in the Output Summary genetic distances matrices based on the kinships as well as the standard genetic distance matrices based on allele frequencies GDMx Specifies the metric of genetic distance between populations to be used when a function includes the variable GDIST When x 0 the default GDIST is Nei s standard genetic distance D Specify x 1 for the genetic
198. gram many rates will be evaluated with fewer significant digits for example inbreeding coefficients are calculated to 5 significant digits mortality rates greater than 0 999999 are rounded to 1 0 and dispersal rates smaller than 0 00001 are rounded to 0 0 If the use of the value requires an integer e g a number of individuals to be harvested VORTEX may truncate round or probabilistically round the value to obtain an integer see descriptions of input rates above so it is best to include the intended type of rounding within the function itself so that the user controls exactly how non integer values will be treated The flexibility to specify population rates as functions rather than as fixed constants allows users to model specific population dynamics that might be known to be appropriate for some species or that are of interest in a theoretical analysis With some creativity and perhaps considerable effort VORTEX can now model many of the kinds of population dynamics that can be envisioned As just a few examples gt it might be known that carrying capacity will change at some determined date in the future 105 it might be believed that reproductive rates will change over time perhaps due to some management action the density dependence observed in reproduction might not fit the shapes of the curves allowed in previous versions of VORTEX mortality rates might change over time or respond in a complex way to population de
199. grationRand lt CumulativeMigrationProb pSource pDestinarion BREAK from LOOP Animal will try to migrate to pDestination END IF END LOOP IF Population pDestination at carrying capacity IF tried 9 times before to find an open population ECOLOGICAL BULLETINS 48 2000 Animal dies Never found an open population into which to migrate BREAK from LOOP CONTINUE with next animal END IF IF CumulativeMigrationProb p Destination NumberPopulations 0 Animal dies 11 Cannot migrate away from pDestination BREAK from LOOP CONTINUE with next animal END IF Set MigrationRand RAND Set pSource pDestination 1 Moves on from population pDestination old pDestination becomes current pSource WHILE MigrationRand gt CumulativeMigrationProb pSource NumberPopulations Set MigrationRand RANDO Must migrate somewhere so draw a new random number END WHILE END IF END LOOP Change animal s population to pDestination Adjust tallies of population sizes Increment size of pDestinarion decrement size of pSource END animal LOOP END FUNCTION MIGRATE BEGIN FUNCTION HARVEST for population p FOR each age x 1 HARVEST lumps all animal above breeding age as a single class IF VumberMales p x lt NumberMales ToBeHarvested p x All males age x die ELSE WHILE number harvested lt NumberMales ToBeHarvested p x Choose at random a living male in age class x Male di
200. gren Gulve P 1994 Distribucion and extinction patterns within a northern metapopulation of the pool frog Rana les sonae Ecology 75 1357 1367 Sj gren Gulve P and Ray C 1996 Using logistic regression to model metapopulation dynamics Large scale forestry extir pates the pool frog In McCullough D R ed Metap opulations and wildlife conservation Island Press Washing ton D C pp 111 137 Soul M E 1980 Thresholds for survival maintaining fitness and evolutionary potential In Soul M E and Wilcox B A eds Conservation biology An evolutionary ecological perspective Sinauer pp 151 169 Soul M E 1987 Viable populations for conservation Cam bridge Univ Press Starfield A M 1997 A pragmatic approach to modeling J Wildl Manage 61 261 270 Starfield A M and Bleloch A L 1986 Building models for conservation and wildlife management MacMillan New York Stephens P A and Sutherland W J 1999 Consequences of the Allee effect for behaviour ecology and conservation Trends Ecol Evol 14 401 405 Varvio S L Chakraborty R and Nei M 1986 Genetic varia tion in subdivided populations and conservation genetics Heredity 57 189 198 Vucetich J A and Creel S 1999 Ecological interactions social organization and extinction risk in African wild dogs Conserv Biol 13 1172 1182 Vucetich J A Peterson R O and Waite T A 19
201. have been maintained or even increased for a number of years the principal threat was that a local catastrophe e g disease epidemic severe storm could decimate the population Clark 1989 Lacy et al 1989 Mirande et al 1991 The primary recovery actions therefore needed to include the establishment of additional populations Tragically some taxa such the eastern barred bandicoot Perameles gunnii in Australia may be critically threatened simultaneously by deterministic factors and stochastic processes Lacy and Clark 1990 PVA is formally an assessment of the probability of extinction but PVA methods often focus on other indicators of population health Mean and variance in population growth Lindenmayer and Lacy 1995a 1995b 1995c changes in range distribution and habitat occupancy Hanski and Gilpin 1991 1997 and losses of genetic variability Soul et al 1986 Lande and Barrowclough 1987 Seal 1992 Lacy and Lindenmayer 1995 can be analyzed and monitored Although not yet common monitoring of population health could also utilize measures of developmental stability Clarke 1995 physiological parameters such as body condition Altmann et al 1993 or levels of the hormones related to stress and reproduction Sapolsky 1982 1986 or the stability of behavior and the social structure of the population Samuels and Altmann 1991 The interactions and synergism among threatening processes will often cause numerical distributiona
202. he species you are modeling has a short generation time and life span on the order of weeks or months such as mice or shrews for example true calendar years would be an inappropriate time scale to use for modeling population dynamics In this case a year for this type of species may actually represent only one or a few months VORTEX does not use the value that you put into this box the box is there primarily to remind you if you choose to use a duration of the time step that is different the one calendar year However this value is important if you link your VORTEX model to other simulations via the METAMODEL MANAGER software see www vortex10 ore MeMoMe aspx for more information METAMODEL MANAGER uses this variable to know how to synchronize the VORTEX simulation with other simulations that might be using a different time cycle When specifying demographic inputs it is vitally important that you consistently adjust input values to be appropriate to the time cycle that you are using see Box below for more an example Calculating input parameters when the time cycle is less than one year Consider a hypothetical rodent population where the average generation time is 180 days In order to model this population most effectively in VORTEX the user must adjust the time cycle to account for this shortened generation time In this case we will define a VORTEX year as 90 days Consequently events whose occurrences ar
203. he top dropdown list When you are ready to exit the STsetup window be sure that you have saved your ST if you have made any changes by hitting Accept or Accept and Close When providing a list of values to be sampled for an ST parameter separate the values with semi colons not with commas After you first create an ST don t forget to go into the Input pages to insert the SV1 SV2 etc into the desired input parameters Otherwise the SVs will be varied across the series of scenarios run in the ST but they will have no effect When you create and Accept STs the settings for those STs are saved within your VORTEX project You will then need to save the project before or when exiting VORTEX Be careful when you edit the STbase scenario after you create an ST Any changes that you make in that scenario in the input will apply to all the copied scenarios in the series for that ST This is of course useful in that you can change some parameters after creating the ST but you need to be aware that if you make edits to the STbase later they will be applied to the ST Be aware that the STbase scenario that is created and the ST specifications are intimately linked If you delete the STbase scenario in the Input tab then the associated ST specifications will disappear also If you delete the ST in the STsetup window then the STbase scenario will be deleted from the scenario list in the project You can edit the GSvar
204. hics and genetics its dynamics and fate can become dominated by a number of random or stochastic processes as outlined above and by Shaffer 1981 Thus even if the original deterministic causes of decline are stopped or reversed the instability caused by the action of stochastic processes acting on small populations can cause the extinction of a population 134 In nature most threatening processes have both deterministic and stochastic features For example a high level of poaching might be seen as a deterministic factor driving a wildlife population toward extinction but whether an individual animal is killed might be largely a matter of chance In a PVA poaching might be modeled as a deterministic process by killing a determined proportion of the animals or it might be modeled as a stochastic process by giving each animal that probability of being killed but allowing the exact numbers killed to vary over time If the population is large and the percent of animals killed is high then these two ways of modeling the effects of poaching will yield the same results the deterministic component of poaching dominates the population dynamics If the population is small or the percent of animals killed is very low then the numbers killed in a stochastic model and in nature might vary substantially from year to year the stochastic nature of poaching further destabilizes the population Which of the various deterministic and stochastic factors are im
205. identity I x 2 for gene identity Jxy and x 3 for Gst See the Genetics section for more information on these measures of between population genetic distance KM A matrix will be provided by the user to specify the kinships among some or all of the initial individuals provided via a studbook see Genetics section The name and path of this file with the kinships must be the same as the studbook file except with extension kin The file must contain coefficients of kinship usually symbolized f sometimes termed the coefficient of consanguinity NOT coefficients of relationship r Detailed explanation of the different measures of relatedness and methods for estimating kinship from genealogical or genotypic data are beyond the scope of this manual Seek help from a population geneticist The format of the file should be a simple text file with an initial line that lists the IDs matching the studbook numbers of the individuals for which kinships will be provided followed by lines giving the kinships as follows Comments to be ignored by the program are preceded with 3 9 11 Joe A2 IDs can be any combination of numbers and letters but cannot contain spaces commas or semi colons Another comment note that delimiters can be tabs spaces semi colons but NOT periods because of the confusion that causes with non American data formats The decimal delimiter used should be whatever is appropriate for the dat
206. idity The Initialization value is then used replacing any Default value that had been entered at the start of each iteration If there is no Default value given for a state variable then the Initialization is also used for calculations that are done before the iterations start It is not common that you would need to enter a Default value for a GS or PS variable because usually the Initialization can be used for the same purpose However if an initialization function contains the variable R for run or iteration as is sometimes useful in automated sensitivity analyses then a Default value for the state variable or a Default value for R can be used to ensure that the state variable is set appropriately for deterministic calculations State Variables extend the flexibility and power of functions for data input and also allows you to create new output measures of interest However just as the use of functions can be challenging especially if they become complex the use of State Variables to enhance functions is best left to experienced users of Vortex Even when using State Variables or any functions it is wise to first build the project without them and then add them in gradually An aside for those who are willing to dive deeply into using functions and user specified variables to develop models of complex biological systems VORTEX provides the capacity to run the population simulation simultaneously functionally i
207. ifferent people can describe rather distinct kinds of analyses with the same terminology while others use different terms to describe nearly identical approaches The ever changing concepts of PVA and PHVA are confusing but the flexibility of the processes is also their strength Current tools are inadequate to address fully the challenges of stemming the losses of biodiversity The PVA PHVA framework allows and encourages rapid application of new tools data and interpretations into increasingly effective conservation programs Methods for Analyzing Population Viability An understanding of the multiple interacting forces that contribute to extinction vortices is a prerequisite for the study of extinction recolonization dynamics in natural populations inhabiting patchy environments Gilpin 1987 the management of small populations Clark and Seebeck 1990 and the conservation of threatened wildlife Shaffer 1981 1990 Soul 1987 Mace and Lande 1991 Shaffer 1981 suggested several ways to conduct PVAs Perhaps the most rigorous method and the one that would produce the most defensible estimates would be an empirical observation of the stability and long term fates of a number of populations of various sizes Berger 1990 presented a good example of this approach in which he observed that populations of bighorn sheep in the mountains of the western USA persisted only when the populations consisted of more than 100 animals A few other studi
208. imulation model for population viability analysis Ecological Bulletins 48 191 203 Much of the material from the first two papers is incorporated into an Appendix The last two are reprinted at the end of this manual Many references to uses of VORTEX are available on web at http www Vortex10 org VortexReferences aspx Users are encouraged to add their own papers to the list of references on the Vortex10 org website Using this manual This document provides an initial description of how to use VORTEX version 10 It updates information that was in the manual for version 9 and it provides new information on features that have been added or changed from version 9 The main part of the manual focuses on the details of using the VORTEX user interface Text that you would type as input is shown in Bold Microsoft San Serif font There are also appendices that provide more background about the structure of the program and its use for Population Viability Analysis The references are still being updated and expanded and more will be added Boxes throughout the manual provide helpful hints information about making the transition from version 9 to version 10 examples or case studies and other side comments Table of Contents entries are hyperlinked to those pages Table of Contents Table 0f Contents di A A A A A 3 Got Mat iS a dota Settee 6 AI san nn RON 6 A Note About Cost nt a te bateo naa belen theses 6 Starting VORTEX a ia 7 Running V
209. in the project file as fully specified scenarios An important note about regional data formats Vortex will use whichever numeric data format e g 0 50 or 0 50 for 4 is appropriate for the regional settings on the computer However Project files cannot be transferred between computers that use different numeric data formats unless they are first manually edited to convert the data Input files The VoRTEX project files will be saved in xml format Although it is easiest to enter input values from the user interface the project files that specify input values can be edited directly in a browser or text editor if great care is taken to format everything in the file properly This can be useful if VORTEX scenarios are being created by an external shell program Conversion hint The change to xml files was made because they can be more forgiving of possible errors in the file format and in the future this will make it easier to open old projects in upgraded versions of Vortex Be careful however that after you save a project in the xml format you will later want to open that new xml file and not the prior vpj file from Vortex9 VORTEX 10 can still read VORTEX 9 vpj project files However because the syntax of some variables used in functions has been changed see below some editing of input values may be necessary to get a VORTEX 9 project to run correctly in VORTEX 10 Files saved in VORTEX 10 format cannot be read subsequent
210. in theo ry and practice Blackwell ECOLOGICAL BULLETINS 48 2000 Kirkpatrick S and Stoll E 1981 A very fast shift register se quence random number generator J Comp Phys 40 517 Lacy R C 1993 VORTEX A computer simulation model for population viability analysis Wildl Res 20 45 65 Latour A 1986 Polar normal distribution Byte August 1986 131 132 Lindenmayer D B Lacy R C and Pope M L 2000 Testing a simulation model for population viability analysis Ecol Appl 10 580 597 Maier W L 1991 A fast pseudo random number generator Dr Dobb s Journal May 1991 152 157 Miller P S and Lacy R C 1999 VORTEX Ver 8 users manual A stochastic simulation of the simulation process IUCN SSC Conservation Breeding Specialist Group Apple Valley Minnesota Mills L S and Smouse P E 1994 Demographic consequences of inbreeding in remnant populations Am Nat 144 412 431 Morton N E Crow J F and Muller H J 1956 An estimate of the mutational damage in man from data on consanguineous marriages Proc Nat Acad Sci USA 42 855 863 Pielou E C 1977 Mathematical ecology Wiley Starfield A M and Bleloch A L 1986 Building models for conservation and wildlife management MacMillan 203 Ecological Bulletins 48 39 51 Copenhagen 2000 Considering threats to the viability of small populations using individual based models Robert C Lac
211. ing depression more severe in a stressful environment Zoo Biol 13 195 208 Mills L S and Smouse P E 1994 Demographic consequences of inbreeding in remnant populations Am Nat 1 14 412 431 Mills L S et al 1996 Factors leading to different viability pre dictions for a grizzly bear data set Conserv Biol 10 863 873 Mirande C Lacy R and Seal U 1991 Whooping crane Grus americana conservation viability assessment workshop re port IUCN SSC Captive Breeding Specialist Group Ap ple Valley Minnesota Pettersson B 1985 Extinction of an isolated population of the middle spotted woodpecker Dendrocopos medius L in Swe den and its relation to general theories on extinction Biol Conserv 32 335 353 Piattelli Palmarini M 1994 Inevitable illusions How mistakes of reason rule our minds Wiley Pounds J A and Crump M L 1994 Amphibian declines and climate disturbance the case of the golden toad and the har lequin frog Conserv Biol 8 72 85 Rabenold K N 1990 Campylorhynchus wrens the ecology of delayed dispersal and cooperation in the Venezuelan savan na In Stacey P B and Koenig W D eds Cooperative breeding in birds Cambridge Univ Press pp 159 196 Rabenold P P et al 1991 Density dependent dispersal in social wrens genetic analysis using novel matriline markers Anim Behav 42 144 146 Ralls K Ballou J D and Templeton A 19
212. inoc oon leo ss eros in the Garamba National Park Congo formerly Zaire the entire range of the only re maining population of the tax on and the number projected dashed line from the 1985 population Error bars show the standard deviation across simulations of the projected population size each year Adapted from Lacy 1996 ECOLOGICAL BULLETINS 48 2000 nize that our assessments may be crude Because all PVA models include only a subset of potentially threatening processes it is possible that many PVAs overestimate via bility Lacy 1993 1994 and that our error will tend to be greatest in the smallest populations i e those which are most critically in need of effective conservation action Ac cordingly margins for error and ongoing monitoring of results should always be part of implementation see also Akcakaya 2000 Although the dynamics of small populations can be complex and subjected to many stochastic processes exist ing PVA models can provide good representations of dy namics of many such populations PVA models have pre dicted well the dynamics of some critically rare species such as the whooping crane Brook et al 1999 and the northern white rhinoceros Ceratotherium simum cottoni see Fig 5 Brook et al 2000 found that PVA models that are sufficiently detailed and for which there are ade quate data for estimating parameters can provide unbiased and reasonably a
213. invoked by giving the appropriate codes separated by semi colons or spaces if more than one in the box A few of the current undocumented options are P obtain the mate for each female from an Svar labeled MATE If MATE 1 then a mate is selected at random from the available males The Svar labeled MATE will be the index of the individual to be used as the mate if available This option allows the user to assign specific male x female pairings A few uses of this option might be to assign specific male female pairings from animals in a studbook used as the starting population or to provide a means by which another program through Metamodel Manager assigns the pairings To invoke this option give the special option code P An Individual State Variable must also be created and given the label MATE It can be any of IS1 IS2 etc If the ISVar of MATE is not provided then this option is ignored and this provides a means to have the option invoked for some scenarios but not for others in a project file When mates are assigned to breeding females if the ISvar MATE is a non zero number and if that number matches the ID for a living animal of either sex and of any age then that animal is assigned as the mate for the female The value of MATE for males is ignored I e males are assigned to females based on the value of MATE for the females but not the reverse If the value of MATE is 0 or negative then the
214. ion planning and management the simple model of population growth as a constant annual rate of change is inadequate for our needs The fluctuations in population size that are omitted from the standard ecological models of population change can cause population extinction and therefore are often the primary focus of concern In order to understand and predict the vulnerability of a wildlife population to extinction we need to use a model which incorporates the processes which cause fluctuations in the population as well as those which control the long term trends in population size Many processes can cause fluctuations in population size variation in the environment such as weather food supplies and predation genetic changes in the population such as genetic drift inbreeding and response to natural selection catastrophic effects such as disease epidemics floods and droughts decimation of the population or its 140 habitats by humans the chance results of the probabilistic events in the lives of individuals sex determination location of mates breeding success survival and interactions among these factors Gilpin and Soul 1986 Models of population dynamics which incorporate causes of fluctuations in population size in order to predict probabilities of extinction and to help identify the processes which contribute to a population s vulnerability are used in Population Viability Analysis PVA For the purpose of predicting vul
215. ion among the array of people with strong interest in or responsibility for a conservation effort e g governmental wildlife agencies conservation NGOs and the local people who interact with the species or its habitat or with particular expert knowledge about the species its habitats or the threats it faces e g academic 133 biologists conservation professionals other wildlife biologists experts on human demographics and resource use Conservation problems are almost always multi faceted involving not only complex dynamics of biological populations but also interactions with human populations the past present and future impacts of humans on habitats and human political social and economic systems Alvarez 1993 Bormann and Kellert 1991 Clark 1989 1993 Many people need to contribute knowledge expertise and ideas in order to achieve the recovery of threatened species Population viability analyses can provide a framework for incorporating the many needed kinds of knowledge into species conservation efforts because PVAs do allow the assessment of many kinds of factors that threaten the persistence of populations Lacy 1993a Lindenmayer et al 1993 The Conservation Breeding Specialist Group CBSG of the IUCN s Species Survival Commission especially has advocated and used workshops centered on PVAs to provide guidance to conservation assessment and planning Over the past few years the PVA workshop as an approach to species
216. ion for population growth GN _ Je dt K where r is the intrinsic rate of population increase N is population size and K is carrying capacity Mathematically K can be thought of as the population size limit at which the rate of growth dN dt is equal to zero Some ecologists define K as a ratio of the total rate of food production in the habitat P to the per capita rate of food consumption necessary for survival M Since a population of size N must consume food resources at a rate of NM just to stay alive there are P NM resources available for the production of new individuals If NM exceeds P then resources available for reproduction become negative and the population must decrease in size When N is very small for example when a population is re established in its native habitat the potential growth rate is very close to exponential If the population exceeds its carrying capacity the number of individuals will be reduced until N lt K The carrying capacity then can be thought of as representing a stable equilibrium population size Many population ecologists describe the gradual approach towards this equilibrium in terms of damped oscillations in population growth Empirically one could estimate the habitat carrying capacity for a given animal species by calculating the total food supply appropriate for that species that is available in the habitat and dividing that value by the rate of that species consumption of its
217. ion of the mtDNA can also be specified by using LOCUS 1 in any mutation rate function and asking for mutation to be modeled at nLoci 1 loci one more than the number of neutral loci being modeled Read initial allele frequencies from file VORTEX normally starts the simulation with each founder individual carrying unique alleles at the modeled locus or loci For testing changes in known or assumed starting frequencies of alleles at loci you can specify that the simulation should sample from a known distribution of allele frequencies when it assign alleles at your additional loci to founders This option might be used to test expected patterns of microsatellite DNA alleles or to test the evolution of alleles with specific selected effects on demography Although the alleles at neutral loci in VORTEX usually have no impact on fitness it is possible to specify that demographic rates are functions of genotypes The starting allele frequencies are specified in a text file with the following format 3 342 33 33 34 25 25 25 25 3 5 63 The first line specifies the number of loci modeled The next line gives the number of alleles for each of these loci The subsequent lines give the allele frequency distributions for the loci Note that as for all input values in VORTEX the decimal delimiter in these files must be entered as a comma rather than a point when the computer is using European or many other non American data formats
218. ion size N as inbreeding and genetic drift are more rapid in a population that fluctuates in size than in a stable popula tion of the same mean size Together with other factors which can reduce breeding success in smaller populations this can cause the ratio of the effective population size to the total size N N to diminish as a population becomes smaller Hence while N might be 500 when N 1000 N may be 30 when N 100 and just 10 when N 50 In yet another example of the interaction between ge netic and demographic threats to population viability the joint effects of stochasticity in these two processes have been found to lead to consequences which can be opposite those predicted from purely genetic models A number of authors have reported that a subdivided population will retain more gene diversity over time than will a single pan mictic population because genetic drift will by chance fa vor different alleles in the various isolated populations Boecklen 1986 Varvio et al 1986 Lacy 1987 However the models on which this conclusion is based assume that populations are constant in size The apparently beneficial effect of subdivision is partly due to an artifact of the mod els in which model constraints create more equal distribu tion of reproductive success and therefore higher N_ when the population is divided into subunits of fixed size Barton and Whitlock 1997 and partly due to the protec tion of different all
219. ions are fast and do not require much memory if inbreeding depression is modeled as due 100 to recessive lethal alleles and if no function uses inbreeding I or kinship KIN as a variable Special options New Special Options available on the Project Settings page e Create an output a file of gene diversity heterozygosity each year of each iteration Note that an output file of N for each year of each iteration is now always produced e Output a file of the value of PS1 through PSx with the x being a number for each population each year of each iteration e Output a file of the value of GS1 through GSx with the x being a number each year of each iteration e Do not show messages to the user while running This can be useful if many scenarios are running when the computer will not be attended e Delay 1 year mortality until Mortality is imposed on all age classes Normally VORTEX imposes the 1 year mortality immediately after a brood is produced This avoids having the population grow to very large size during the Breed step when a species has high fecundity and high 1 year mortality This immediate imposition of 1 year mortality allows these early deaths to be removed before the kinship calculations are done often thereby allowing VORTEX to run much more quickly because large numbers of kinships don t need to be calculated for newborns that immediately die The option to delay 1 year mortality
220. ions share no alleles Genetic distances can also be calculated from the matrix of kinships that is calculated from the pedigree The calculations based on kinships will usually be more accurate than those based on allele frequencies because the kinship calculations are not affected by the random sampling error associated with a small number of loci However the calculations based on frequencies of simulated alleles will be faster if the kinship matrices are not otherwise required for non recessive model inbreeding depression These equivalent genetic distance matrices based on kinships will be included in the Output Summary if you give the Special Option MKD If this option is specified then values of GDIST used in any function will be the values obtained from the kinships rather than the values estimated from allele frequencies 79 How is the genetic distance or similarity between populations measured A full explanation of the many measures of genetic distance would require a long section of a textbook and those interested are encouraged to consult Nei 1987 Hedrick 2000 or other texts for detailed derivations A brief description of the metrics provided in VORTEX is given here Most measures of genetic distance start with the expected heterozygosity that is the heterozygosity that would be observed if a diploid population were in hardy Weinberg equilibrium Often this is termed just heterozygosity but that is a
221. is described by an exponential decline S Spe F in which So is the survival of non inbred individuals F is the inbreeding coefficient b is the average number of lethal alleles per haploid genome half the number per diploid individual and S is the resultant survival rate Morton et al 1956 Figure B 1 gives the expected relationship between the extent of inbreeding and juvenile survival for a series of hypothetical scenarios differing in the total number of lethal equivalents Even if the overall inbreeding depression is due only partly to recessive lethal alleles the relationship between inbreeding and survival might be expected to be roughly an exponential decline of this form By observing the relationship between survival and inbreeding the coefficient b in the above equation can be measured The value b is a measure of the severity of the effects of inbreeding not in terms of how inbred the population is as that is measured by F but rather in terms of how much fitness is depressed for any given level of inbreeding and it is the number of recessive lethal alleles per haploid genome that would cause the observed rate of inbreeding depression This concept is called the number of lethal equivalents in the population A population with 4 0 lethal equivalents per diploid individual b 2 0 might have 4 lethal alleles per individual or it might have 8 alleles per individual which each cause 50 reduction in survival when homozygous
222. ks G and Walsh A 1996 Hierarchical analysis of inbreeding depression in Peromyscus polionotus Evolu tion 50 2187 2200 Lande R 1988 Genetics and demography in biological conser vation Science 241 1455 1460 Lande R 1995 Mutation and conservation Conserv Biol 9 782 791 Lindenmayer D B and Lacy R C 1995 Metapopulation via bility of Leadbeater s possum Gymnobelideus leadbeateri in fragmented old growth forests Ecol Appl 5 164 182 Lindenmayer D B et al 1995 A review of the generic computer programs ALEX RAMAS space and VORTEX for model ling the viability of wildlife populations Ecol Model 82 161 174 ECOLOGICAL BULLETINS 48 2000 Lindenmayer D B McCarthy M A and Pope M L 1999 Arboreal marsupial incidence in eucalypt patches in south eastern Australia a test of Hanski s incidence function meta population model for patch occupancy Oikos 84 99 109 Lindenmayer D B Lacy R C and Pope M L 2000 Testing a simulation model for population viability analysis Ecol Appl 10 580 597 Lynch M and Walsh B 1998 Genetics and analysis of quanti tative traits Sinauer Margolis H 1996 Dealing with risk Why the public and the experts disagree on environmental issues Univ of Chicago Press Menges E S 2000 Applications of population viability analyses in plant conservation Ecol Bull 48 73 84 Miller P S 1994 Is inbreed
223. l physiologic behavioral and genetic responses to concordantly reflect species decline and vulnerability It remains important however to understand and target the primary causal factors in species vulnerability The recent proposal to base IUCN categories of threat on quantified criteria of probability of extinction or changes in such indicators as species range numbers and trends Mace and Lande 1991 Mace et al 1992 Mace and Stuart 1994 IUCN Species Survival Commission 1994 reflects the increased understanding of the extinction process that has accompanied the development of PVA and 135 simultaneously demands that much more progress be made in developing predictive models gathering relevant data on status and threats and applying the PVA techniques Population and Habitat Viability Analysis PHVA Population and Habitat Viability Analysis is a multi faceted process or framework for assisting conservation planning rather than a singular technique or tool It is often interwoven with other techniques for managing complex systems such as decision analysis Maguire 1986 Maguire et al 1990 Even when viewed as the PHVA workshop all such conservation workshops involved and required substantial pre workshop and post workshop activities Some PHVA workshops have been extended into multiple workshops and less formal smaller collaborative meetings often focused on subsets of the larger problems of species conservation Although PHVAs
224. l ST that can help you focus later STs on the more important parameters Hitting the Run ST button will run the full set of scenarios created for that ST When you run the ST sampled scenarios VORTEX will also automatically first run a scenario that uses the base values and this base scenario can later be compared in tables and plots to the sampled scenarios The graph of population size will be shown during this run of the base scenario but will not be displayed during all the runs of the sampled scenarios for the ST You can also run the base scenario back in the main VORTEX Run window and it is sometimes useful to do that before running all the ST scenarios in the ST module to confirm that the scenario has all required VORTEX input to obtain a baseline set of results and because this will produce the full set of VORTEX output files including the description of input deterministic results etc for this baseline case The results from base scenario run within the ST module and the base scenario run in the main window will be given slightly different labels so results from both sets of runs are saved and they may differ due to random stochastic variation VORTEX will normally produce only a subset of the output files for each of the possibly very many scenarios that are created in the ST These output files summarize the affect of each tested variable for analysis see below If you need a more complete and detailed output fr
225. l inbreeding and kinships set to 0 this section X to subsequent populations Maximum number of female mates blank or O for no limt 3 Optional Criteria for acceptable mates SIRE1 DAM1 Number of times to try to find a mate 10 Optional Criteria for separating a longterm pair PAIRTENURE gt 3 Genetic Output V Produce a file in GenePop format at the end of each iteration Y Produce a file of allele frequencies and probabilities of persistence Replace initial population with studbook from file VORTEX can start the simulation with a known or assumed population that has a defined pedigree structure This option allows the user to provide to VORTEX a population pedigree a studbook that might describe a captive population or a wild population that has been monitored closely for a number of generations For entering the initial population from a studbook the format can be a text file with extension ped of the format created by the SPARKS studbook program available from the International Species Information System www isis org for use in PMX available at www vortex10 org PMx aspx Alternatively the studbook file can be any text file that contains a header of format 60 ID Sire Dam Sex Selected Alive Population Svars followed by a line for each individual with data in the sequence given in the header The csv export file created by SPARKS for PMX can be used as the studbook input file in VORTEX
226. lation size carrying capacity numbers of juveniles animals in the first age class subadults greater than 1 year but not yet breeding age adult females adult males all females or all males and gene diversity expected heterozygosity Individual characteristics that can be entered as variables in these functions include ID sex age number of mates 0 or 1 for females and monogamous males possibly more for polygamous males inbreeding coefficient and genotypes at modeled loci Almost all demographic rate parameters such as the percent of females breeding each year environmental variation in breeding litter clutch size sex ratio mortality rates environmental variation in mortality catastrophe frequency and severities carrying capacity dispersal dispersal mortality occurrence of harvest and supplementation and definition of extinction can be specified to be functions of the above population and individual variables Functions are evaluated each time that the demographic rate is called e g each year for a function for carrying capacity or numbers of individuals harvested or supplemented for each individual in each year for a function of a reproductive parameter mortality or dispersal rate Functions return rational numbers positive or negative numbers that may include digits after a decimal delimiter calculated to double precision 8 byte numbers with about 17 significant digits However for speed within the pro
227. lculations assume that there is no limitation of mates 1 e there are always enough breeding males to mate with all breeding females Other complications arise if there are catastrophes in the simulation model In those cases VORTEX adjusts the fecundity and mortality rates to account for the effect of catastrophes averaged across years For more information on the details of life table analysis refer to any number of general ecology or population biology texts such as Pielou 1977 Krebs 1994 or Caughley 1977 74 Why does the population growth rate in the simulation stochastic lambda almost always end up smaller than the growth rate calculated from the birth and death rates deterministic lambda There are several reasons for this and they are some of the reasons that stochastic simulations are valuable First the lambda calculated from vital rates is an expected mean growth rate if all vital rates are constant at the values entered into the model However if birth and death rates fluctuate over time even due just to random chance as they always do in the field and as they will in any stochastic simulation model then the lambda that is calculated from the means will systematically overestimate long term average population growth The reasons for this are complicated but basically arise from the fact that good and bad years don t cancel each other out E g if a population alternates between lambda 1 1 and lambda 0 9 i
228. lled harvest Can it sustain poaching Would a corridor connecting fragmented habitats improve long term viability Could the same effect be achieved by translocating a few individuals What will happen to population viability if mortality increases for individuals dispersing between habitat patches What will happen to the wildlife population if trends in human populations and human impacts on the environment continue unabated 143 The VORTEX Population Viability Analysis Model The VORTEX computer program is a simulation of the effects of deterministic forces as well as demographic environmental and genetic stochastic events on wildlife populations It is an attempt to model many of the extinction vortices that can threaten persistence of small populations hence its name VORTEX models population dynamics as discrete sequential events that occur according to probabilities that are random variables following user specified distributions VORTEX simulates a population by stepping through a series of events that describe an annual cycle of a typical sexually reproducing diploid organism mate selection reproduction mortality increment of age by one year migration among populations removals supplementation and then truncation if necessary to the carrying capacity Although VORTEX simulates life events on an annual cycle a user could model years that are other than 12 months duration The simulation of the population is iterated man
229. lp command which can be invoked from the Help menu from the icon or from any window by hitting F1 will open the manual in Acrobat Reader which must exist on the computer for the manual to be used The Help command will try to go to the page of the manual that is appropriate for where you were in the program but you can browse through the file or search with ctrl F for key words to find the help that you need The vortex 10 org website includes a FAQ section to which users can post questions and answer questions posted by others Under the top menus is a row of buttons that provide quick ways to get to many of the same features that are available in the menus Below these are a series of five tabbed sections Each of these is explained to some extent below Within these tabbed sections there are various methods to navigate around parts of the section On most screens if you hover the mouse over a label e g for an icon or menu item or for an input variable or input table VORTEX will often pop up short text a tooltip that explains the button or variable further When you hover over a data entry box it will often pop up a tooltip that states what kind of data is expected One clue as to if a data entry box expects a text or can accept a function in place of a number is that often the box will be relatively small if you must enter a simple number but it will be long if you should enter text or can enter a function To ent
230. lt n l then some Ds were infinite and not tallied n D below diagonal n l above diagonal n G on diagonal Population 1 Population2 Population 100 99 Population2 0 99 Send to Report Save As Print 78 Genetic distances are normally calculated from allele frequencies and the matrices of distance given in the Output Summary are calculated from the allele frequencies across the loci specified for summary statistics see Genetics To obtain more precise measures you can model more neutral loci You can also observe how pre existing genetic structure is projected to change over time by specifying starting allele frequencies and then having genetic summary statistics calculated on only those additional loci A variable GDIST p1 p2 that gives the genetic distance between populations p1 and p2 is available for use in functions with GDIST p1 p1 being a code for the genetic distance between p1 and the metapopulation so that the genetic distance at each year of the simulation can be obtained by setting a Population State variable to GDIST p1 p2 Which of the genetic distance metrics is provided in this variable can be set via the Special Option GDMx with standard genetic distance D being the default if the special option is not used Set x to 1 to have GDIST provide genetic identites I x 2 for gene identities J and x 3 for Gst The value of GDIST will be set to 1 if D is undefined because the two populat
231. luctuations in the probabilities of reproduction and mortality are modeled in VORTEX as binomial distributions while environmental variation in carrying capacity is modeled as a normal distribution Note that the distinction between demographic stochasticity and environmental variability is a subtle one even some professional population biologists have been confused by this Demographic stochasticity is the variation in an observed vital rate due to the sampling variation that is inherent because each individual an observation is an independent and random sample from a population with a given mean or probability Hence it is the variation in sample means X around a fixed population mean 27 Environmental variation on the other hand is variation due to extrinsic factors that vary over time in the population mean itself i e the population mean is different each year Putting this information together we conclude that the variation across years in the frequencies of births and deaths both in real populations and our simulated VORTEX populations will have two components the demographic variation resulting from binomial sampling around the mean for each year and additional fluctuations due to environmental variability In actuality catastrophic events to be discussed in more detail later in the User s Manual also contribute to the overall observed variation across many years of data but they are treated separately from s
232. lues Using such functions provides considerable flexibility but you should use them cautiously if you are not yet fully familiar with the VORTEX model A cautionary note about the optional modifier functions and similar criteria on other input screens Don t make the mistake of entering a 0 if you don t want to use that optional function because that will often be interpreted by VORTEX as a function that always turns off the process because the criterion always fails with 0 false If you don t want to use an optional function then just leave the box blank Don t allow dispersal into saturated populations This option will stop individuals from entering a population if it is already at its carrying capacity thereby preventing that immigration from immediately causing the population to exceed K and be truncated If a dispersing individual had been scheduled to be moved into a population that is already at K then the individual will move to a different population instead if there is an unsaturated one available to receive immigrants Use Dispersal to move a fixed number of individuals rather than a percent With this option checked the values in the dispersal matrix specify a fixed N of individuals that will disperse 35 rather than a percent If that many individuals are not available to disperse VORTEX will move all of those that are available Dispersal Rates In the table at the bottom of this page you enter disper
233. lues about which you were most uncertain At least you can do this if you made good notes along the way to document where you had initially to put in a guess 44 Mortality Rates In this next section of input you enter the age sex specific mortalities In the language of matrix life table analysis e g Caughley 1977 Caswell 2001 VORTEX defines mortality as the mortality rate qx or the percentage of animals alive at age x that die before reaching age x 1 Enter mortality rates as a percent between 0 and 100 for each age sex class Once reproductive age is reached the annual probability of mortality remains constant over the life of the individual and is entered only once but see the section on Functions for information on how to relax this assumption File Simulation Help fe Det D ST Text Output Tables and Graphs Project Report elete Reorder Current Default Scenario y Scenario Settings Mortality Rates Section Notes T Species Description Mortality of females as State Variables Population 1 Population 2 Dispersal Mortality from age 0 to 1 50 50 Reproductive System SD in 0 to 1 mortality due to EV 10 10 Reproductive Rates Mortality from age 1 to 2 10 10 SD in 1 to 2 mortality due to EV 3 3 FREE Annual mortality after age 2 10 10 NAAA SD in mortality after age 2 3 3 Initial Population Size a Carrying Capacity
234. ly by VORTEX 9 Sensitivity Testing specifications in a VORTEX 9 vpj file will not be read into VORTEX 10 because the ST module has been completely changed After reading any Vortex9 vpj files into Vortex10 go through all input sections to be certain that values were translated correctly between versions and fix any that were not A caution about directly editing the Project file XML uses the symbols gt and lt in a special way to demarcate data fields Therefore you can t type a function that uses these symbols into the XML file or you will corrupt the file Within XML files the greater than and less than symbols are converted to the codes amp gt and amp lt VORTEX does this conversion automatically when it saves and then reads the xml Project file but you will need to do it if you edit the xml file outside of the VORTEX interface Output files The output data that are displayed in text tables and graphs are all saved in files that are placed in the VOutput subfolder of your project folder Mostly the files are formatted so that they can be imported into Excel and they data will all be in columns with appropriate headers This allows the data to be analyzed easily by statistical or other software outside of VORTEX Navigating around VORTEX VORTEX has four basic levels of navigation At the top of the VORTEX window are a few high level menus for File operations running the Simulation and asking for Help The He
235. ly independent Demographic sto chasticity is intrinsic to all populations regardless of the stability of the environment As a binomial sampling proc ess it is highly dependent on the population size Environ mental variation results from variation in habitat quality over time and is unrelated to population density The var iance in demographic rates caused by environmental varia tion would be additive with variation due to demographic stochasticity Goodman 1987 Environmental variation is not usually affected by the local size of the wildlife population except in those cases such as predator prey interactions in which the organisms have large effects on their local environment However the threat to population viability caused by a given level of en vironmental variation would be more severe in smaller populations because smaller populations are closer to ex tinction Moreover the amount of environmental varia tion would be highly dependent on the total area of habitat occupied by a population Many environmental stresses are localized so a population exploiting a large area would benefit from the averaging of any environmental fluctua tions that are not synchronous over the entire range Indi viduals might use spatial variation in environmental condi tions to allow escape from temporal variation in the envi ronment Kindvall 1996 Even if individuals do not move away from areas with temporarily poor conditions tempo rar
236. m it the user specifies in an STsetup window the parameters and their ranges to be explored VORTEX then creates within STbase some new global state variables with labels SV1 SV2 etc for sensitivity variable defined with functions that specify that the values will vary over the range to be tested The user then must edit the STbase scenario to place these SVs into values or functions specifying the parameters to be examined with the ST You can create multiple STs associated with a VORTEX project and each ST can specify any number of parameters that will be varied Multiple parameters would be varied within one ST if the desire is to test each value against the range of values for the other parameters I e main effects and all interactions among the variables can be tested If the desire is to test different uncertain parameters or sets of parameters one at a time while holding all other parameters constant then those separate tests should be placed into separate STs in the VORTEX project ss sens viy Testing sp EE ST analysis MyST1 bal Sampled 5 Latin Hypercube Sampling Factorial Single Factor Template scenario samples T MyST1 Variables to be tested Synonym BaseVal Minimum Maximum Increment Value List a b c GS5 50 70 GS6 40 50 30 40 50 60 70 GS7 10 20 GS8 15 20 Accept ST scenario Delete ST Run ST Run as Pop based Display Graphs Accept and Close Cancel E Cre
237. maximum age and the variable often therefore has little effect on population dynamics Maximum Number of Broods per Year VORTEX allows you to model more than one brood being produced by each female within each year The maximum number that can be produced is asked here so that VORTEX can set up a table on next page of input where you will specify what percent of the adult females produce each possible number of broods Maximum Number of Progeny per Brood Enter the most individuals born to a given female within a brood You can enter the maximum number that has ever been recorded even though such an event may be quite rare on the next input page you can then assign a low probability of occurrence to this maximum value Note that you can combine all the broods produced by a female within each year into just one brood in which case you would give a maximum number of broods as 1 and the maximum brood size as the total number born during the year A reason to not combine broods within a year might be if you want brood size or survival to be a function of which brood 1 2 etc is being considered Such differences among early and late broods would need to be entered on the next input page as functions of BROOD VORTEX needs to know the maximum possible brood size so that it can set up a table on the next input page where you will specify the probability of each possible brood size However you will have the option of entering a me
238. ment carrying capacity in other ways by specifying that some demographic rates e g reproduction or mortality are functions of N but then it is your responsibility to determine what density dependent functions will achieve the K that you want SD in K Due to EV If you think that the habitat carrying capacity varies over time due to environmental variation EV you can enter a standard deviation SD here to account for this variability For example the habitat might support different population sizes in different years due to changing conditions such as rainfall or food resources The standard deviation should be entered as a number of individuals not as a percentage of K for example if K 2000 with a standard deviation of 10 then enter 200 Be careful If you enter a standard deviation for the carrying capacity that is greater than EF K 3 then the value for K could drop to zero during your simulation resulting in an immediate extinction event 52 Trend in K VORTEX allows you to simulate changes in the carrying capacity Such changes may be positive or negative and result from human activities such as resource utilization or corrective management strategies or from intrinsic ecological processes such as forest succession To include a trend in carrying capacity check the box Then specify the time period during which the trend will occur and the annual rate of change in K The trend will begin in year 1 and continue for the s
239. mortality is provided for cases in which you want to tally disperse harvest or otherwise consider newborns before they are subjected to the 1 year mortality Note however that any deaths due to inbreeding depression are imposed at birth regardless of this option During harvest instead of killing individuals that are harvested set their ISx variable to 0 If x is not specified it is assumed to be IS1 This option can be used for example to contracept a specific number of animals each year assuming that you also set the probability of breeding to be a function of IS1 Use an Individual State variable to specify the order in which individuals are chosen for pairing This option works similarly to the Mean Kinship option in Genetics but it allows the user to create an Svar that determines the priority for breeding For example pairs can be made first for older animals or more dominant ones or the ones with the lowest inbreeding This option would normally be used with the Breed to K option in Genetic Management as otherwise all females would be available to breed albeit in the specified order The priority for pairing will be from the lowest value of the specified Svar first to the highest last If a negative is placed before the ISvar code in the box then the breeding priority will be dynamic meaning that the Svar will be updated with its Transition function after each pairing is made In this way the breeding p
240. n alternating years the long term growth rate will be lt 1 0 The same thing happens with survival rates alternating between 80 and 90 survival is not as good as a constant survival of 85 because survival compounds in a multiplicative way rather than in an additive way The population ecology textbooks usually don t tell the students that the standard life table methods are systematically biased toward over estimating population growth This oversight occurs because the methodologies came from human demography in which the population sizes are so large that there is almost no fluctuation in rates over time so the bias is tiny in human population projections Second lambda projects the population growth if the population starts at a stable age distribution If instead the population currently has an age distribution that will result in a temporary baby bust a lack of prime breeding age animals then the population can decline for a number of years until that age distribution settles down to the expected long term average Third calculations of deterministic lambda ignore a number of density dependent processes that can depress growth at small population sizes These include inbreeding effects and also things as simple as random fluctuations in sex ratio sometimes making it hard for all the females to obtain mates 75 Output Summary The third section of Text Output lists the basic status of each population at each year of the
241. n catastrophes and inbreeding effects is minimal Life table analyses implicitly assume that age specific birth and death rates are constant through time they yield over estimates of long term population growth if there is any variation in demographic rates The deterministic population growth rate r is calculated by solving the Euler equation Sleme j i in which and m are the age specific mortality and fecundity rates respectively for age class x to x 1 and the summation is over all age classes Lambda is related to r by A The stable age distribution or the proportion of the population at each age class cx is given by ES The determination of a stable age distribution for males in a given population becomes a bit more complicated if the mortality schedules are different for the two sexes In this case r is calculated based on female life history tables since females usually control population growth but the s used in the age distribution equation are those for males Moreover the exact form of the equation is dependent on when the age classes were censused In the above equation co is the proportion of the population aged 0 plus a small increment just after the breeding season but before mortality is imposed In order to build the initial population VORTEX omits age class 0 because the simulations begin just before the breeding season and re scales the age distribution in order to sum to 1 0 The life table ca
242. n it might be more efficient much faster with no detectable change in results to run the scenario as a population based simulation Note that inbreeding calculations are fast and do not require much memory if inbreeding depression is modeled as due 100 to recessive lethal alleles and if no function uses inbreeding I or kinship KIN as a variable Extinction Definition VORTEX gives you two methods to define extinction of your population For most sexually reproducing species ultimate biological extinction is assured whenever the population has declined to the point that it no longer has individuals of both sexes In the first and most common choice extinction is simply defined as the absence of at least one sex You also have the option to assess the probability of a population dropping below a user defined threshold size termed quasi extinction The use of quasi extinction risk offers a useful alternative to the standard extinction risk If you chose to have the simulation tally quasi extinctions you need to specify the threshold critical size below which a population is considered extinct The simulation will however continue to run as the population may grow again to a size above this threshold Such recovery from quasi extinction would be tallied as a recolonization event Note that however you define extinction for the purpose of tallying extinctions in the Tables amp Graphs section see below you will be able t
243. n Size page select Stable Age Distribution enter a total N to generate that distribution Then change the selection to be the Proportional Age Distribution This distribution is then locked in for the scenario even as you enter the functions that you need for various demographic rates Another option is to enter your functions for rates on various input pages Then go to the State Variables input page and enter Default values for the parameters in your functions so that the default values will represent the mean or otherwise appropriate values for the deterministic calculations that will be used to obtain the Stable Age Distribution An advantage of this method is that then the Deterministic results displayed by Vortex will be meaningful 51 Carrying Capacity a Vortex 10 BigCat v10 CM j v1 le Soy File Simulation Help B eh amp Det D st Project Settings Simulation Input Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current Baseline X Baseline PBM AbundantPrey LowEV 2Pops 3Pops 10Pops MyST1 Scenario Settings Carrying Capacity Section Notes Species Description State Variables Poet Dispersal Carrying Capacity K 100 Reproductive System SD in K due to EV 0 Reproductive Rates Mortality Rates EV in K can be a tricky concept because K is usually defined as the population size that can be Catastrophes sustained in the habitat over the long te
244. n a function A number of new built in variables and functions are available for use See the list below for the set of variables operators and functions now available 107 Specification of Demographic Rates as Functions Dependencies of demographic rates on population and individual parameters are entered into VORTEX by specifying the functional relationships There are two ways that you can enter a function rather than a constant for an input variable you can type the function directly into the input box for specifying the rate or you can open a Function Editor to help you develop the function to describe the relationship If you type a function directly into an input box you must precede the function with an sign to distinguish the specification of a rate as a function rather than as a constant When you finish editing a function in the Function Editor the Function Editor can insert the function back into the active input box when you accept the function It is usually easier and safer to build a function first within the Function Editor and then send it over to the input page Parentheses brackets and braces may be used interchangeably to indicate the order of operations The case of function names and variables is ignored All letters that are entered in a function within the Function Editor are converted to upper case by VORTEX The separator used between variables in a binary operator must be a semi colon
245. n parallel with one or more other models that might describe the dynamics of parts of an overall system The program METAMODEL MANAGER can manage the flow of data and the sequence of simulation steps among multiple simulation models including VORTEX See Lacy et al 2014 for a presentation of the concept of meta models and the METAMODEL MANAGER software For example several instances of VORTEX can run simultaneously each modeling a different species that influence each other s dynamics as in predator prey systems or competition An epidemiological modeling program OUTBREAK can model the dynamics of an infectious disease in the population VORTEX and OUTBREAK can be run at the same time on the same simulated population with VORTEX simulating demographic and genetic changes and constantly informing OUTBREAK of the current census of the population while OUTBREAK models the changes of disease state susceptible latent infected infectious recovered and constantly informs VORTEX which individuals are in each state The disease states can then be used to modify reproduction survival dispersal or other demographic rates for individuals in the meta model METAMODEL MANAGER and OUTBREAK are available on the VORTEX website http www vortex10 org 33 Dispersal This section of input is accessible only if you specified in the Scenario Settings that your Scenario is to have more than one population If you are modeling a metapopulation you n
246. n status and identifiable threats to persistence into analytical or simulation models of the extinction process 4 assessment of the probability of survival over specified periods of time given the assumptions and limitations of the data and model used 5 sensitivity testing of estimates of extinction probability across the range of plausible values of uncertain parameters 6 specification of conservation goals for the population 7 identification of options for management 8 projection of the probability of population survival under alternative scenarios for future conservation action 9 implementation of optimal actions for assuring accomplishment of conservation goals 10 continued monitoring of the population 11 reassessment of assumptions data models and options and 12 adjustment of conservation strategies to respond to the best information available at all times There are many uncertain aspects of population dynamics especially of endangered taxa including few data on species biology and habitats uncertain political and social climate for implementing conservation actions and the unpredictability inherent in small populations due to the many stochastic forces that drive population dynamics The rapid development of PVA as a research and management tool and the concurrent but not always parallel expansion of the scope of what conservation threats options and actions are considered in PHVA workshops has led to confusion D
247. nce it is strongly encouraged that after you have your function entered in the demographic rate you then test that function to be sure that it represents the relationship that you wanted If your cursor is currently on the table hitting crtl F or the function icon fx will open the Function Editor with the density dependent function for the population of the table column on which the cursor is located Depending on the shape of the density dependence curve you have specified and the mortality rates you will enter later your population may never be able to reach the carrying capacity K also to EF be specified later The combination of density dependence in both reproduction and survival will determine over what range of sizes the population is expected to experience average net growth and over what range it would be expected to decline due to deaths outnumbering births 40 Reproductive Rates This section of input asks for parameter values that specify reproductive rates Note that you decide when in the development of the next generation the birth is defined to occur For mammals you would probably use parturition as the point at which offspring are tallied For oviparous species however you can start to tally offspring at egg laying or at hatching or at fledging or at any other developmental stage that makes sense to you and for which you can specify the demographic rate parameters For amphibians you may choose to start each a
248. ned as In RO r When VORTEX does the deterministic calculations it averages the impact of any catastrophes on fecundity and survival so that the demographic rates are reduced to the means across all catastrophe and non catastrophe years It also adjusts for unequal sex ratio and calculates a separate T for females and males under the assumption that fecundity is driven by females and that the population s total fecundity is then evenly allocated to the adult males In these calculations it does not consider the effects of inbreeding density dependence and stochastic fluctuations due to EV all of which cause the demographic calculations to vary in unpredictable ways 19 Scenario Settings Scenario Name The Scenario Name can be almost any label that you want However like the Project Name it will be used in the filenames for output files so do not use any characters such as or that might be invalid within a filename Z Vortex 10 New Project CAVort File Simulation Help B amp Det ST Project Settings ext Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current Default Scenario y Default Scenario Scenario Settings Perens Species Description ee Scenario name Default Scenario Dispersal Reproductive System Number of iterations 100 Reproductive Rates Number of years timesteps 100 Mortality Rates Duration o
249. ned by the nature and extent of the genetic load identified in the input process and the intensity of inbreeding the population undergoes Note that a Special Option allows the genetic statistics above to be calculated across all runs extant and extinct Following these yearly reports the output file presents a series of final summary information that includes The final probability of population extinction and the converse the probability of population persistence If at least 50 of the iterations went extinct the median time to extinction Of those iterations that suffer extinctions the mean time to first population extinction with SE and SD across iterations The mean times to re colonization and re extinction of those simulations that went extinct The mean final population size with SE and SD across iterations for all populations including those that went extinct e g had a final size of 0 The mean final population size for those iterations that do not become extinct with SE and SD across iterations The final age sex composition of the extant populations 76 e The mean population growth rate r with SE and SD across iterations When harvesting or supplementation are included in your model VORTEX will report the mean population growth rate for years without harvest or supplementation for years with harvest or supplementation and averaged across all years VORTEX reports the growth rate as the exponential grow
250. nerability to extinction any and all population processes that impact population dynamics can be important Much analysis of conservation issues is conducted by largely intuitive assessments by biologists with experience with the system Assessments by experts can be quite valuable and are often contrasted with models used to evaluate population vulnerability to extinction Such a contrast is not valid however as any synthesis of facts and understanding of processes constitutes a model even if it is a mental model within the mind of the expert and perhaps only vaguely specified to others or even to the expert himself or herself A number of properties of the problem of assessing vulnerability of a population to extinction make it difficult to rely on mental or intuitive models Numerous processes impact population dynamics and many of the factors interact in complex ways For example increased fragmentation of habitat can make 1t more difficult to locate mates can lead to greater mortality as individuals disperse greater distances across unsuitable habitat and can lead to increased inbreeding which in turn can further reduce ability to attract mates and to survive In addition many of the processes impacting population dynamics are intrinsically probabilistic with a random component Sex determination disease predation mate acquisition indeed almost all events in the life of an individual are stochastic events occurring with certain
251. nged up to 5 of their residents each year Rates of genetic decay slowed as dispersal rates were increased but the individual based stochastic model consistently showed that population subdivision caused faster genetic decay from the metapopulation a result not predicted from many analytical genetic models Characteristics of highly vulnerable species Summarizing this discussion of the threats to viability of small populations we can identify some of the characteris tics of populations that lead to the most complicated population dynamics as populations become small and which therefore might require the most detailed and indi vidual based PVA models Especially vulnerable species would include those with non breeding helpers such as striped back wrens and naked mole rats species with co operative foraging such as many parrots and social carni vores and species with group defense behaviors such as musk ox and many primates Species with precise mecha nisms for mate choice such as many bird species could have demographic and genetic problems when that choice becomes limited Monogamous species will have depressed reproduction when there is demographic stochasticity in the sex ratio Species with low fecundity are particularly vulnerable to inbreeding depression Mills and Smouse 1994 be cause they can withstand less depression of survival before population growth rates become negative and because they will recover more slo
252. ngle Factor a If Sampled is chosen then for each scenario created in the series for the ST a value is randomly chosen for each of the tested parameters from across the range specified With a large number of samples the parameter space can be thoroughly explored and statistical analysis such as a multiple regression can be used to test for impacts of each parameter and all combinations b Latin Hypercube Sampling LHS is a method of sampling that more evenly covers the parameter space and thus is more efficient than random sampling The number of samples S to be obtained from the n dimensional space for n parameters and the range for each parameter are specified The algorithm then divides each parameter range evenly to obtain 1ts S values Sampling then proceeds by the random selection of a value from for each parameter with this sampling repeated S times under the constraint that each of the S values of each parameter is chosen once An advantage of LHS is that the n dimensional space can be represented well with a manageable number of samples and the number of samples required to explore the uncertainty in each parameter does not increase with the number of parameters c With the Factorial option every combination of parameter values is tested and thus the range of values for each parameter must be a discrete set not a continuous distribution This option provides the greatest statistical power for testing the effects of each p
253. nimal s life in the VORTEX model at metamorphosis Whenever you define an individual s life to begin you must make sure that the first year mortality rates you specify in the next input section are appropriate for the choice you made about when to start recording offspring For example if you tally offspring starting at hatching then the clutch sizes you specify on this page will be in terms of the number of hatches and your first year mortality will be from hatching through the subsequent 12 months If you choose to start offspring at fledging then the clutch size will be specified in terms of the number of fledglings and survival will be from fledging onwards Vortex 10 New Project C VortexlOProjecta New Project New Projectami os File Simulation Help o amp Det ST Project Settings Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current Default Scenario z Default Scenario Scenario Settings Reproductive Rates Section Notes Species Description State Variables Dispersal Population 1 Population 2 aroda ties Sectors adult females breeding 50 50 SD in breeding due to EV 10 10 Mortality Rates Catastrophes Distribution of broods per year enter as percents Mate Monopolization Population 1 Population 2 Initial Population Size 0 Broods 0 0 Carrying Capacity 1 Broods 100 100 Harvest Supplementation Genetics Specify the distribution o
254. nnual fluctuations due to EV SD equal to 10 Populations 3 and greater will experience independent annual fluctuations while populations 1 and 2 will fluctuate synchronously The use of year Y in the seed for the random number causes a new random number to be used each year The use of R iteration or run in the seed causes the sequence of seed values to be different in each simulation The inclusion of P gt 2 100 SRAND P within the seed causes a different sequence of random 120 numbers to be chosen for each population after the first two have been evaluated The seeds must include Y R 100 to ensure that every year iteration is independent If you use Y R as the seed then year 3 of iteration 1 will have the same value as year 2 of iteration 2 etc In the simpler example of EV in K given above no seed was needed or specified so an independent random number will be selected each iteration each year and each population These examples show how elaborate and non intuitive the functions can become when you want to create even moderately complex models of population dynamics Using Functions to Examine Genetic Evolution The parameters available for use in functions defining demographic rates include an individual s paternally inherited allele V and the maternally inherited allele Z of the normally non selected locus which is monitored for tracking genetic diversity The symbols for these variables V and Z have no intuitive m
255. now when any quantitative definition is given at all File Simulation Help i oF amp det p st Project Settings Simulation Input Tables and Graphs Project Report Plot Table Teminal 9 Interval For which year do you want the graph displayed 0 Use Ofor final year Scenarios to include Ines El J opulations to be included Bigger Pop1 D lt O 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 N Sendto Report Save As Print _ Update Plot 89 Custom Plots Selecting Custom plots lets you pick any of a number of output variables to be plotted against year Variables available for plotting are e P survive The proportion of iterations in which the population is not extinct e P extinction The probability that the population becomes extinct PE that year e Detr The deterministic growth rate calculated from mean birth and death rates e Stoch r The mean population growth rate experienced in the simulations averaged across all years in which the population was extant Note that with the default sequence of events in a year stochastic r will be calculated before carrying capacity truncation e N all The mean population size across all populations extant
256. nsity inbreeding might impact fecundity adult survival or might affect the two sexes differently dispersal might be age and sex dependent fecundity mortality or the effects of catastrophes might be age dependent environmental variation might occur with a periodicity that is longer than a year or catastrophes might have multi year effects YYY Vv V V WV Note that VORTEX includes within the input the option to model reproduction as a density dependent function and an option to model carrying capacity as having a linear change over a specified number of years Easy access to these two particular functions are provided because they are needed more frequently than are detailed functional dependencies of most other rates Even for these two rates however you can specify these functions to have almost any shape if you use the function editor to specify the rates For most users and for most purposes there will be no need to model demographic rates as functions it is usually fully adequate to specify fixed demographic rates rather than functions Specification of rates as functions can be difficult the appropriate form of the function is rarely known the function parameters are usually very difficult to estimate and it is not trivial to enter a function correctly If alternative functions need to be examined in sensitivity testing the number of combinations of input parameters to be explored can quickly become overwhelming Consequently
257. nt Plan for the Tree Kangaroos of Papua New Guinea and Population and Habitat Viability Assessment for Matschie s Tree Kangaroo Final Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Bormann F H and S R Kellert 1991 Ecology Economics and Ethics The Broken Circle New Haven Yale University Press Boyce M S 1992 Population viability analysis Annual Review of Ecology and Systematics 23 48 1 506 Brussard P 1985 Minimum viable populations how many are too few Restoration and Management Notes 3 21 25 Burgman M S Ferson and H R Ak akaya 1993 Risk Assessment in Conservation Biology New York Chapman and Hall Caswell H 2001 Matrix Population Models 2 ed Sunderland MA Sinauer Caughley G 1977 Analysis of Vertebrate Populations London John Wiley and Sons 154 Charlesworth D and B Charlesworth 1987 Inbreeding depression and its evolutionary consequences Annual Reviews of Ecology and Systematics 18 237 268 Clark T W 1989 Conservation Biology of the Black Footed Ferret Philadelphia Wildlife Preservation Trust International Clark T W 1993 Creating and using knowledge for species and ecosystem conservation Science organizations and policy Perspectives in Biology and Medicine 36 497 525 Clark T W R M Warneke and G G George 1990 Management and conservation of small populations Pages 1 18 in Clark T W and J H Seebeck eds Management and Conserv
258. o K For example you could remove only juveniles or only inbred individuals If this criterion evaluates to 1 or more for an individual then the individual is in the pool that is subject to removal If it evaluates to a number less than 1 then that is the probability that the individual will be available for removal This option is not available in population based models Prioritize K truncation based on ISvar Another option allows you to use an Individual State variable to specify the order in which individuals are removed when K is exceeded This option requires the user to create an Svar that determines which individuals will be removed first For example K truncation can be applied first to the oldest individuals or those with the highest inbreeding or those with the highest Mean Kinship The order of removing individuals will be from the lowest value of the specified Svar first to the highest When using this option it is important to use a sequence of events for the annual cycle that will ensure that the ISvars are updated when they are used for determining the order of K truncate individuals Usually this means that an ISUpdate event will need to be inserted just before Ktruncation See section on Scenario Settings If a negative is placed before the ISvar code in the box then the order will be dynamic meaning that the ISvar will be updated again with its Transition function after each individual is removed and the list then re s
259. o assess the probability of quasi extinction across the range of final population sizes Number of Populations VORTEX can model a single isolated population or a complex metapopulation composed of any number of populations A metapopulation is a group of populations which because they often occupy fragmented discontinuous habitat exchange individuals with varying frequency Note that because of the added complexities associated with metapopulations these models will often run considerably slower than the corresponding single population models Population labels The names that you give to each population are used only to label output Use any names that you want but as with Project and Scenario names do not use any characters such as or that might be invalid within a filename because the population names will be used within some filenames Note that the order of your Populations can later affect the ease of data entry e g you can EF quickly copy demographic rates from a population to later populations but not to earlier ones or even the functioning of the model e g in the Translocation option the last population will usually be used as a holding location Therefore it is often useful to think a minute about what order you want to have your populations 22 Annual sequence The sequence of events in the annual cycle can be specified to be something other than the default EV setting annual rates Breedin
260. occur because the parameters have never been measured on the population Uncertainty can occur because limited field data have yielded estimates with potentially large sampling error Uncertainty can occur because independent studies have generated discordant estimates Uncertainty can occur because environmental conditions or population status have been changing over time and field surveys were conducted during periods which may not be representative of long term averages Uncertainty can occur because the environment will change in the future so that measurements made in the past may not accurately predict future conditions Sensitivity testing is necessary to determine the extent to which uncertainty in input parameters results in uncertainty regarding the future fate of the population If alternative plausible parameter values result in divergent predictions for the population then it is important to try to resolve the uncertainty with better data Sensitivity of population dynamics to certain parameters also indicates that those parameters describe factors that could be critical determinants of population viability Such factors are therefore good candidates for efficient management actions designed to ensure the persistence of the population The above kinds of uncertainty should be distinguished from several more sources of uncertainty about the future of the population Even if long term average demographic rates are known with precision variati
261. ocumentation of the program flow and algo rithms is provided here so that users of VORTEX can con firm that the model is performing the analyses that are in tended and so that PVA practitioners in general can see an example of the structure of an individual based PVA mod el The VORTEX program is available at http www2 netcom com rlacy vortex html The pseudo code presented below is an English language outline of the program flow and primary algo rithms used by VORTEX which is written in the C pro gramming language This pseudo code omits coding for 1 input routines for reading parameters from files and or keyboard 2 output routines for writing results to files 3 specification of default parameter values 4 checks for ille gal values error handling 5 memory management and initialization of memory 6 details of C coding to achieve algorithms 7 routines for on line help 8 routines for graphical display of functions specifying demographic rates population sizes during simulations simulation re 192 sults 9 routines for evaluating equations that specify de mographic rates e g breeding mortality as functions of population and individual variables e g population size gene diversity year age sex inbreeding see note 3 be low 10 tallies of mean within population statistics and metapopulation summaries 11 algorithms for calculating basic statistics such as means standard deviations stand ard e
262. ode of the software entrusted for the analyses More prac tically confidence is gained in the reliability of generic soft ware tools as more people use the programs and compare the generated results to expectations from statistical theory and to results for simple and well known cases Also users of statistical software are expected to be sufficiently famil iar with the methods of statistical analysis to be able to choose appropriate models to apply to their problem to be able to provide the proper input and to be able to interpret the results Unlike the situation for statistical methods however there are not yet widely accepted and published accounts of standard methods for population viability analysis The methods of population based models e g Starfield and Bleloch 1986 Burgman et al 1993 are extensions of the methods of population ecology and demography e g Pie lou 1977 Caswell 1989 but many details of model con struction require decisions about algorithms and methods that are not fully delineated in general treatments The methods of individual based PVA models have been only cursorily described in the scientific literature Below is an outline of one widely used PVA software package VOR TEX ver 8 20 The basic approach taken in the VORTEX model is described in Lacy 1993 in Lindenmayer et al 2000 and other papers describing applications of VOR TEX and in the software manual Miller and Lacy 1999 Detailed d
263. odels and may not be fully recognized in conservation plans At low population densities the social systems of many species may be disrupted Such Allee effects are one type of density dependence in reproductive success Although the impor tance of understanding and modeling density dependence has been stressed by some authors Mills et al 1996 Brook et al 1997 most of the attention has been given to changes in demographic rates as the population ap proaches carrying capacity Yet it is not when a population is near carrying capacity that we need to be concerned about extinction Allee effects at the low end of density can be incorporated into several of the widely available ge neric PVA models e g RAMAS Space Ak akaya and Ferson 1992 VORTEX Lacy 2000 but this feature seems rarely to be used Individual based models can be tailored to provide detailed representations of specific so cial systems and this approach was used to look at how the interactions of stochastic processes and pack structure im pact viability of wolves Vucetich et al 1997 and wild dogs Vucetich and Creel 1999 Disruptions of the breeding system can occur for rea sons that range from the obvious to the subtle At very low population densities animals may be unlikely to encoun ter any potential mates when they are ready to breed and non selfing plants may not be adequately pollinated Menges 2000 Sumatran rhinoceroses Dicerorhinus su matrensi
264. of the time or 4 12 of the time SQR 1 44 1 2 LN 1 60 0 47 LOG10 1 60 0 20412 EXP 0 47 1 60 1 042 0 2 0 1 0 2 0 3 0 6 0 2 0 3 0 POW 10 0 20412 MAX 3 12 4 21 4 21 MI N 3 12 4 21 3 12 MOD 33 8 33 8 1 MOD 33 5 5 3 5 l 0 0 0 10 0 20412 1 60 Logical Boolean Operators ES Is equal to NOT Not equal to AND amp amp And I Or Greater than Negation Less than Greater than or Less than or equal COMPARE Compare two values IF Conditional evaluation TRUE 1 0 FALSE 0 0 3 2 0 1 3 4 1 3 4 1 3 4 AND 3 4 3 4 OR 3 4 3 gt 4 0 3 lt 4 1 3 gt 3 1 3 lt 3 1 COMPARE A B A B F A gt B 5 10 5 if A gt B or 10 if A lt B 10 gt 5 TRUE ITRUE FALSE FALSE TRUE 1 if A gt B or 1 if A lt B or 0 if 114 Valid Vortex Operators Function Description Example Trigonometric Operators SIN Sine SIN PI 2 1 0 COS Cosine COS PI 2 0 0 TAN Tangent TAN PI 4 1 0 ASIN Arcsine ASIN 1 0 1 5707963 ACOS Arccosine ACOS 0 0 1 5707963 ATAN Arctangent ATAN 1 0 0 7853981 DEGREES Convert Radians to Degrees DEGREES PI 4 45 RADI ANS Convert Degrees to Radians RADI ANS 45 PI 4 0 7854 Random Number RAND Uniform random 0 1 RAND 0 2341 or0 8714 or NRAND Normal random deviate NRAND 0 512 or 0 716 or UNI FORM Uniform random A B UNI FORM 1 5 1 5 or 3 60r
265. of varying detail experi mental data and observations on natural populations For a variety of reasons PVA models for small popula tions may need to be highly specific with respect to how they model breeding systems dispersal behavior and ge netic processes Simple generalizations of population ge netics theory may be misleading because most of that the ory was based on large sample approximations For exam ple generalizations about effects of dispersal among small populations often have assumed that an infinite number of such populations exist Many metapopulation models as sume that the system has reached extinction recoloniza tion equilibrium Variation in demographic rates num bers of individuals and other population statistics rarely follow a normal distribution Effects of threatening proc esses on populations are rarely linear or log linear and threshold effects in which there are sharp discontinuities in effects are possible The effects of multiple threats are often synergistic rather than additive Many of the parameters required to build specific de tailed models of small population dynamics can only be estimated well with long term and extensive data It is clearly difficult to obtain large samples from small popula tions and conservation action may have to precede long term field studies in order to ensure that the populations persist long enough to permit extended study Obtaining a complete enumeration
266. olution 52 900 909 Lacy R C and T W Clark 1990 Population viability assessment of the eastern barred bandicoot in Victoria Pages 131 146 in Clark T W and J H Seebeck eds Management and Conservation of Small Populations Brookfield IL Chicago Zoological Society Lacy R C N R Flesness and U S Seal eds 1989 Puerto Rican Parrot Population Viability Analysis Report to the U S Fish and Wildlife Service Apple Valley MN Captive Breeding Specialist Group SSC TUCN Lacy R C and D B Lindenmayer 1995 A simulation study of the impacts of population sub division on the mountain brushtail possum Trichosurus caninus Ogilby Phalangeridae Marsupialia in south eastern Australia II Loss of genetic variation within and between sub populations Biological Conservation 73 131 142 Lacy R C and P S Miller 2002 Incorporating human populations and activities into population viability analysis Pages 490 510 in S R Beissinger and D R McCullough eds Population Viability Analysis Chicago University of Chicago Press Lacy R C Petric A M and Warneke M 1993 Inbreeding and outbreeding depression in captive populations of wild species Pages 352 374 in Thornhill N W ed The Natural History of Inbreeding and Outbreeding Chicago University of Chicago Press Lande R and G F Barrowclough 1987 Effective population size genetic variation and their use in population management Pages 87 123 in Soul M E
267. om each scenario e g you want the annual census data or summary statistics for each iteration you can check the option to Create all population statistic files Be aware however that depending on which optional output you requested in Special Options checking this box can lead to a very large number of files created in your project VOutput folder Editing ST scenarios After creating and saving and ST you can later return to the STsetup to change some of its settings but only if you had remembered to accept your ST and then save your VORTEX project If you change the ST name your edits will be saved as a new ST and your old one will remain as it was under the old name If you change the Template then the old ST and its STbase scenario 97 will be deleted and replaced by the one that you edit and save If you just change some of the settings for variables to be tested then the existing ST is edited You can remove a variable from an ST by clicking on its row and then hitting the Delete key the Delete key on your keyboard not the Delete ST button on the STsetup window Be aware however that when you delete a row from the table the SV and GS synonyms for any subsequent variables in the table will be changed You can remove an ST including removing its STbase scenario by hitting the Delete ST button Some cautions and hints 1 Be sure to give your ST a new name replacing the New ST label in t
268. on in which individuals breed die and are of each sex Envi Start Read in parameters Set Iteration 1 Create initial individuals No Set year f Determine annual modifiers for EV Determine if catastrophes occur Mortality Harvest of individuals Supplement with new individuals Dispersal among populations ronmental variation in demographic rates is imposed by sampling rates from specified distributions during each simulated year Catastrophes which occur with specified probabilities cause one year reductions in reproduction and survival Genetic effects are modeled as reduced survi vorship of inbred individuals End Calculate and output mean census statistics Yes Iteration gt ni Increment iteration Yes t gt ny Increment year f Annual census of Demographic status Genetic variation Extinction status Remove excess individuals Fig 1 Flow chart of the primary components of the Vortex simulation Each step from Create initial individuals through Annual census is applied to each population in a modeled metapopulation year ny number of years simulated np number of populations ni number of iterations N population size K carrying capacity EV environmental variation ECOLOGICAL BULLETINS 48 2000 193 VORTEX program pseudo code BEGIN PROGRAM VORTEX Initialize random number generator See Note 1 FOR
269. on Help fe Det D ST Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current Default Scenario Default Scenario Section Notes Scenario Settings Reproductive System Species Description State Variables AR 5 Monogamous 0 Polygynous Hermaphroditic Long erm monogamy Long erm polygyny Dispersal Reproductive System Age of first offspring females 2 Maximum age of female reproduction 10 cos a Rates Age of first offspring males 2 Maximum age of male reproduction 10 Mortality Rates Maximum lifespan 10 Catastrophes Mate Monopolization Maximum number of broods per year 1 Initial Population Size Maximum number of progeny perbrood 2 Carrying Capacity Sex ratio at birth in males 50 Harvest Supplementation Genetics Population 1 Population 2 Density dependent reproduction rr E Copy input values from Breeding at low density P 0 50 50 Breeding at carrying capacity PON 25 2 Allee parameter A 1 1 Steepness parameter B 2 to subsequent populations Monogamous Polygamous Hermaphroditic Long term Monogamy or Long term Polygamy VORTEX models breeding systems as monogamous vs polygamous vs hermaphroditic and short term vs long term With monogamous breeding there must be a male for every breeding female males may therefore become a limiting factor restricting breeding
270. on in golden lion tamarins In Young A and Clarke G eds Genetics demography and population viability Cambridge Univ Press in press Ellis S et al 1992 Alala akohekohe and palila population and habitat viability assessment reports IUCN SSC Captive Breeding Specialist Group Apple Valley Minnesota Fahrig L and Merriam G 1985 Habitat patch connectivity and population survival Ecology 66 1762 1768 Fahrig L and Merriam G 1994 Conservation of fragmented populations Conserv Biol 8 50 59 Fisher R A 1958 The genetical theory of natural selection Dover New York Foley P 1994 Predicting extinction times from environmental stochasticity and carrying capacity Conserv Biol 8 124 137 Forman L et al 1986 Genetic variation within and among lion tamarins Am J Phys Anthropol 71 1 11 Frankel O H and Soul M E 1981 Conservation and evolu tion Cambridge Univ Press Frankham R 1995a Conservation genetics Annu Rev Genet 29 305 327 Frankham R 1995b Inbreeding and extinction a threshold ef fect Conserv Biol 9 792 799 Franklin I R 1980 Evolutionary change in small populations In Soul M E and Wilcox B A eds Conservation biol ogy An evolutionary ecological perspective Sinauer pp 135 149 Gilpin M E and Soul M E 1986 Minimum viable popula tions the processes of species extinction In Soul
271. on of a population of 15 20 pairs of the middle spotted woodpecker Dendrocopos medius which had been isolated 30 yr before Pettersson 1985 In Finland Sac cheri et al 1998 found that local populations of the Glanville fritillary butterfly Melitaea cinxia with lower het erozygosity indicative of greater inbreeding had lower egg harching rate larval survival and adult longevity Ap parently as a consequence these populations had much higher probabilities of extinction Following Franklin 1980 and Soul 1980 only pop ulations with effective sizes below ca 50 have been com monly perceived to be at risk of significant inbreeding de pression To have an effective population size of 50 a typi cal natural population of a large mammal might need a total population size of ca 200 It is worth reconsidering the likely cumulative effects of inbreeding on the viability of such a population Inbreeding would accumulate at a rate of 1 per generation After 10 generations the 10 cumulative inbreeding may cause a 5 20 reduction in survival and in fecundity Ralls et al 1988 Lacy et al 1996 Lynch and Walsh 1998 The consequent reduction in population growth would be sufficient to cause low fe cundity species to decline Yet many wildlife managers with responsibility for populations of approximately this size assume that they can ignore effects of inbreeding and most PVA models for populations of such size omit the impacts
272. on over time caused by fluctuating environmental conditions will cause uncertainty in the fate of the population at any given time in the future Such environmental variation should be incorporated into the model used to assess population dynamics and will generate a range of possible outcomes perhaps represented as a mean and standard deviation from the model In addition most biological processes are inherently stochastic having a random component The stochastic or probabilistic nature of survival sex determination transmission of genes acquisition of mates reproduction and other processes preclude exact determination of the future state of a population Such demographic stochasticity should also be incorporated into a population model because such variability both increases our uncertainty about the future and can also change the expected or mean outcome relative to that which would result if there were no such variation Finally there is uncertainty which represents the alternative actions or interventions that might be pursued as a management strategy The likely effectiveness of such management options 142 can be explored by testing alternative scenarios in the model of population dynamics in much the same way that sensitivity testing is used to explore the effects of uncertain biological parameters Often the uncertainty regarding a number of aspects of the population biology current status and threats to persistence is too l
273. ons and recolonizations through the simulation Output VORTEX outputs 1 probability of extinction at specified intervals e g every 10 years during a 100 year simulation 2 median time to extinction if the population went extinct in at least 50 of the simulations 3 mean time to extinction of those simulated populations that became extinct and 4 mean size of and genetic variation within extant populations Standard deviations across simulations and standard errors of the mean are reported for population size and the measures of genetic variation Under the assumption that extinction of independently replicated populations is a binomial process the standard error of the probability of extinction is reported by VORTEX as SE p p in which the frequency of extinction was p over n simulated populations Demographic and genetic statistics are calculated and reported for each subpopulation and for the metapopulation 147 Appendix 2 Primary changes from Vortex 9 to Vortex 10 Input files The VORTEX 10 project files will be saved in xml format The change to xml files was made because they can be more forgiving of possible errors in the data file format and in the future this will make it easier to open old projects in upgraded versions of VORTEX Be careful however that after you save a project in the xml format you will later want to open that xml file and not some prior vpj file from VORTEX 9 VORTEX 10 can
274. ons for Conservation Cambridge Cambridge University Press Soul M M Gilpin W Conway and T Foose 1986 The millenium ark How long a voyage how many staterooms how many passengers Zoo Biology 5 101 113 Starfield A M and A L Bleloch 1986 Building Models for Conservation and Wildlife Management New York Macmillan Thomas C D 1990 What do real population dynamics tell us about minimum population sizes Conservation Biology 4 324 327 Walker S and S Molur eds 1994 Population and Habitat Viability Analysis PHVA Workshop for Indian Nepali Rhinoceros Zoo Outreach Organisation CBSG India Coimbatore 159 Werikhe S L Macfie N Rosen and P S Miller eds 1998 Can the Mountain Gorilla Survive Population and Habitat Viability Assessment Workshop for Gorilla gorilla beringei Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Wright S 1977 Evolution and the Genetics of Populations Vol 3 Experimental Results and Evolutionary Deductions Chicago University of Chicago Press Zar J H 1996 Biostatistical Analysis 3 ed Englewood Cliffs Prentice Hall 160 Reprints Lacy R C 2000 Structure of the VORTEX simulation model for population viability analysis Ecological Bulletins 48 191 203 Reprinted with permission of the publisher Note This paper describes the structure of VORTEX version 9 It is still largely appropriate for version 10 but you should be aware that
275. opolization input page directly prompts for the one measure of the degree of polygyny that is used directly by Vortex Buttons provide access to simple pop up utilities to calculate the of males in the breeding pool from either the siring offspring or the mates breeding male as in the images below These calculations will assume that the distribution of mates per male in the breeding pool is Poisson Functions cannot be entered for these rates because the Males in the breeding pool is calculated from these values at the time of input data entry so that parameters entered into a function would not yet be available for the calculation Mate Monopolization 0 E Mean mates successful sire owes Lox If you earlier specified that the species has a monogamous breeding system you are asked specify only the percentage of the total adult male population that makes up the pool of available breeders and each male can breed with only one female each year and these alternative ways to specify mate monopolization are not available nor would they be meaningful Remember that not all males within this pool may breed in a given year depending on the number of adult females that are successful breeders 49 Initial Population Size In this section of input you specify the number of individuals at the start of your simulation and the age initial structure There are three options for how to enter the data Vor
276. or extinct e N extant The mean population size only for those remaining extant e GeneDiv The mean expected heterozygosity or gene diversity remaining in the extant populations e Inbreeding 1 mean observed heterozygosity remaining in the extant populations e Alleles The mean number of alleles remaining within extant populations from an original number equal to twice the number of founder individuals e Lethals The mean number of lethal alleles remaining within extant populations e TE Of iterations that suffer extinctions the mean time to first population extinction e Median TE If at least 50 of the iterations went extinct the median time to extinction Along standard output variables you have the option of selecting any of the GSvars or PSvars that were in your scenario Z Vortex 10 BigCat vi0 CAVortex1 OProjects Samples Bigcat v cd 1 File Simulation Help 0 eh amp det st Project Settings Simulation Input Text Output Tables and Graphs Project Report Custom Plot y Plot Table Errorbars None SE SD l Custom Plot Data Specification Baseline Plot x axis up through year 0 for data maximum Plot y axis 0 2 want the of variable Plsurvive Somutes to inclale Plnancion EXC ra A AbundantPrey Niextant LowEV Nfall Mean Stoch r 2Pops GeneDiv 1 3Pops ariel E 10P les hao
277. or reproduction or survival in one population will lead to similarly good years in all other populations If this degree of correlation is set to an intermediate value then EV will be partly correlated among populations Environmental variation in the metapopulation context can be considered to exist at two levels local population specific and global acting across all populations The total EV when expressed as a variance rather than a standard deviation as entered by the user is simply the sum of the EV existing at these two levels The correlation of EV among populations that you enter then is simply the proportion of the total EV when expressed as a variance that is global in scope i e common to all populations The Statistics of Demographic Stochasticity and Environmental Variability Demographic stochasticity is the random fluctuation in observed birth rate death rate and sex ratio of a population resulting from stochastic sampling processes even if the probabilities of birth and death remain constant over time This annual variation in numbers of individuals that are born that die and that are of a given sex can be specified from statistical theory and would be expected to follow binomial distributions Environmental variability is the annual fluctuation in probabilities of birth and death arising from random fluctuations in the environment e g weather abundance of prey or predators prevalence of nest sites etc Annual f
278. orted In this way the order of removals can be set for example to be determined by a Mean Kinship that is updated after each individual is removed from the population Note that to achieve removals of the individuals with highest MK the ISvar would need to be set to MK because removals are from the lowest to highest 53 What Exactly s Carrying Capacity Anyway Carrying capacity rarely in the field of resource management has a term been so frequently used to the confusion of so many MacNab 1985 The definition and use of the concept of carrying capacity is one of the more tricky issues in population viability analysis and for that matter in much of population ecology Pick up any number of textbooks on ecology or wildlife management and you are likely to find that each one presents a slightly different formal definition of carrying capacity In fact some authors e g Caughley 1977 choose not to use the term altogether in their presentation of the mathematics of population growth In the context of wildlife management the habitat carrying capacity for a particular population can be defined as the maximum number of individuals that environment can sustain over time in the absence of unnatural disturbances and without inducing harmful trends in the abundance of the resources required by that population We can gain more insight into this concept by considering the familiar and admittedly simplistic logistic equat
279. ost demographic rates as functions of time density and other parameters Demographic stochasticity VORTEX models demographic stochasticity by determining the occurrence of probabilistic events such as reproduction litter size sex determination and death with a pseudo random number generator For each life event if the random value sampled from a specified distribution falls above the user specified probability the event is deemed to have occurred thereby simulating a binomial process Demographic stochasticity is therefore a consequence of the uncertainty regarding whether each demographic event occurs for any given animal Random deviates from binomial distributions with mean p and standard deviation s are obtained by first determining the integral number of binomial trials N that would produce the value of s closest to the specified value according to N p 1 p s2 N binomial trials are then simulated by sampling from the uniform 0 1 distribution to obtain the desired result the frequency or proportion of successes If the value of N determined for a desired binomial 144 distribution is larger than 25 a normal approximation is used in place of the binomial distribution This normal approximation must be truncated at 0 and at 1 to allow use in defining probabilities although with such large values of N s is small relative to p and the truncation would be invoked only rarely To avoid introducing bias with this truncation
280. ow need to specify a few parameters that help to define the system of dispersal of individuals among populations and the rates of dispersal of individuals between populations File Simulation Help B amp Det sT Project Settings Simulation Input Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current Default Scenario Default Scenario Scenario Settings Dispersal Among Populations a AER Section Notes Species Description State Variables Di ing dl Age range Youngest 1 Oldest 5 Reproductive System i E Y Y PE Dispersing sex es Males Y Females Mortality Rates Survival of dispersers 50 Catastrophes Mate Monopolization Dispersal modifier function optional Initial Population Size E Dont allow dispersal into saturated populations Carrying Capacity E Use Dispersal to move a fixed number of individuals rather than a percent Harvest capita Import Rate Matrix Apply muttiplier of 2 0 Genetics Esport Rate Matrix Fillmatrix with 1 0 Copy input values from Enter percents of individuals in each age sex class that disperse between each pair of populations each year Population 1 X Population Population2 hesen y as r la 2 5 95 to subsequent populations Dispersing classes Age Range Youngest and Oldest In these boxes enter the youngest and oldest ages of those individuals that move between pop
281. pecified duration The program will model a liner trend over this time period More complex patterns of K can be specified by entering a function for Carrying Capacity Implement K based on a limit on some population variable other than N As anew option in VORTEX 10 K can be specified to be a criterion other than a limiting N E g K can be a limiting number of females or of adults or of individuals with IS1 1 or of some function of variables The proportion by which K exceeds the limiting value will determine the proportion of individuals across all age and sex classes that will be removed For example if breeding sites are limiting with a maximum of 50 you could enter K 50 and then specify to Implement K as a limit with the Population variable to be tested being F the number of adult females However in such a case it might be better to more explicitly build the limitation of nest sites into a density dependence function for breeding on the Reproductive Rates page Caution If you specify that K is a limitation on some population tally other than total N then be aware that if you use K as a variable in any function e g some density dependent function then the K used in your other functions will be the one entered on this screen During K truncation remove only individuals meeting criteria Another option allows you to specify that only certain classes of individuals will be removed to bring the population back down t
282. portant to consider in a PVA will depend on the species biology the present population size and distribution and the threats it faces For example orang utans may be threatened by forest destruction and other largely deterministic processes but inbreeding and randomly skewed sex ratios resulting from highly stochastic processes are unlikely to be problems at least not on a species wide basis On the other hand even if the remnant Atlantic coastal rainforest of Brazil is secured for the future the populations of golden lion tamarins Leontopithecus rosalia which can persist in that remnant forest are not sufficiently large to be stable in the face of stochastic threats Seal et al 1990 Rylands 1993 4 Ballou et al 1997 The identification of the primary threats facing a taxon via a comprehensive PVA is important for conservation planning For example tamarin populations might be stabilized by the translocations and reintroductions that are underway and planned but an orang utan PHVA recognized that releases of confiscated pet orang utans are unlikely to have a conservation benefit for those populations which are facing habitat destruction not stochastic fluctuations and inbreeding For many species such as the whooping crane Grus americana the temporarily extinct in the wild black footed ferret Mustela nigripes and the Puerto Rican parrot Amazona vitatta only a single population persisted in the wild Although those populations may
283. pulation by natural selection when inbreeding occurs As a result many individuals may die in the early generations of inbreeding but when they die they take their lethal alleles with them to the grave and subsequent generations of individuals have fewer lethal alleles to cause inbreeding depression This process is often referred to as purging the genetic load of lethal alleles On the other hand selection is ineffective at purging inbreeding depression when the inbreeding depression results from a general advantage of heterozygotes over all homozygotes or to a lesser extent when it is caused by recessive sub lethal alleles To model the effects of lethal alleles which can be removed by selection during generations of inbreeding VORTEX assigns to each individual at the start of a simulation some unique lethal alleles If inbred descendants happen to receive two copies of the same lethal allele they are killed To model the component of inbreeding depression that is not effectively reduced by selection VORTEX calculates the inbreeding coefficient of each individual and then applies an exponential equation like the one above but using just a part of the total lethal equivalents to determine how much that individual s survival is reduced To incorporate these two mechanisms of inbreeding depression VORTEX needs to know i e you need to tell it how much of the overall inbreeding depression lethal equivalents to assign to lethal allel
284. put means SDs and SEs across iterations for Probability of extinction PE p I SE SQRT PE 1 PE Numberlterations PopulationSize p GeneDiversity p 1 Gene Diversity Heterozygosity expected under Hardy Weinberg equilibrium ObservedHeterozygosity p 1 mean inbreeding coefficient NumberAlleles p LethalFrequency p END year LOOP END population LOOP Calculate and report within population means of above summary statistics Call program for displaying graphical displays of trends in PopulationSize GeneDiversity Mean inbreeding coefficient 1 ObservedHeterozygosity Probability of population persistence to year Probability of extinction in that time interval Read in DoAnotherScenario IF DoAnotherScenario is FALSE BREAK from scenario LOOP 195 END IF END scenario LOOP END PROGRAM VORTEX BEGIN FUNCTION READ_SPECIES_PARAMETERSO O Get input parameters from keyboard or input file de scribing simulation parameters inbreeding effects and ba sic species life history Read in Input Output file names Read in NumberOflterations Read in NumberOfYears Read in ExtinctionDefinition Extinction can be defined as no animals of one sex or as the population size falling below a specified minimum Read in NumberOfPopulations Read in InbreedingGeneticLoad Read in ProportionLoadDueToLethals Read in EVCorrelationBetweenReproductionAndSurvival IF NumberOfPopulations gt 1 Read in E
285. r 20 If you wish to obtain a relatively crude picture or your results use 100 iterations Once you are comfortable with the model and wish to obtain a more rigorous description of the simulated population s behavior it is not excessive to enter 500 or even 1000 iterations Note that commas are not used when specifying larger numbers during the input process even if your computer is set to use American data formats 20 Number of years How far into the future do you wish to project your population The usual answer to this question is 100 to 200 years although a shorter duration can be entered so that you can assess the validity of your input parameters or to examine the short term viability of a population If you simulate your population for just a few decades however you should be aware that processes controlling population dynamics might be leading the population toward extinction but especially for long lived species the final extinction may not occur until a later time By the time that the factors influencing extinction are apparent the process may be so far along as to be almost irreversible One of the major advantages of PVA modeling is that it can reveal the instability of a population long before it would be apparent through field observations Duration of each year in days VORTEX does not necessarily require years to be defined as calendar years Rather the program operates more broadly in terms of time cycles If t
286. r creating STs you will want to exit the ST module to edit the input values see below before returning to the STsetup window to run the STs 8 After Accepting an ST you can go back to the top dropdown list and select New ST to create another ST that defines a set of parameters to be varied repeating steps 6 and 7 above Again be sure to give it a new name not New ST and be sure to save it by accepting after it has been created 9 Close the STsetup window and go into project Input to edit the STbase scenario that has been created a Go to each parameter that you wish to vary in the ST and insert the desired SV into a function for that parameter E g FemalesBreeding might be set to SV1 b Save your VORTEX project c Return to the STsetup to now run your sensitivity tests 96 Running ST scenarios l To run the set of scenarios within an ST first select the saved ST from the top drop down list and then re confirm that all of its settings to be certain that it is the ST you want If you need to change anything in the ST remember to Accept those changes before running the tests Also after you leave the STsetup remember to save the overall project again It can also be useful to run the ST scenarios as population based models Run as Pop based button Population based models exclude some sources of stochasticity but they run much more quickly Thus they are useful for providing an initia
287. r large and complex programs is formidable One possible remedy to the problem of PVA users needing to understand the models being used is for practi tioners to develop their own computer programs This would result in the user having a full understanding of a model that would be specifically designed for the analysis Development of user specific and case specific models is usually not practical however as many population biolo gists are not skilled computer programmers and the time required to develop a complex model is often prohibitive Moreover a complex computer program developed by and used by one person will sometimes contain serious pro gramming errors The testing of programs that are widely used may be a necessary prerequisite for reliable popula tion viability analyses to be employed effectively in biodi 191 versity conservation Finally the flexibility and expansive capabilities of generic PVA software to model a large diver sity of population processes will often lead PVA practition ers to consider threats to population viability that would otherwise have been neglected Widely available PVA software can serve the same role as do statistical analysis packages The ease of use flexible application to diverse needs and extensive prior testing fa cilitate many applications that would not otherwise be at tempted Ideally perhaps all users of statistical methods would write their own programs or otherwise study the c
288. re deleterious when homozygous and beneficial when present in heterozygous combination with other alleles Thus under heterozygote advantage the impact of inbreeding on survival does not diminish during repeated generations of inbreeding Unfortunately for relatively few species are data available to allow estimation of the effects of inbreeding and the magnitude of these effects apparently varies considerably among species Falconer 1981 Ralls et al 1988 Lacy et al 1993 and even among populations of the same species Lacy et al 1996 Even without detailed pedigree data from which to estimate the number of lethal equivalents in a population and the underlying nature of the genetic load recessive alleles or heterozygote advantage PVAs must make assumptions about the effects of inbreeding on the population being studied If genetic effects are ignored the PVA will overestimate the viability of small populations In some cases it might be considered appropriate to assume that an inadequately studied species would respond to inbreeding in accord with the median 3 14 lethal equivalents per diploid reported in the survey by Ralls et al 1988 In other cases there might be reason to make more optimistic assumptions perhaps the lower quartile 0 90 lethal equivalents or more pessimistic assumptions perhaps the upper quartile 5 62 lethal equivalents In the few species in which inbreeding depression has been studied carefully about half of
289. re handled in a different way in VORTEX 10 so that they are both more flexible and powerful but also easier to use Therefore and STs defined in a VORTEX 9 project file will be ignored when the old vpj file is loaded into VORTEX10 See a separate document describing the VORTEX 10 Sensitivity Tests for more information about how to use STs in VORTEX 10 Text Output contains a tab to display a summary of results from Sensitivity Tests Graphs of ST results include the same graphs available for all scenarios and some additional plots that are useful for comparing the relative effects of variables tested in a ST All the data that are used for ST graphs are available in files with extension stdat with the same data format as the dat files used for graphing non ST scenarios so the ST results can also be analyzed and graphed in other programs Tables and Graphs This section now provides quick access to 6 standard graphs of simulation results as well as the option for Custom Graphs that provides the same array of variables for graphing that were available in version 9 Some of the arrangements of graphs that were available in VORTEX 9 such as graphing Populations or Variables across the x axis are no longer available Often those graphs were difficult to interpret and not very useful and very few people ever used them 152 The populations to be graphed for the selected scenarios are now specified via a simple list of checkboxe
290. re well tested and deemed to be broadly useful Simulation Input Navigate between the pages of input by clicking on the labels in the left side column It often makes sense to enter data in the sequence in which the pages are listed but you can enter data in any order Adding deleting re ordering and moving among Scenarios The Add Delete and Reorder buttons for Scenarios are fairly intuitive The two methods for moving between Scenarios are to use the DropDown list or to click on a Scenario label from the horizontal list If there are many Scenarios or they have long names then the horizontal list will extend beyond the window and further Scenarios can be accessed from a small DropDown at the far right edge of the list Section Notes On each page of input you can and should enter Notes to document the sources of data or perhaps the uncertainty about data values Notes about input values are entered within a text box for each input section When you save your Project these notes are inserted into the file with inp extension that lists all the input values for a scenario They are also automatically placed into a separate text file with extension notes that lists only the Notes Short cuts when you have multiple populations On the input pages described below if you have more one population then there will be a tool below the list of input pages that lets you copy all population specific values from any population to all
291. riority can be set to a function of for example the number of pairs already produced PAIRS variable Include extinct and extant runs in Genetic summary statistics Normally population statistics reporting gene diversity expected heterozygosity observed heterozygosity numbers of alleles and genetic distances include only those iterations that were not extinct even if extinction is defined in your scenario as N gt some critical size This option will include all runs even extinct ones and even ones that have N 0 and therefore genetic summary statistics of 0 in the calculation of means and SDs for genetic summary statistics However this option does not affect the optional output file with allele frequencies and genetic distances will not include runs when N 0 for one of the populations Include extinct and extant runs in GSvar and PSvar summary statistics Normally means and SDs reported for global and population state variables include only those iterations that were not extinct even if extinction is defined in your scenario as N gt some critical size This option will include all runs even extinct ones and even ones that have N 0 and therefore state variables of 0 in the calculation of means and SDs for GDvars and PSvars 14 Undocumented options are usually very special cases that won t be used by many people or are options that are still being tested and are not yet ready for widespread use The options are
292. rm You can use it to impose fluctuations in habitat quality or E extent but be careful not to double count EV that is affecting mortality Mate Monopolization Initial Population Size Carrying Capacity Future change in K E Harvest Over how many years 5 Supplementation Annual increase or decrease 10 Genetics gt Copy input values from 2 Implement K based on a limit on some population variable other than N Caution If you define K as a limit on something A other than N that will have implications for any Population variable to be tested against K F nine shicsane K Y During K truncation remove only individuals meeting criteria A lt 5 this section to subsequent populations E Prioritize K truncation based on Svar 0 use negative for dynamic O for none Caution Prioritized K truncation can be very slow especially if dynamic Copy Carrying Capacity K The carrying capacity describes the upper limit for the size of your simulated population within a given habitat VORTEX implements carrying capacity as a probabilistic truncation across all age classes when K is exceeded at the end of the year or whenever in the annual sequence you have K truncation For example if N 1 25 K then additional mortality will be imposed such that the survival probability for any individual during the K truncation is 1 1 25 0 80 so that after the truncation the expected population size is K You can imple
293. rom the last population during a Translocation For example you can specify that only individuals with low inbreeding will be released or only those with an IS variable that is set to the recipient population number In this way you can although sometimes with difficulty control which individuals are translocated into which populations Population Supplemented If you want to supplement your population s check this box You must then provide the values on the subsequent lines to define the nature of the supplementation First Last Year of Supplement The supplementation can begin and end at any time during the stipulated length of the simulation Enter the years in which you wish to begin and end supplementation Interval Between Supplements If you wish to supplement every year within the specified time frame enter 1 If you wish to supplement every other year enter 2 Optional Criteria for Supplements You can specify here some criteria that will restrict supplementation to occur only if the population status meets certain conditions You enter this as a function For example if you enter N K lt 0 25 then supplements will be added only if the ratio of the population size to the varying capacity is at less then 0 25 and if it is a supplementation year as defined above Leave the table cell entry as 1 if you do not want to provide any criterion for supplementing Female Male Ages being Supplemented Enter the number of females an
294. roup SSC IUCN Morton N E Crow J F and Muller H J 1956 An estimate of the mutational damage in man from data on consanguineous marriages Proceedings of the National Academy of Sciences USA 42 855 863 Nei M 1987 Molecular Evolutionary Genetics Columbia University Press NY O Brien S J and Evermann J F 1988 Interactive influence of infectious diseases and genetic diversity in natural populations Trends in Ecology and Evolution 3 254 9 Odum A et al eds 1993 Aruba Island Rattlesnake Population and Habitat Viability Assessment PHVA Workshop Apple Valley MN Captive Breeding Specialist Group SSC IUCN Pergams O R W R C Lacy and M V Ashley 2000 Conservation and management of Anacapa Island deer mice Conservation Biology 14 819 832 Petit S and L Pors 1996 Survey of columnar cacti and carrying capacity for nectar feeding bats on Cura ao Conservation Biology 10 769 775 Pielou E C 1977 Mathematical Ecology New York John Wiley and Sons Ralls K Ballou J D and Templeton A R 1988 Estimates of lethal equivalents and the cost of inbreeding in mammals Conservation Biology 2 185 93 Ricklefs R E 1979 Ecology 2 ed New York Chiron Robertson A 1960 A theory of limits in artificial selection Proceedings Royal Society of London 153B 234 49 Rohlf F J and R R Sokal 1981 Statistical Tables 2 ed New York W H Freeman and Company Ruggiero L F G D Hayward an
295. rrors and medians across years and across iterations Variables for storing input intermediate calculations and output are indicated in the pseudo code by italicized labels Many of the variables are arrays e g a value stored for each population or for each age class or for each indi vidual as suggested by the loops within which they are calculated and used The indices of such arrays are indicat ed within brackets e g MortalityRate p s x for each population p sex s and age x VORTEX uses many more variables not shown in the pseudo code for facili tating calculations and accumulating sums sums of squares and other components needed for the basic statis tics reported in the output In the pseudo code loops are indicated with FOR and END LOOP statements or by WHILE and END WHILE statements Conditional actions are indicated by IF and END IF statements or by IF ELSE and END IF ELSE statements BREAK indicates that program flow exits from the bottom of a loop CONTINUE indicates that program flow jumps back to the next value at the top of the loop Multiplication is indicated by the asterisk symbol indicates exponentiation SQRT indicates the positive square root Function modules defined outside of the main body of the pseudo code program are labeled in the form FUNC TION and are specified below the main VORTEX program The actual C code is subdivided into many smaller functions the pseudo code
296. rwise would be calculated by the program and this will also affect the kinships of all descendants of those individuals Note that when the KM option is used often you will want the calculations of expected heterozygosity gene diversity to be based on the kinships rather than on the allele frequencies at simulated loci To achieve that use the next Special Option KG This option causes the calculations of expected heterozygosity gene diversity to be based on the kinships rather than on the allele frequencies at simulated loci as is otherwise done by VORTEX When initial kinships are 0 the default these two methods of calculating gene diversity will yield very similar results However if you specify different kinship structure among the initial individuals via the Genetics option to specify all starting kinships or via the Special Option KM then it will often be more useful to see the gene diversities that arise from those initial kinships Note that the initial kinships have no effect on the initial alleles assigned at the modeled loci and thus have no effect on genetic metrics calculated from allele frequencies Caution Special Options are applied to all scenarios in your project Therefore if you want to apply a special option to only some scenarios you will need to remember to toggle that option on and off when you run the different scenarios Some Special Options may be moved into the standard input sections after they a
297. ry shibboleths Wildlife Society Bulletin 13 403 410 157 Maguire L A 1986 Using decision analysis to manage endangered species populations Journal of Environmental Management 22 345 360 Maguire L A R C Lacy R J Begg and T W Clark 1990 An analysis of alternative strategies for recovering the eastern barred bandicoot in Victoria Pages 147 164 in Clark T W and J H Seebeck eds Management and Conservation of Small Populations Brookfield IL Chicago Zoological Society Manansang J A MacDonald D Siswomartono P S Miller and U S Seal eds 1996 Population and Habitat Viability Assessment for the Babirusa Babyrousa babyrussa Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Miller P S and R C Lacy 2003a Integrating the human dimension into endangered species risk assessment Pages 41 63 in F R Westley and P S Miller eds Experiments in Consilience Integrating Social and Scientific Responses to Save Endangered Species Island Press Washington DC Miller P S and R C Lacy 2003b Metamodels as a tool for risk assessment Pages 333 351 in F R Westley and P S Miller eds Experiments in Consilience Integrating Social and Scientific Responses to Save Endangered Species Island Press Washington DC Mirande C R Lacy and U Seal eds 1991 Whooping Crane Grus americana Conservation Viability Assessment Workshop Report Apple Valley MN Captive Breeding Specialist G
298. s All years up to an optional user specified limit are now shown on the graphs and tables so there is no longer an option to plot only specific years from within the range Lines labels as shown in the graph legend and on the table can now be edited from a table that is accessed from an Edit Line Labels button below the graph After editing you must either Accept or Cancel your changes Functions The variable for inbreeding I is expressed as a proportion 0 to 1 scale rather than a percent Default values for any variables used in functions can be specified in the input on the State Variables page If specified these values will be used when evaluating functions at the start of a simulation for initial determination of deterministic growth rates and stable age distribution For any variables pertaining to individuals e g age sex genotypes these default values will be each year when evaluating functions that are needed for population level calculations such as the number of pairings to reach K if that option is chosen or functions defining harvest or supplementation Order of precedence of operators within any parentheses follows standard rules rather than the strict left to right application of operators of VORTEX 9 Syntax for using GSvars PSvars ISvars and related functions has changed as follows GS1 rather than GS 1 PS1 rather than PS 1 PPS1 p rather than PPS 1 p IS1 rather than IS 1 ITOT r
299. s removal of young individuals for translocation programs etc ees File Simulation Help BS amp Det st Project Settings Simulation Input Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current New Scenario Default Scenario Default Scenario Copy Default Scenario Copy2 5 Scenario Settings Harvest Section Notes F Species Description V Implement as Translocation Percent survival during Translocation 50 State Variables Dispersal Reproductive System aa 1 Population 2 Reproductive Rates Population harvested Ww Ea z First year of harvest 1 1 Mortality Rates Last year of harvest 50 20 ph a Interval between harvests 0 2 ph wal Optional criteria for harvest Initial Population Size Optional criteria for individuals Carrying Capacity F Number of females of each age to be harvested Supplementation Population 1 Population 2 Genetics Harvest from age 1 to 2 1 2 Harvest from after age 2 2 2 Copy input values from Population1 Number of males of each age to be harvested Population 1 Population 2 Harvest from age 1 to 2 J 10 2 Harvest from after age 2 M 5 2 AF il il Implement as Translocation With this option the last population is used as a holding location An undocumented Special Option allows you to set the holding population to be some other population Any indivi
300. s assumed to be not in the living population at the start of the simulation but it can still be used as an ancestor of other individuals in the genetic calculations ISvars should be at the end of the line of data and the number if ISvars to be read from each input string is given by the x in undocumented option Ix see Special Options above Alternatively if the header for the studbook file includes codes IS1 IS2 etc then these ISvars will be read from the file Any lines in the studbook file that start with or f are assumed to be comment lines and are ignored when individual records are read If you are modeling extra genetic loci it is possible to specify in the studbook data file what genotypes should be assigned to the individuals in starting population This option can be useful if you have a studbook population that has been genotyped at a number of loci and you wish to project how well those alleles are maintained into the future Note that this is somewhat like the option to specify starting allele frequencies see below but you further specify the exact genotypes of each initial individual To do this you specify in the header of the studbook file where the genotypic data will be by using the codes VV2 ZZ2 VV3 ZZ3 etc as the labels for the maternal and paternal alleles of extra locus 2 3 etc and MT as the label for the mtDNA haplotype Note that these allele codes are the same as are used in functions
301. s delayed and litter sizes were smaller when the only available partner was the one that had been less preferred Species with complex social systems may be especially vulnerable to problems resulting from low population density For example striped back wrens Campylorhynchus nuchalis have very low breeding success unless they have at least two adult non breeding helpers sharing in defense against nest predators and breeding success is related strongly to the number of such helpers Rabenold 1990 If such a population were to decline in numbers recruit ment could stop when few birds remained to serve as help ers One population was rescued from demographic de cline when immigrants from nearby populations joined remnant breeding groups Rabenold et al 1991 Presum ably extirpation of the local population would have oc curred if there had not been nearby sources of immigrants Inbreeding depression and loss of genetic diversity At least two kinds of genetic problems can impact the vi ability of small populations reduction of fitness of indi viduals resulting from inbreeding and loss of genetic di versity due to random genetic drift Lacy 1997 There has been much written about e g Frankel and Soul 1981 Schonewald Cox et al 1983 Hedrick and Miller 1992 Frankham 1995a but also much debate over e g Lande 1988 1995 Caughley 1994 Caro and Laurenson 1994 Hedrick et al 1996 the importance of genetics to conser
302. s now exist at densities of only a few per protected area Field surveys in Malaysia in 1995 found tracks of one juvenile among 35 sets of tracks and one of 21 adult fe males captured in the prior decade was pregnant AsRSG 1996 If the population were breeding as expected for a thinoceros species ca 30 of adult females should be pregnant at any time and ca 15 of the animals should be under two years of age Although detailed studies of de mography have not been carried out in part because of the difficulty of studying secretive animals that are at low den sity in the forest it is plausible that the scarcity of mates is causing a near cessation of breeding over much of the frag mented range Even if some potential mates are available small popu 44 lations may provide little opportunity for mate choice The extent to which a reduced pool of possible mates may be causing breeding delays or failures in small natural popula tions has not been explored This problem could be exacer bated if the potential mates are all closely related to the choosing individual or to each other Ryan 2000 found that when given a choice of unfamiliar distantly related females in a Y apparatus male Peromyscus polionotus rhoad si mice preferred the less related female even when differ ences in kinship averaged only f 0 013 about the level of second cousins When subsequently paired with one or the other female from the choice test breeding wa
303. s quick access to 6 standard graphs of simulation results as well as the option for Custom Graphs that provides an array of output variables for graphing The populations to be graphed for the selected scenarios are specified via a simple list of checkboxes All years up to an optional user specified limit are shown on the graphs and tables Lines labels as shown in the graph legend and on the table can now be edited from a table that is accessed from an Edit Line Labels button below the graph After editing you must either Accept or Cancel your changes Sometimes changes to graph settings will not immediately result in a changed graph Usually this happens because the cursor is still on the changed setting so the program has not yet accepted and processed the change that is being made In such cases the graph can be updated with the current settings by clicking the Update Plot button When any graph is displayed the data used in creating that graph can be viewed and optionally saved or printed by going to the Table tab Double clicking on a graph will open the Chart Properties in which you can change any of the settings and even change the data for the graph Note the Tables amp Graphs tab will not be visible if you have not yet run any scenarios because there are no data to be shown in the Tables amp Graphs 84 Standard Graphs N vs Year the same as the N all graph in the custom graphs Z Vort
304. sal rates for females are effectively reduced by 35 relative to male dispersal An unseeded random number is used so that dispersal will be determined independently each female Note that the dispersal rates entered subsequently D will be those applied to males with females having lower rates A similar approach can be used to create age specific dispersal rates or dispersal mortality Alleles confer differential reproductive rates 50 0 y 40 10 V 2 10 2Z 2 o 4001 In this case half of the alleles a 35 0 L specifically those with even numbers cause 2 300 an increment of 10 in the breeding rate of their 25 0 carriers An individual that is homozygous for S 20 0 an even numbered allele will have a breeding 5 15 0 rate equal to 60 while those homozygous for 10 0 an odd numbered allele will have a rate equal 5 0 to 40 0 0 0 10 20 30 40 50 Allele Identifier 129 25 Overdominance for survival all unique founder alleles RATE 20 10 V Z An infinite alleles model in which homozygotes have a mortality of 30 while the rate for heterozygotes is 20 26 Overdominance for survival two functionally distinct founder alleles RATE 20 10 V 2 Z 2 A two allele model in which homozygotes with two odd or two even alleles have a mortality of 30 while the rate for heterozygotes is 20 27 Outbreeding depression for breeding rate upon introgression from supplemented individuals
305. sal rates to specify the probability that a given individual of the appropriate age sex class will disperse from population A to population B in a specific year That is a rate of 1 00 indicates a 1 probability that an individual will migrate from population A to population B Dispersal rates need not be symmetric among populations enter whatever probability you deem appropriate for each pair of populations Enter 0 to indicate no exchange of individuals between a pair of populations The values on the diagonal of the table the percents of individuals that do not disperse each year is automatically calculated by the program so that the rows will sum to 100 In the Dispersal Rates section are four commands that can make it easier to enter dispersal rates Import Rate Matrix allows you import the table values from a semi colon delimited text file This file can be created in Excel or whatever software you choose It must contain values for all cells of the table including the labels although the labels in the file will be ignored and will not over write what shows on the screen The easiest way to see the format of the rate matrix file is to select Export Rate Matrix and then look at the file that was created With these commands you can create a large matrix in a spreadsheet program and then import it into VORTEX and you can export rate matrices for modification or for re use in other VORTEX projects When you have only a few
306. selected for breeding pool but adult males do exist Add one male at random to breeding pool END IF IF monogamous FOR each male in breeding pool m Set MaleUsed m FALSE Flag to indicate male is available for pairing END LOOP END IF IF hermaphroditic IF only one breeding female AND ProportionSelfing p 0 EXIT BREED END IF END IF FOR each female Dam in breeding pool Let BreedRand RAND GETBREEDRATE 11 BreedRate is probability of breeding for che female given by the user either as a constant ProportionFemalesBreeding or as a function of population size and other parameters See Note 3 IF BreedRate 0 CONTINUE LOOP with next breeding female END IF Find a mate IF hermaphroditic IF RAND lt ProportionSelfing p Let Sire Dam ELSE Choose a Sire at random from breeding pool WHILE Sire is Dam Choose a new Sire END WHILE END selfing IF ELSE ELSE not hermaphroditic Choose a Sire at random from the male breeding pool ECOLOGICAL BULLETINS 48 2000 IF monogamous WHILE Male Used Sire Choose a new Sire END WHILE Set MaleUsed Sire TRUE 11 Flag Sire as unavailable for future Dams END IF END IF ELSE Find the litter size for that pairing IF MaximumLitterSize gt 0 Set CumulativeProbLitterSize 0 1 BreedRate FOR each possible litter size 7 Set CumulativeProbLitterSize n CumulativeProbLitrerSize n 1 ProbLitterSize p n Breed
307. servation The perspective offered here is necessarily biased by personal experiences in conservation we will not attempt an exhaustive historical account of this field Population viability analysis originally described methods of quantitative analysis to determine the probability of extinction of a population Shaffer 1981 first defined a minimum viable population MVP as the size at which a population has a 99 probability of persistence for 1000 years but it might be more meaningful biologically to consider it to be the size below which a population s fate becomes determined largely by the stochastic factors that characterize extinction vortices One concept of population viability analysis is any methodology used to determine an MVP Shaffer 1990 More broadly PVA is the estimation of extinction probabilities and other measures of population performance by analyses that incorporate identifiable threats to population survival into models of the extinction process Brussard 1985 Gilpin and Soul 1986 Burgman et al 1993 Lacy 1993 1994 Shaffer s 1981 original term minimum viable population MVP has fallen into disfavor Soul 1987 even as the PVA approach has risen in popularity Shaffer stressed that an MVP was an estimate of the population size below which the probability of extinction was unacceptably high that different populations would have different MVPs and that the MVP determined for a population would depend on the thr
308. set at the mean homozygosity of modeled loci but it will affect the inbreeding of individuals The mean inbreeding of individuals can be determined by setting IS1 and then setting PS1 IMEAN1 66 The optional value to which initial kinships are set can be a function that includes a distribution by using a RAND function the populations of the two individuals PX or just P population of first individual PY population of second individual the ISvars X1 or 151 X2 X3 etc state variables for the first individual Y 1 etc state variables for the second individual or anything else e g Y or R This allows you to set initial kinships to be variables from a distribution to be different for within vs between population pairs to change during a simulation e g higher for new supplements that arrive later or to be functions of some property e g age of the individuals Note that every pairwise kinship among founders is normally set to the same value as the inbreeding coefficients of founders This should be approximately correct for randomly breeding populations because the inbreeding coefficient is equal to the kinship between the parents However in small populations the inbreeding coefficients will on average be a little less than the average kinship because the average kinship increases slightly from generation to generation Also it may be that individuals actively avoid inbreeding in which case inbreeding migh
309. shows only the flow of the overall program and its largest modules The functions RAND and NRANDO indicate respectively that a ran dom number is generated from the uniform 0 1 distribu tion or from a unit normal distribution Explanatory comments following pseudo code sec tions are preceded by More extensive explanations are given in notes following the code As an individual based PVA simulation model VOR TEX represents each individual in memory simulates life events such as sex determination breeding mortality and dispersal which could occur to each individual and mon itors the status of each individual and the population as a whole The characteristics tracked for each animal are sex alive dead status population membership age inbreeding coefficient and two alleles at each of six loci In addition VORTEX maintains a matrix of kinship coefficients be tween all pairs of living animals as this provides inbreeding coefficients for any offspring VORTEX models changes to a population as a series of discrete events that occur once per year or other time in terval The annual sequence of demographic events is ECOLOGICAL BULLETINS 48 2000 breeding mortality age 1 yr migrate disperse among populations harvest managed removals supplementa tion managed additions carrying capacity truncation census Fig 1 Occurrences of events are probabilistic demographic stochasticity emerges from chance variati
310. sical and biotic environment that was different from the current landscape For example in largely contiguous habitat with local competition for breeding territories the optimal dis persal pattern might be for subadults to always disperse and to disperse in a random direction When habitat is highly fragmented and often unoccupied however it might be adaptive to remain near the natal site unless local densities are very high Ronce et al 2000 and to develop dispersal behaviors that more efficiently locate suitable habitat for example habitat with an excess of inhabitants of the opposite sex Many metapopulations may be occu pying recently fragmented landscapes for which their evolved dispersal strategies are suboptimal In PVA mod els it might be important to consider that dispersal strate gies that are stabilizing at one population density can be come destabilizing at different population densities Disruption of breeding systems represents another ex ample of interactions between processes As populations become small individuals may become closely related to most or all potential mates In a number of species indi viduals have been observed to avoid mating with genetic relatives Keane 1990 Inbreeding avoidance in a small population could lead to frequent failures to locate any suitable mates The suppression of breeding might be con 46 sidered a form of inbreeding depression but it may not be recognized as such sin
311. simulating patterns of molecular genetic data that might arise from the population dynamics Note that although the label says neutral loci you can create fitness differences among genotypes by specifying that demographic rates are functions of the alleles carried by individuals There is not often any good reason to add more neutral loci to your simulation unless you intend to specify the initial allele frequencies see below or model fitness differences between alleles If you run enough iterations to obtain reliable demographic results then the genetic results based on the default single locus will usually also be sufficiently precise Loci included in summary statistics When you add loci to the genetic model you can then specify if genetic statistics such as heterozygosity are to be calculated based on the default neutral locus or only on your additional loci or both If you specify starting allele frequencies at your additional loci see below then you may want to have genetic statistics calculated only for 62 those loci or you may instead want the genetic statistics calculated only for the default infinite alleles locus Note that the simulated loci have no effect on the calculations of inbreeding of individuals as individual inbreeding coefficients are calculated from the pedigree and the impacts of inbreeding are determined by the calculated inbreeding coefficients for the portion of inbreeding depression not caus
312. some other combination of recessive deleterious alleles which equate in effect with one lethal allele per individual VORTEX partitions the total effect of inbreeding the total lethal equivalents into an effect due to recessive lethal alleles and an effect due to loci at which there is heterozygote advantage superior fitness of heterozygotes relative to all homozygote genotypes To model the effects of lethal alleles each founder starts with a unique recessive lethal allele and a dominant non lethal allele at up to five modeled loci 145 By virtue of the deaths of individuals that are homozygous for lethal alleles such alleles can be removed slowly by natural selection during the generations of a simulation This diminishes the probability that inbred individuals in subsequent generations will be homozygous for a lethal allele Heterozygote advantage is modeled by specifying that juvenile survival is related to inbreeding according to the logarithmic model In S A BF in which S is survival F is the inbreeding coefficient A is the logarithm of survival in the absence of inbreeding and B is the portion of the lethal equivalents per haploid genome that is due to heterozygote advantage rather than to recessive lethal alleles Unlike the situation with fully recessive deleterious alleles natural selection does not remove deleterious alleles at loci in which the heterozygote has higher fitness than both homozygotes because all alleles a
313. sonae metapopulations Rather than modeling causal processes as is done in individual based models lo gistic models can use observed correlates of population transitions to generate predictive models of metapopulation trends Individual based models require detailed data on the factors driving population processes while logistic transition incidence models require detailed data on the important correlates of population transitions over significant periods of time Generalized analytical models can be extremely valua ble for discerning many broad trends e g Belovsky 1987 but they do not provide the situation specific repre sentations that are needed to assess local threats to specific small natural populations nor usually the time specific projections that are needed to understand non equilibrial systems Thus detailed and often individual based models are more appropriate for comparing management options for endangered species recovery and local conservation planning We should also retain some skepticism regarding the generality of theoretical results until they have been confirmed to apply to simulated or better real popula tions in which the unrealistic assumptions of the theoreti cal model have been relaxed There have been recent en couraging confirmations of the ability of PVA models to predict population dynamics Brook et al 2000 but more comparisons are needed among analytical results simulation results from models
314. ss By default VORTEX will conduct the harvest after newborn animals have aged to become 1 year old in the annual cycle so the youngest individual that can be harvested is one year old If you have changed the sequence of events on the Scenario Settings page to put a Harvest in between Breed and Age then age class 0 individuals will also be available for harvest in the table If the number to be harvested is a function that evaluates to a non integral number VORTEX will use probabilistic rounding see PROUND in the section on Functions so that the mean number harvested is not biased If the program attempts to harvest individuals from an age class and finds an insufficient number of individuals the simulation will continue without the harvest of those individuals determined not to exist VORTEX will then report at the end of the simulation in the text output file that some of the attempted harvests could not be carried out 56 Supplementation You also have the option of adding individuals to each population This option can simulate supplementation through for example a translocation or releases from a captive breeding program As with the harvest option supplemental individuals can be added at any time and interval within the specified time frame for the simulation EF unrelated to both each other and to any other individual in the recipient population Consequently supplementation is a means of increasing genetic diversity as w
315. ssarily being in the middle of the tested ranges of the variables 101 There are two options for controlling how the spider plots appear When the x axis is standardized then all variables are plotted on a 0 to 100 scale that covers the range of values sampled Non standardized plots see below show the lines for each variable plotted against the values that were tested Because different variables might be on very different scales often the non standardized spider plots will have lines that cover discrete segments of the x axis Maybe these are spider plots with the legs pulled off In non standardized plots the result for the base is plotted at each place along the x axis that represents the base value of a tested variable f l Plot Table 1 ST Analysis MyST3 y Spider plot of N m SV1 PBreed SV2JMot SV3 AFMort SV4 AMMort Baseline Ervorbars None SE SD Spider Plot Options 250 X axis Standarized 9 Not standardized 2404 4 110 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 Value of tested ST variable Serio pos Sm C For standardized spider plots you also have the option of having the x axis scaled relative to the Base or relative to the Midpoint If scaled relative to the midpoint then each line will extend from 0 to 100 on the x axis scale with the midpoint of the tested range b
316. status and recovery options for a species will change as a species declines Therefore it is important to consider carefully which PVA model is most appropriate for a par ticular analysis Lindenmayer et al 1995 Akcakaya and Sj gren Gulve 2000 An individual based simulation program that models the stochastic processes of small pop ulations in detail would probably not be the best model for examining viability of a population which numbers in the 40 tens of thousands Similarly a population based structured model which ignores factors such as fluctuations in sex ra tio mate availability and inbreeding would probably not be the most accurate model for a population which falls below 100 individuals Many perhaps all presently used PVA models assess only some of the threats facing small populations and therefore may underestimate probabili ties of extinction and difficulties in species recovery In this paper I will describe some of the threats to small populations that are not included in most PVA models This discussion will provide guidance as to when more de tailed individual based PVA models may be necessary to represent well the dynamics of small populations Most of the processes I will discuss are particularly important for species with low intrinsic growth rates and stable social sys tems and somewhat less so for those with high fecundity and little structure to the social or breeding system There fore these consider
317. sted under different structural assumptions Different participants in the process should assess and interpret the results Such sensitivity testing reveals which components of the data model and interpretation have the largest impact on the population projections This will indicate which aspects of the biology of the population and its situation contribute most to its vulnerability and therefore which aspects might be most effectively targeted for management In addition uncertain parameters that have a strong impact on results are those which might be the focus of future research efforts to better specify the dynamics of the population Close monitoring of such parameters might also be important for testing the assumptions behind the selected management options and for assessing the success of conservation efforts Closely parallel to the testing of uncertainties in the present situation is the testing of options for management PVA modeling allows one to test the expected results of any given management action under the assumptions of the model and within the limitations of present knowledge on the computer before implementation in the field This process can guide selection of the management options most likely given current knowledge to be effective and will define target recovery goals that should be obtained if our knowledge is adequate and the recommended actions are followed A PHVA workshop on the Black Rhinoceros in Kenya s 11 rhino san
318. ster if you turn of the graphs of changing population sizes e Do not show any messages to the user while running This option can be useful if many scenarios are running when the computer will not be attended e Do not include last population in metapopulation tally This option is sometimes useful when the last population represents an external source population for dispersal into your other populations or is the temporary holding population for a model with translocation e Produce a census file This file with extension yr can be useful if you want a detailed tally of the population year by year The file can become large so you need to specify for how many of the iterations you want to see such details e Produce a file of all living animals at the simulation This file with extension ani is useful if you want to see details about each individual The file can become large so you need to specify for how many of the iterations you want to see such details e Produce a file of all animals created in the iterations with extension all You need to specify for how many of the iterations you want to see such details Even with a listing for just one iteration the file can be very large so use with caution One use of this file is to feed it into a pedigree analysis such as PMx see www vortex 10 org PMx aspx to conduct much more detailed genetic and demographic analyses on a simulated population Some further editing of the headers o
319. stimate the parameters that are needed for the model of population dynamics to be applied Often data are not available from which to estimate certain key parameters In those cases subjective and objective but non quantified information might be solicited from the assembled experts values might be obtained from data on related species or a factor might simply be omitted from the model While such a non precise process might consist simply of intuitive judgments made by experts it is important to specify how values for the parameters in the model were obtained The resulting limitations of the analyses should be acknowledged and a decision made if how by whom and when the missing data would be collected so that more refined analyses could be conducted With the PVA model projections of the most likely fate and distribution of possible fates of the population under the specified assumptions are made Because so much of a PVA the data the model and even the interpretation of output is uncertain a PVA that provides an estimate of the probability of extinction under a single scenario is of very limited usefulness An essential component of the PHVA process therefore is sensitivity testing Ranges of plausible values for uncertain parameters should be tested to determine what effects those uncertainties might have on the results In addition several different PVA models might be examined at a PHVA workshop or the same general model te
320. t Report Scenarios Add Delete Reorder Current Default Scenario y Default Scenario a Scenario Settings State Variables Sacilon Notes F Spedes Desatot Dispersal Variable Label Initialization function Transition function Reproductive System GS1__ HabitatQuality 100 100 Y 0 05 GS2 FadeRate E Reproductive Rates veda ii Mortality Rates Catastrophes Mate Monopolization Initial Population Size Select for which population you want to set functions PATA Population State Variables Population 7 Harvest Variable Label Initialization function Transition function Supplementation PS1 Area 200 PS1 Genetics PS2 2YearOlds 25 ITOT2 Copy input values from this section X to subsequent populations Individual State Variables Add Delete Add Outbreak Vars_ Add Spatial Vars_ Variable Label Initialization function Birth function Transition function IS1 Color 1 DAM1 SIRE1 2 IS1 1 GS2 152 2year A 2 0 IF A 2 1 0 Default Values for Variables Used in Functions Variable Default Value A N GSvars PSvars and ISvars can be referenced in functions by either the state variable number 1 e GS1 PS3 IS7 or can be referenced by their labels Be sure not to use a label that is the same as a built in function such as DAM SIRE PARITY with the exception of a special use of MATE see section on Functions and POPULATION see below Global Sta
321. t be accessible 110 Variables and Operators Available for Use in Functions The following tables list the many variables and operators that are available for use in VORTEX functions Note that it is important to be aware when the variables are updated as the simulation is running For many variables it is obvious for example the variable Y for year is incremented at the beginning of each year of the simulation But population tallies such as N F M J and G are updated before each event e g Breed Mortality Harvest in the annual cycle Thus for example N at the beginning of Mortality will be the number of individuals after the reproduction event has occurred unless you changed the sequence of events in the annual cycle Tallies of reproduction PAI RS BROODS PROGENY are incremented as each individual reproduces and this permits you to modify the breeding rates of subsequent individuals based on the reproductive success already accumulated Dispersal tallies MMI GRANTS and EMI GRANTS are updated within the dispersal process However you should not use these two variables to modify dispersal rates themselves because it is not predictable in what order individuals will disperse or when the dispersal tallies are updated within the dispersal event If you want to use the dispersal tallies from a prior Dispersal step in the annual cycle to modify rates in a second or later Dispersal step then set a Population State variable to
322. t be much less than the average kinship If you want to set the initial inbreeding coefficients to be different than the initial pairwise kinships there is a trick that you can use Set the initial kinships to 1 0 inbr I gt 0 kin In which inbr is the value to which you want to set the initial inbreeding coefficients and kin is the value of the initial kinships This trick works because inbreeding starts as the default 0 and then it is calculated so it will be set to inbr when an individual is first created and then kinships to all other individuals are determined Note that if you want to set the initial inbreeding to 0 but the initial kinships to something else then you need instead to set inbr to some very tiny number such as 0 00001 so that I gt 0 will trigger the setting of kinships to kin There are three ways in which VORTEX can determine the kinships among individuals and thus the inbreeding coefficients of their offspring and it is important to know how these methods interact and which takes precedence The default assumption is that founders are unrelated to each other and non inbred and then the kinships among later generation individuals are determined from standard pedigree analysis However as described above the initial kinships and inbreeding coefficients can be specified by the user If this option is chosen then these specified kinships replace the values of 0 that are first assigned to founders The third me
323. t trends from complex processes 2 permit comparison among systems 3 facilitate analysis of causes of processes acting on the system and 4 make predictions about the future A complete description of a natural system if it were possible would often decrease our understanding relative to that provided by a good model because there is noise in the system that is extraneous to the processes we wish to understand For example the typical representation of the growth of a wildlife population by an annual percent growth rate is a simplified mathematical model of the much more complex changes in population size Representing population growth as an annual percent change assumes constant exponential growth ignoring the irregular fluctuations as individuals are born or immigrate and die or emigrate For many purposes such a simplified model of population growth is very useful because it captures the essential information we might need regarding the average change in population size and it allows us to make predictions about the future size of the population A detailed description of the exact changes in numbers of individuals while a true description of the population would often be of much less value because the essential pattern would be obscured and it would be difficult or impossible to make predictions about the future population size In considerations of the vulnerability of a population to extinction as is so often required for conservat
324. t values of state variables to be updated with their Transition functions before Dispersal or Harvest or Supplementation You can also update only GSvars PSvars or ISvars in any order if you want for example to have PSvars contain a tally e g using ITOT1 of an updated ISvar You can insert additional censuses e g after breeding or after dispersal if you want to see the population counts at various points in the annual cycle If there are additional censuses in a year then output files will tally statistics at each census rather than only once per year 23 Species Description This input page asks a few questions about aspects of the population dynamics that will be applied across all populations of your simulation File Simulation Help fe Det D ST Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current Default Scenario y Default Scenario Scenario Settings Species Description Section Notes Species Description State Variables Y Inbreeding depression Dispersal Reproductive System a A Reproductive Rates Percent due to recessive lethal alleles 50 Mortality Rates Default value of 6 29 for Lethal Equivalents is the combined mean effect of inbreeding on a fecundity and first year survival reported by O Grady et al 2006 Realistic levels of inbreeding P depression strongly affect extinction risk in wild populations Biological Conservation 133
325. tandard annual environmental variability 80 Excluding outlier Including outlier EV only Frequency 20 30 40 50 60 70 80 90 100 20 30 40 50 60 70 80 Annual Demographic Rate Annual Demographic Rate The left panel above shows ten years of expected values of a given demographic rate say juvenile mortality in a simulated wildlife population Each bell shaped curve depicts the probability distribution we would expect from demographic stochasticity acting on that rate in that year Actually these little curves of demographic stochasticity would be binomial but the normal distributions are close enough for illustration purposes For example the expected rate in year 1 is 15 2 However when the fate of each juvenile in the population is considered it is possible that the actual rate may deviate from 15 2 solely from this sampling process In addition the expected mortality changes from year to year due to environmental variation with each annual curve again reflecting the sampling variance demographic stochasticity expected for that year s value Note that these curves become tighter the standard deviation resulting from demographic stochasticity decreases as the means deviate from near 50 In addition notice that the mortality rate in year 7 is particularly high perhaps a catastrophic event occurred in that year to produce such high mortality With annual rate data in hand w
326. taneously Genetic processes VORTEX models loss of genetic variation in populations by simulating the transmission of alleles from parents to offspring at a hypothetical neutral non selected genetic locus Each animal at the start of the simulation is assigned two unique alleles at the locus Each offspring created during the simulation is randomly assigned one of the alleles from each parent VORTEX monitors how many of the original alleles remain within the population and the average heterozygosity and gene diversity or expected heterozygosity relative to the starting levels VORTEX also monitors the inbreeding coefficients of each animal and can reduce the juvenile survival of inbred animals to model the effects of inbreeding depression Inbreeding depression is modeled as a loss of viability of inbred animals during their first year The severity of inbreeding depression is commonly measured by the number of lethal equivalents in a population Morton et al 1956 The number of lethal equivalents per diploid genome estimates the average number of lethal alleles per individual in the population if all deleterious effects of inbreeding were due entirely to recessive lethal alleles A population in which inbreeding depression is one lethal equivalent per diploid genome may have one recessive lethal allele per individual it may have two recessive alleles per individual each of which confer a 50 decrease in survival or it may have
327. tation models 1 for mtDNA MATE ID of mate NMATES mates of a male PAI RTENURE years a female has been paired to her mate 0 in the year when paired 1 when not paired MALLELE 1 for maternal allele 0 for paternal allele used only for determining mutation rate BROOD brood number for that female in that year BROODSI ZE offspring born within current brood DI ST Euclidean distance between potential mates only if X and Y exist as ISvars MK1 MK2 MK3 Mean kinship of the individual to population 1 2 3 MKMETA Mean kinship of the individual to the metapopulation Note that some of these variables have one letter synonyms that still work as they did in VORTEX 9 but it is much safer to use the full name for the variable Note also that the following variables are available only during the breeding cycle as pairs are created and offspring produced DI ST DAMn SI REn KIN BROOD and BROODSI ZE 113 Valid Vortex Operators Function Description Example ABS NEG CEIL FLOOR ROUND PROUND Absolute value Negative Ceiling Truncate Round SQRT SQR LN LOG LOG10 EXP Square root Natural logarithm Base 10 logarithm e raised to the power Addition Subtraction Multiplication Division POW MAX MIN MOD Exponentiation Maximum Minimum Modulus Probabilistic Round ABS 10 NEG 10 10 CEIL 3 12 4 FLOOR 3 12 3 ROUND 3 12 3 ROUND 5 5 6 PROUND 3 12 3 88
328. te The binomial distribution that has a standard deviation closest to the desired EV is determined by solving the equation for the binomial vari ance V p 1 p n for the parameter n when given the mean p and variance V SD The parameter n is then rounded to the nearest whole number If n lt 26 the bino mial distribution with parameters p and is used for EV Because of the rounding step necessary to produce the dis crete binomial distribution this distribution will often have a slightly different variance than that entered by the user If n gt 25 the normal distribution with mean p and variance V will be used to model EV In such cases the normal distribution very closely approximates the bino mial distribution The binomial distribution is restricted to the interval 0 to 1 and it fits well the distribution of demographic rates across years observed in some natural populations e g Lacy 1993 The PVA program INMAT Mills and Smouse 1994 uses the related beta distribution for this purpose and it too is restricted to the biologically mean ingful 0 to 1 interval In contrast the normal distribution extends infinitely in both directions although the tails be yond 0 and 1 are typically very small in those cases for which VORTEX uses a normal distribution to model EV For example if p 0 5 and SD 0 1 so that the binomial parameter n 25 the limiting case for VORTEX to use the normal approximation then the ar
329. te Variables You can enter any number of global state variables describing some characteristic of the overall system These state variables must be numeric values or something that can be coded as a numeric value Global state variables may describe any characteristic e g climate management strategy or disease frequency that you will want to be able to apply to all the populations in your model 30 To create one or more global state variables click the Add button for each variable you will be creating A variable can be removed by clicking on its row and then hitting the Delete button For each variable you then enter into the table a label which can be any text that will help you to remember what parameter you were representing For each GS variable you need to enter two functions or constants to define a an initialization function Init fn the starting value for each population at the beginning of the simulation and b a transition function Transition fn the change in state if any each year of the simulation These functions are entered in the same way as other functions that can be used to specify demographic rates see section on Functions Population State Variables You can enter any number of population state variables describing some characteristic of each population If you have just one population then there will be no difference between how a GS variable is used and how a PS variable is used
330. ter this as a function For example if you enter N K gt 0 8 then harvests will only occur if the ratio of the population size to the varying capacity is at least 0 8 and if it is a harvest year as defined above Leave the table cell entry as 1 if you do not want to provide any harvest threshold criteria The optional criteria for harvest allow you to specify conditions under which a population will be harvested These criteria would be entered as a function of population properties e g N Y or population state variables which evaluates to 0 to prevent a population from being harvested that year evaluates to 1 or more to allow harvest and evaluates to a number between 0 and 1 to give that probability of a population being harvested Optional criteria for individuals A new option was added to allow criteria to be specified that constrain which individuals are available for harvest These criteria would be entered as a function of individual properties e g age sex or individual state variables which evaluates to 0 to prevent an individual from being harvested evaluates to 1 or more to allow harvest and evaluates to a number between 0 and 1 to give that probability of an individual being available for harvest Female Male Ages being Harvested Enter the number of females and or males that you will harvest at each time interval defined for each age class through adults Enter 0 for no individuals to be harvested in a given age cla
331. tex 10 New Project CAVortexlOPro File Simulation Help hau fe Det D ST Project Text Output Tables and Graphs Project Report Scenarios Add Delete Reorder Current New Scenario y Default Scenario New Scenario Default Scenario Copy Default Scenario Copy2 Section Notes Scenario Settings Initial Population Size Species Description State Variables Note Stable age distribution may not be meaningful if some demographic rates are functions of other parameters Dispersal Also initial population can be replaced by studbook population imported from a file Reproductive System To determine distribution Reproductive Rates Use stable age distribution Use specified age distribution Enter proportional values for age distribution Mortality Rates Catastrophes Mate Monopolization Population 1 Population 2 Initial Population Size 50 50 p Initial Population Size Carrying Capacity Harvest Supplementation Population 1 Population 2 Population 1 Population 2 Genetics Female age distribution Male age distribution Copy input values from this section Zi to subsequent populations cov te e HB NY WwW woo 2 2 N0N0000amn Bt NWWW oo 0NQ4Ya og If you choose Use stable age distribution then you will enter the initial N and VORTEX will allocate them to the age sex classes according to the expected age distribution calculated
332. th r rather than the arithmetic growth rate lambda because the mean r over time is equal to the long term r Whereas the geometric mean lambda is the long term lambda This mean growth rate is calculated from the mean across years and across iterations of N in one year over N in the prior year With the normal sequence of steps in a year this ratio is calculated before any truncation of N due to exceeding carrying capacity Thus if K 100 N year 0 80 N year 1 before truncation at K 120 the growth rate used in the mean would be r In 120 80 0 405 even though the growth rate experienced after considering the truncation for K would be In 100 80 VORTEX normally reports the growth calculated before truncation for K because that better reflects the demographic potential for population growth However you can change when in the simulated year the growth rate is calculated by changing the position of the rCalc step on the Scenario Settings input page File Simulation Help 0 B amp det st Project Settings Simulation Input Text Output Tables and Graphs Project Report Input Summary Deterministic Results Output Summary Output Tables ST Tables Scenario Default Scenario Population Population1 Year 100 N Bdinct 1 P E 0 010 N Surviving 99 P S 0 990 Mean size all populations 87 24 1 87 SE 18 73 SD Means across extant populations
333. that effectively eliminated the taxon The probability that a population of 100 breeders would all be males is essentially zero so it might be assumed that ran dom fluctuations in sex ratio are unimportant in popula tions approaching such a size However fluctuations in sex ratio can depress population growth significantly even in such cases In a population of 100 breeders we expect ca 50 females and 50 males But due just to demographic sto chasticity the number of females will deviate by 5 or more one standard deviation from this expectation in about one third of the years In monogamous species such as most birds this means that typically lt 50 pairs could be formed The mean depression in reproduction relative to a population with a constant equal sex ratio can be calculat ed from the mean absolute deviation of the binomial dis tribution Due solely to the random fluctuations in sex ra tio reproduction in a monogamous population with 100 adults would be depressed by ca 8 This level of reduced population productivity is enough to cause low fecundity species to switch from positive population growth to long term population decline and eventual extinction Brook et ECOLOGICAL BULLETINS 48 2000 al 1999 found that interaction of the breeding system with fluctuations in the sex ratio strongly influenced pro jections for population growth of whooping cranes Figure 2 shows the mean depression in breeding caused by random
334. that is created in the STbase scenario for each SV This allows you to modify the way that the ST will sample values across the series of iterations run within the ST For example you could change the sampling from a uniform distribution across the parameter space to a normal distribution However be aware that if you return to the STsetup window and again Accept the ST VORTEX will overwrite any changes that 98 you made to the GS synonymous SV variables with the default sampling scheme defined by the STsetup settings Output and further statistical analysis of ST results When ST scenarios are run VORTEX usually produces only a subset of the normal output files and it uses special extensions for the two files that it does create If you are running say 1000 scenarios within an ST you normally would not want to see or have fill up a folder on your disk 1000 copies of the same or very similar inp input det full deterministic results yr detailed census data N a tally of population size for every year of every iteration and other files If you do want to see one set of each of the normal output files run the base scenario The only output files created during the ST runs is a stdat file for each scenario in the series run for the ST and a stsum file that contains the final results for each scenario in the series These files are the same format as the dat and sum files created by normal non ST runs of VORTEX scenarios
335. the desired synchrony or lack of synchrony If two functions contain the same seed values they will return the same random number Seed values must be distinct to create independence of random numbers Proper use of random number seeds can be difficult Think carefully about the effect of any seed that you use in a function to be certain that it will produce the same random numbers when you want them and independent random numbers otherwise Any variable e g A for age Y for year R for run P for population included within the seed will cause the same random number to be chosen for each case with the same value for those variables A Y R P For example if you specify SRAND P within a function then each population will get an independent random number and that set of random numbers will be the same over all calls to evaluate that function such as for every year every run and every individual within each population If you specify SRAND P 100 Y then each population will get a new independent random number each year of the simulation but the set of random numbers will be the same across all runs of the simulation You would normally want to include the variable R in the random number seeds e g SRAND R 10000 P 100 Y in order to cause the random numbers to be independent among runs See the examples below for further information about random number seeds The seeds used by VORTEX will be converted to integers between 0 an
336. the effects of inbreeding are due recessive lethal alleles and about half of the effects are due to heterozygote advantage or other genetic mechanisms that are not diminished by natural selection during generations of inbreeding although the proportion of the total inbreeding effect can vary substantially among populations Lacy and Ballou 1998 A full explanation of the genetic mechanisms of inbreeding depression is beyond the scope of this manual and interested readers are encouraged to refer to the references cited above VORTEX can model monogamous or polygamous mating systems In a monogamous system a relative scarcity of breeding males may limit reproduction by females In polygamous or monogamous models the user can specify the proportion of the adult males in the breeding pool Males are randomly reassigned to the breeding pool each year of the simulation and all males in the breeding pool have an equal chance of siring offspring Deterministic processes VORTEX can incorporate several deterministic processes in addition to mean age specific birth and death rates Density dependence in mortality is modeled by specifying a carrying capacity of the habitat When the population size exceeds the carrying capacity additional morality is imposed across all age classes to bring the population back down to the carrying capacity Each animal in the population has an equal probability of being removed by this truncation The carrying capacity can
337. the program now has options that were not available in version 9 see above Lacy R C 2000 Considering threats to the viability of small populations using individual based models Ecological Bulletins 48 39 51 Reprinted with permission of the publisher 161 Ecological Bulletins 48 191 203 Copenhagen 2000 Structure of the VORTEX simulation model for population viability analysis Robert C Lacy Lacy R C 2000 Structure of the VORTEX simulation model for population viability analysis Ecol Bull 48 191 203 The structure of the VORTEX computer simulation model for population viability analysis is outlined The program flow is described here in order to provide a detailed specificarion of the structure of a widely used population viability analysis model VORTEX is an individual based simulation program that models the effects of mean demographic rates demographic stochasticity environmental variation in demographic rates catastrophes inbreeding depression harvest and supplementation and metapop ulation structure on the viability of wildlife populations The model facilitates analysis of density dependent reproduction and changing habitat availability and most demo graphic rates can optionally be specified as flexible functions of density time popula tion gene diversity inbreeding age and sex VORTEX projects changes in population size age and sex structure and genetic variation as well as estimating pro
338. ther folders The default project file type searched for will be an xml file but the dropdown list also allows you to instead search for VORTEX 9 vpj files E Open Organize v New folder YX Favorites Name Date modified Type HZ Desktop de VOutput 3 12 2014 5 12PM Filefolder Downloads beginning pop 700 xml 3 3 2014 2 18 PM XML Document We Dropbox Conservation xml 3 12 2014 5 12 PM XML Document E Recent Places 2 Hainan Gibbon xml 3 8 2014 12 21 PM XML Document New Project xml 2 11 2014 2 54 PM XML Document HZ Desktop Libraries ES Documents J 5 items File name Vortex Project File xm Unlike version 9 Vortex cannot have several projects open at once However you can start several instances of Vortex and have each one running a different project On modern multi core processors several concurrent Vortex s may run almost as quickly as a single Vortex runs its simulation However don t open the same project simultaneously in several instances of Vortex because they will likely run into conflicts while writing to output files Also it is best not to run multiple projects in the same folder at the same time because a conflict can sometimes occur during the writing of temporary files It is safest to run the multiple projects in different folders Running VORTEX from a Command prompt It is sometimes useful to be able to run VORTEX projects from a command prompt
339. thod is that within Special Options you can specify that the initial kinships of a studbook population or a subset of it are to be read from a file If such a file is provided these kinships will be used in place of any default kinships or the values given in the above Genetic Management option All three of these methods can be involved in the setting of the initial kinships of a Scenario if for example some kinships are specified for studbook individuals other kinships for founders of one or more populations are specified in the Genetic Management option and the default initial kinships of 0 are left in place for yet other populations in the Scenario Keep in mind that kinship coefficients and the inbreeding coefficients calculated from them will impact inbreeding depression only to the extent that inbreeding depression is due to heterozygote advantage rather than recessive lethals See section on Inbreeding Depression The recessive lethal alleles are modeled with simulated loci with each founder carrying unique lethal alleles and the frequencies of those lethal alleles is not affected by whatever you specify for initial kinships and inbreeding 67 Maximum number of female mates The option allows you to put a constraint on the number of females to which a male can be paired each year This option can be useful to constrain harem size or to prevent a single male from dominating breeding when pairs are selected by using a static MK list
340. tion for each iteration of the year of extinction if extinction occurs final population size and if extinction does not occur the final gene diversity mean inbreeding coefficient and number of alleles remaining The data in this table can be used to analyze the full distribution not just the mean and SD of the times to extinction final population sizes and genetic statistics The Save As button will export the tables as text files delimited with semi colons or commas or as Excel files MN O BARA lo File Simulation Help D fe Det D ST Tables and Graphs Project Report su GeneDiv Inbreed 82 ST Tables The last tabbed page of Text Output provides the same information as the Scenario Summaries of the Output Tables but with results from ST Analyses This tab will be blank if no Sensitivity Tests have been run Other Output Files Another standard output file with extension N provides a tally by year and iteration of the population size These are the data that are used to create the display of N while the simulations are running There are several other optional output files See Special Options under Project Settings above Note that the N file and the optional output files can be very large but they also provide the raw data that can be fed into other programs for further statistical analysis 83 Tables and Graphs This section provide
341. tion of extinction This can be useful if you want to know the likelihood that the population will fall below some goal that might be set for management reasons or because other analyses suggest that such a population size is a threshold below which population dynamics enter an unstable or otherwise undesirable zone An application that might be especially valuable is in the determination of threatened status and setting recovery goals for species Carroll et al 2014 The US Endangered Species Act defines a Threatened species as one that is likely to become Endangered in the foreseeable future If Endangered for a species is specified for example to be a more than 20 chance of extinction within 100 years then sensitivity testing might indicate that Endangered should be defined to be a population with N less than for example 160 Interval quasi extinction graphs examined for simulations with different starting populations sizes might then indicate that a population with initial N 500 has a 50 chance of falling below this Endangered threshold within the next 100 years as in the next Figure so that criterion defining Threatened status or the reverse the delisting goal for exiting from Threatened status would then be set at N 500 This could be a rigorous method to define the threshold for the Threatened status in a way that 88 is consistent with the wording of the law as opposed to the wild guess hand waiving that is usually done
342. tion persistence at small numbers It is also possible to use models that include both the effects of inbreeding on demographic rates and the effects of reduced genetic variability on vulnerability to environmental variation and ability to survive catastrophes The individual based mod el VORTEX Lacy 2000 can accommodate such depend encies on inbreeding and similar effects could be built into population based matrix models as in INMAT by Mills and Smouse 1994 Parameterization of models with ge netic demographic interactions is difficult but data are in creasingly available on the effects of inbreeding on demo graphic rates Ralls et al 1988 Brewer et al 1990 Saccheri et al 1998 persistence through environmental stress Miller 1994 Keller et al 1994 and population extinc tion Frankham 1995b Saccheri et al 1998 Interactions among threatening processes Although each process described above can individually threaten the viability of small populations synergistic in teractions exacerbate the impacts of many of the processes and are at the center of extinction vortices Gilpin and Soul 1986 Interactions among threats are sufficiently 45 complex that they are often omitted from analytical PVA models and from the functions driving demographic pro jections in simulation models Most analytical models are constructed by deriving the impact that a factor would have when acting in isolation from other threatening proc
343. tion size N at throughout Mortality calculations will be the value arising from the prior Breeding cycle and the population size N used in Supplementation will be the value after the prior Harvest assuming the default sequence of events in the year This timing of updates to population counts is different than in Vortex 9 in which the values were updated only once each year in the Census within the fixed annual cycle Even without specifying rates as functions many of the rates used in VORTEX can be specified to be different for different years sexes ages or inbreeding levels e g age specific mortality inbreeding depression in juvenile mortality linear trends in K etc Be aware that the effects of any functions entered are imposed on top of such dependencies that might be given in the standard input format For example EV in carrying capacity could be specified via standard input or via a function of the type K 100 10 NRAND thereby giving an annual level of EV in K equal to a standard deviation of 10 An advantage of creating EV by specification within functions rather than more simply as a parameter given to VORTEX is that you have greater control over how EV is implemented in the model For example it is possible to specify that EV is concordant between two populations but not with others RATE 50 10 SNRAND Y R 100 P gt 2 100 SRAND P In this function the overall mean demographic rate is 50 with a
344. tis ses dsat dk Pesta e A ER tines 92 Sensitivity Tests ii a dad aiii 93 Graphing ST results umi td Ri Ai a A EA didebentss 100 Using Functions in VORTEX ascii poneo agta eiie PE A Ea RAA E Tisa AE EPAR EOE Si 105 Primary changes in Functions from VORTEX 9 to VORTEX 10 ecesesseeseetececeeeeeeeceeeeseeeeeeaeees 106 Specification of Demographic Rates as Functions ooocooccoocconnnonnnonnnonnnonnnonn nooo ccon nono nono nocononos 108 Using the Function Editot sss rrecn i a nono nono noon nono E nono naco EA r rn a rr rr rra 109 Variables and Operators Available for Use in FUNCtiOns cccccsccesscessceeeceeeeeeeeeeseeseeeeeeseeesaes 111 Accessing histories of State Variables ooooonnoninoniconinoninononononnnonnncon ccoo nono noconoconn carr ran nrannnnaos 118 Using Random Numbers in Functions cccccccccsseessecsseceecesecesecsseeseeseeeeeeeeeseesseeeeeenaeeaaes 118 Notes Regarding Function Syntax and USO oooooonncociconoconnonnconnonnnonnccon nooo noco noc nn coronaria cnn rnnnnanars 119 Using Functions to Examine Genetic Evolution ooonccioconocononoconaconnnono corn nnnn oran ornnronnnrnn cnn 121 Examples of Rate FUNCtions ccccccccsseesseesseececeeceecaeceseceseceaeesaeeseeseeeseeeseseeeseeeseeeseeeaaes 122 An Overview of Population Viability Analysis Using VORTEX 0 ccccccccceesseesseeneeesseesseesseenseenseenseens 131 Primary changes from Vortex 9 to Vortex 10 oo ceceseecceseeseeescesecseeeceesecee
345. to enter default values for any variables that you will be using in functions These values will then be used when the functions are evaluated before the start of the simulation to obtain demographic rates for deterministic calculations This can be useful because otherwise deterministic calculations are often meaningless as they are not deterministic or often even determinable Also the deterministic 32 calculations of survival and fecundity schedules will be used in calculating the stable age distribution which might be needed on the Initial Population Size page and for some other options such as the Breed to K option in Genetic Management Note however that if a reproductive rate or a mortality rate is specified as a function of age A then that dependency on age will be considered in the calculations of deterministic population growth and the stable age distribution but not the Breed to K calculations each year even if a default value for A is not provided by the user It can be confusing to know what happens when you enter both an Initialization value for a GS variable or for a PS variable and enter a Default value for that state variable What gets used to first set the value the Default value or the Initialization Any Default value for a state variable is used before the iterations are started i e when deterministic calculations are performed and when input functions are first checked for mathematical val
346. to the VORTEX program folder a document file Change Log for Vortex 10 doc that lists the primary changes that have been made recently to the VORTEX program This change log is also available on the website 11 Creating your Vortex Project Entering data Project Settings Project Name A Project Name can be almost any label that you want However it will be used in the filenames for output files so do not use any characters such as or that might be invalid within a filename You might want to use relatively short Project Names to avoid very long file names Project Notes In the Project Settings you have the option to add any notes that you wish to make to document the Project It is also often helpful to include within these Project Notes the names of the user team that is developing the project this documentation may be especially helpful in workshop or classroom settings We strongly encourage you to take the time to add notes to your Project at this window during specification of input parameters and in your Project Report The extra few minutes you spend documenting your work EF may save you and others many hours of work later when you try to remember what information and logic was used to create the project Unfortunately many PVAs are not reproducible because the authors did not fully document their work gt eee Z Vortex 10 New Project CAVisual Studio 2010 Vortex Vortex10 bin Release
347. ty and instability is being ignored in your analysis A difficulty with these approaches which may add a significant bias if sample sizes are small is that some of the year to year variation observed in reproductive and mortality rates is actually due to the expected demographic stochasticity resulting from random sampling of individuals even if environmental factors do not cause fluctuations in the annual probabilities of birth and death Refer to the Box below for methods of removing this source of variation as a means of estimating EV alone Distribution of broods per year You can specify that each breeding female may have more than one brood or clutch or litter in each year On the previous input page you provided the maximum number of broods that can be produced by a female in a year In this table you now specify what percent of breeding females produce each number of broods Note that this table refers to those females that are the adult females breeding specified immediately above The difference in VORTEX between a female that is not breeding and one that is breeding but produces 0 broods is that in the first case the female will not be paired with a male while in the second case she will This distinction will be important in monogamous species because it determines whether any males are paired with non successful females If you do not use any functions for rates in this table the last row will automatically be filled in so th
348. ty is defined as I Jxy Jx Jy 0 5 and it scales from 0 to 1 for populations that are completely unique sharing no alleles to ones that have identical allele frequencies Nei s standard genetic distance is defined as D In D and it scales from 0 to infinity for populations that are identical to ones that share no alleles note that D becomes undefined when two populations have no alleles in common Finally at least with respect to genetic distance measures reported by VORTEX a very commonly used measure of genetic differentiation is Gsr more commonly symbolized as Fsr although Fsr is used in various contexts not all of which relate directly to allele frequencies Gsr Der Hr Hr Hs Hr Unfortunately there are a number of problems with Gsr as a measure of population divergence the most notable being that it does not actually measure the genetic difference between populations Gg measures the reduction in gene diversity H within subpopulations relative to the gene diversity of the metapopulation If the subpopulations each have high diversity then Gsr will be nearly 0 even if the subpopulations share almost no alleles In fact distinct species can have Gsr 0 so obviously it is not a good measure of genetic divergence The history of Gsr or Fst being used as a measure of population differentiation arises because when there are only two alleles in the metapopulation at each locus studied then populations cannot
349. ulations If both sexes are capable of moving between populations and the ages at which males and females disperse are different you must decide which age s you use for these fields This decision will be based largely upon how conservative you want to be about your estimation of potential risk For example if males begin moving among populations at 3 years of age and females at 5 years of age entering 3 as the youngest age to disperse may underestimate the risk of population decline and or extinction since females are allowed to move at an earlier age in the model It is possible to specify different rates of dispersal for the two sexes or for different age classes by using the Dispersal Modifier Function described below 34 Dispersing Sex es Check the appropriate box es to specify whether males females or both can disperse from the natal population Percent Survival of Dispersers Often dispersal among populations occupying discrete areas of suitable habitat is dangerous Traversing the matrix of unsuitable habitat between populations may expose an individual to additional risks of predation or lack of food and entry into a new population may require competition with the established residents Enter here the survival rate as a percent of individuals that are dispersing between populations The dispersal mortality is imposed separately from other mortality detailed elsewhere in the program A dispersal survival rate of 80 means that
350. ulations for the year END NumberPopulations IF FOR each population p LOCAL_EV_RANDS CATASTROPHES p Determine if catastrophes occur that year Determine carrying Capacity K for year II See Note 3 Add LocalKEVNRand LocalKEV p to CarryingCapacity p 1 Adjust K for local EV Add GlobalKEVNRand GlobalKEV p to CarryingCapacity p II Adjust K for global EV BREED p Go through breeding cycle to produce offspring MORTALITY p Determine who dies that year END population LOOP Add 1 to the age of each animal IF NumberPopulations gt 1 MIGRATE ECOLOGICAL BULLETINS 48 2000 Determine which animals migrate between populations END IF FOR each population p IF year during which animals are to be harvested HARVEST p END harvest year IF END population LOOP FOR each population p IF year during which animals are to be supplemented SUPPLEMENT p END supplement year IF END population LOOP FOR each population p Tally PopulationSize p IF population is not extinct AND population was not extinct prior year 11 Extinction can be defined by the user as the absence of one sex or as the population size falling below a specified lower limit r p log PopulationSize p PopulationSizePriorYear p 1 Calculate population growth rate 7 END IF IF not extinct AND PopulationSize p N gt CarryingCapacity p KY FOR each living animal IF RAND gt
351. ulations after they have become small Caugh ley called for more theory to guide the declining popula tion approach more data to support the small population approach and better use of the strengths of the two ap proaches to guide conservation but he also questioned whether too much emphasis has been given to small popu lation processes in wildlife conservation Hedrick et al 1996 argued that the problems of small populations have at times been under appreciated but also that the process es causing population declines and the processes affecting populations that have become small are inter linked in complex ways so that PVA and conservation biology must encompass both of Caughley s paradigms The problems of small populations have received exten sive theoretical treatment e g Soul 1987 but further assessment of the factors affecting viability of very small populations is needed I will argue that we often underesti mate the importance of these factors in population viabili ty as the magnitude and even direction of some of these effects may be different than has been commonly sup posed Although I believe that the problems inherent in small populations are more numerous and more severe than is commonly recognized the same may be true of the causes of population decline However because additional threats to population viability arise as populations become small the kinds of PVA models that are needed for assess ing the
352. unctions and operators This check will also display the Function with extra parentheses added to make clear the order of operators and will give the function in Reverse Polish Notation to further verify that the function and its order of operators is being interpreted correctly by VORTEX You can and should evaluate the function with any specific set of variable values in order to see if it is returning the result that you expect First in the five tables of variables some of which may be empty if your scenario has no State Variables enter the value that you want assigned to any variable that is used in your function A handy list of Vars used is provided at the bottom of the tables Then hit the Evaluate button to see what value your function returns with those values for the variables If the Evaluate button is disabled that means that your function had invalid syntax and needs to be edited The Plot button will be disabled if the function syntax is invalid 109 As with other graphs in VORTEX you can print or save the graph and you can open the graph Properties by double clicking on the graph After you finish editing and testing a function you can hit Cancel or the close window icon x to return to the VORTEX data entry pages If you hit Accept then the function will be transferred into the current input data box if it was a box that allows a function to be entered Otherwise the Accept button will no
353. us americana could be tracked and censused from its breeding grounds in Wood Buffalo National Park Alberta Canada to its wintering grounds along the Texas Gulf Coast at Aransas National Wildlife Refuge During a Conservation Viability Assessment for this population Mirande et al 1991 estimated mortality rates for the population based on recorded sightings of banded birds From 1976 through 1989 about 234 5 cranes were observed to hatch at Wood Buffalo NP taking the midpoint of the possible range in those few years in which counts were imprecise of which 172 arrived in Aransas the following winter This yields an estimated juvenile survival rate of 73 3 During the 14 years of close monitoring of the Wood Buffalo population the observed variance around the mean survivorship of 0 733 was 0 047 The variance that would be expected from random binomial sampling based on this mean is 0 013 The difference V 0 034 or SD 0 184 can be attributed to environmental variation Mortality after the first year can similarly be determined from either data on banded birds of known age or from winter census reports from Aransas filed since 1938 young of the year are distinguishable from older birds upon arrival at Aransas Since 1938 a total of 2359 birds older than 1 year of age returned to Aransas out of a total of 2594 birds that departed Aransas the previous spring This yields an estimated annual mortality after the first year of 9 06 Among the
354. val across years can be accounted for by de mographic stochasticity Mirande et al 1991 The reduced variation in survival as the population grew in size from 18 birds in 1938 to ca 150 birds in the 1990s is clearly evident Demographic stochasticity has been recognized as a ECOLOGICAL BULLETINS 48 2000 Fig 1 Percent of whooping cranes observed each year on the wintering grounds which 50 did not survive to return the following year In years with no bar shown no birds died 40 Data from Mirande et al 1991 and pers comm 30 20 10 Percent Mortality of Adult Birds 0 Annual mortality of Whooping Cranes 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 potential threat to very small populations but the contri bution it can make to population instability has been un derestimated Based on simple calculations of the proba bility that all individuals will be of the same sex or die synchronously it has commonly been stated that demo graphic stochasticity can cause extinction only when pop ulations fall below ca 10 20 individuals Goodman 1987 Shaffer 1987 However processes that are not seri ous problems when acting alone can become significant contributors to population instability and decline when they act synergistically with other threatening processes The last five dusky seaside sparrows Ammospiza maritima nigrescens were all males an unfortunate but not overly sur prising event
355. variables True False code for whether the scenario is an ST sample number of the scenario being run CENSUS number of the current census same as Y if there is one census event per year 111 Valid Function Variables Population descriptors Dispersal rate from the matrix entered used only in functions modifying dispersal Number adult females Percentage of initial gene diversity expected heterozygosity in the population Mean inbreeding for a population calculated as homozygosity Number of juveniles age 0 1 Carrying capacity Number of adult males in the population Population size Population identifier recipient target population for dispersal or translocation synonym PP Number of subadults age gt 1 lt breeding age Number of females all ages Number of males all ages N for population p Recipient population of a dispersing individual for use in Dispersal Modifier functions PS1 PS2 PS3 PS9 Population State Variables previously defined PPS1 p PPS2 p etc Population State Variables for population p CAT c Number of years since last occurrence of Catastrophe type c CAT C gt maximum years if catastrophe has not yet occurred GDI ST p1l p2 Genetic distance between population p 1 and p2 GDI ST p1 p1 Genetic distance between population p 1 and the metapopulation The metric used can be specified in the Special Options The default is Nei s standard genetic distance
356. variation in the sex ratio for monogamous pop ulations of various sizes Even with 500 breeding individu als the mean number of pairs in the population is 3 6 below what would be available if the sex ratio were fixed at 50 50 This simple example of a threat to the viability of small populations illustrates several important points First the random deviation in sex ratio does not in itself cause extinction except in the very smallest of populations but it can interact with other factors such as the breeding system to depress population growth in a vulnerable popu lation sufficiently to cause extinction Second it is unlikely that biologists observing the population would recognize that fluctuation in the sex ratio was a contributing cause of lower reproduction and population decline Third it would be possible to incorporate the reduction in breeding as an average effect in a simple life table projection How ever to do so requires that the demographic rates were esti mated from a population of the size of the population be ing currently assessed and that the population remains constant in size This last assumption defeats the purpose of PVA The effect of biased sex ratios depressing repro duction in monogamous population of changing size could be modeled as a density dependent effect on repro duction Stephens and Sutherland 1999 Courchamp etal 1999 However I am not aware of any cases in which an analytical or population bas
357. vation of wildlife populations Inbreeding depression the reduction in fitness of in bred individuals frequently occurs when normally out crossing organisms mate with close relatives It is common ly believed that it is a problem only for captive populations which can be substantially buffered from many other risks facing small populations and for a very few and very small natural populations or perhaps only as a transient prob lem that would diminish as selection removes deleterious alleles during repeated generations of inbreeding Yet in creasing numbers of studies are showing that inbreeding depression can impact population viability to a greater ex tent more quickly and less reversibly than previously sup posed Frankham 1995b Lacy 1997 Jim nez et al ECOLOGICAL BULLETINS 48 2000 1994 found that inbreeding caused much lower survival of white footed mice Peromyscus leucopus that had been re leased into a natural habitat than would have been predict ed from laboratory measures of inbreeding depression A population of the greater prairie chicken Tympanuchus cu pido pinnatus which had suffered a demographic decline from ca 25 000 birds to lt 50 birds over 60 yr consequently lost substantial genetic variability and suffered reduced fer tility and egg viability from inbreeding depression Weste meier et al 1998 In Sweden inbreeding depression of fertility may have been the cause of the rapid decline to extincti
358. versity conservation Similarly the manual developed in partnership with the CBSG is provided for downloading because the CBSG cares about saving species and their habitats However the initial development and continuing improvement of the software and manual do represent a significant commitment by these conservation organizations The rate at which improvements can be made is determined by the resources available to support that work If your budget allows it please consider making a donation to support the further development of VORTEX If you find the software to be especially valuable to you consider donating perhaps US 100 a wild guess about the investment of resources per user that have gone into VORTEX or more or less as you feel is appropriate to the Chicago Zoological Society If you find the manual to be especially helpful consider donating to the CBSG As a side benefit to US tax payers donations to either the Chicago Zoological Society or the CBSG are tax deductible Donations to the Chicago Zoological Society should be as a check written to the Chicago Zoological Society sent to Vortex donation CET Chicago Zoological Society Brookfield IL 60513 USA Donations to the CBSG should be sent to Vortex donation CBSG 12101 Johnny Cake Ridge Road Apple Valley MN 55124 USA Starting VORTEX Most users will create and run VORTEX population simulations from within the VORTEX user interface although the functionality of the
359. w Ecol Bull 48 9 21 AsRSG 1996 Report of a meeting of the IUCN SSC Asian Rhi no Specialist Group AsRSG Sandakan Malaysia 29 Nov 1 Dec 1995 Ballou J D 1997 Ancestral inbreeding only minimally affects inbreeding depression in mammalian populations J He redity 88 169 178 Ballou J D et al 1998 Leontopithecus 11 The second popula tion and habitat viability assessment for lion tamarins Leon topithecus Conservation Breeding Specialist Group SSC IUCN Apple Valley Minnesota Barrett S C H and Kohn J R 1991 Genetic and evolutionary consequences of small population size in plants implications for conservation In Falk D A and Holsinger K E eds Genetics and conservation of rare plants Oxford Univ Press pp 3 30 Barton N H and Whitlock M C 1997 The evolution of metapopulations In Hanski I A and Gilpin M E eds Metapopulation biology Academic Press pp 183 210 Belovsky G E 1987 Extinction models and mammalian per sistence In Soul M E ed Viable populations for con servation Cambridge Univ Press pp 35 57 Boecklen W J 1986 Optimal reserve design of nature reserves consequences of genetic drift Biol Conserv 38 323 338 Boyce M S 1992 Population viability analysis Annu Rev Ecol Syst 23 481 506 Brewer B A et al 1990 Inbreeding depression in insular and central populations of Peromyscus mice
360. w York Longman Fisher R A 1958 The Genetical Theory of Natural Selection 2 ed New York Dover Fowler C W 1981 Density dependence as related to life history strategy Ecology 62 602 610 Franklin LR 1980 Evolutionary change in small populations Pages 135 149 in Soul M E and B A Wilcox eds Conservation Biology An Ecological Evolutionary Perspective Sunderland MA Sinauer Associates Foose T J R C Lacy R Brett and U S Seal eds 1993 Kenyan Black Rhino Metapopulation Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Gilpin M E 1987 Spatial structure and population vulnerability Pages 125 139 in Soul M E ed Viable Populations for Conservation Cambridge Cambridge University Press Gilpin M E 1989 Population viability analysis Endangered Species Update 6 15 18 Gilpin M E and M E Soul 1986 Minimum viable populations processes of extinction Pages 19 34 in Soul M E ed Conservation Biology The Science of Scarcity and Diversity Sunderland MA Sinauer Associates 155 Goodman D 1987 The demography of chance extinction Pages 11 34 in Soul M E ed Viable Populations for Conservation Cambridge Cambridge University Press Gunn A U S Seal and P S Miller eds 1998 Population and Habitat Viability Assessment Workshop for Peary Caribou and Arctic Island Caribou Rangifer tarandus Apple Valley MN Conservation Breeding Sp
361. we would not recommend that novice users or students use the function option within VORTEX Primary changes in Functions from VORTEX 9 to VORTEX 10 This section summarizes important aspects of functions that have changed in VORTEX 10 Considerably more pre defined variables are now available for use in functions some of the old version 9 variables have changed or been dropped and the syntax of functions has changed a little Therefore it is important to understand the changes if you will be opening old version 9 projects containing functions The variable for inbreeding I is expressed as a proportion 0 to 1 scale rather than a percent Default values for any variables used in functions can be specified in the input on the State Variables page If specified these values will be used when evaluating functions at the start of a simulation for determination of deterministic growth rates and stable age distribution For any variables pertaining to individuals e g age sex genotypes these default values will be used each year when evaluating functions that are needed for population level calculations such as 106 the number of pairings to reach K if that option is chosen or functions defining harvest or supplementation Order of precedence of operators within any parentheses follows standard rules rather than the strict left to right application of operators of VORTEX 9 Order of precedence of operators evaluated first at
362. werful method for determining the optimal number timing and even individuals for translocation to achieve genetic management goals for a metapopulation such as keeping within population gene diversity sufficiently high or maintaining between population divergence at a desired low or high level The choice between using allele frequency data versus pedigree data to calculate genetic distance metrics is a matter of what kind of data are available In captive and other intensively managed populations for which the pedigree can be tracked through the generations the kinship methods are easily applied and give precise values based on probabilities of shared alleles When the pedigree is not known assays of genotypes e g from allozymes microsatellite DNA SNPs or full sequences can be used to quantify genetic structure via the methods based on allele frequencies But note that some of the measures such as Gsr yield results that are very highly dependent on which measure of genetic diversity is used to obtain allele frequencies When both allele frequency data and pedigree relationships are available either methodology or both can be used and they should give comparable results unless the allele frequency data are inconsistent with the recorded pedigree In simulation models such as VORTEX the data are all hypothetical so we can use either method and make the results as precise as we want 81 Output Tables The fourth se
363. who need also to evaluate the situation Computer simulation models have increasingly been used to assist in PVA Although rarely as elegant as models framed in analytical equations computer simulation models can be well suited for the complex task of evaluating risks of extinction Simulation models can include as many factors that influence population dynamics as the modeler and the user of the model want to assess Interactions between processes can be modeled if the nature of those interactions can be specified Probabilistic events can be easily simulated by computer programs providing output that gives both the mean expected result and the range or distribution of possible outcomes In theory simulation programs can be used to build models of population dynamics that include all the knowledge of the system which is available to experts In practice the models will be simpler because some factors are judged unlikely to be important and because the persons who developed the model did not have access to the full array of expert knowledge 141 Although computer simulation models can be complex and confusing they are precisely defined and all the assumptions and algorithms can be examined Therefore the models are objective testable and open to challenge and improvement PVA models allow use of all available data on the biology of the taxon facilitate testing of the effects of unknown or uncertain data and expedite the comparison of the likely
364. wildlife have been described as extinction vortices Gilpin and Soul 1986 132 What is Population and Habitat Viability Analysis Analyses which have used the VORTEX simulation for guiding conservation decisions refer variously to Population Viability Analysis PVA Population and Habitat Viability Analysis PHVA Population Vulnerability Analysis Population Viability or Vulnerability Assessment and other variants on the name This diversity of terminology has caused some confusion among practitioners of the PVA or PHVA approach and probably even more confusion among wildlife managers who have tried to understand what analysis was being described and whether it could be a useful tool in their efforts to conserve biodiversity The diversity of perceptions about the PVA approach is not limited to its name Different people mean different things by PVA and the definitions and practice of PVA are constantly evolving We don t think it is not the case as has sometimes been suggested that some people are doing PVA correctly and others incorrectly but rather that people are using different if related kinds of analyses and labeling them with the same or similar terms What analysis is correct depends on the need and the application Below we attempt to clarify what PVA is by suggesting a more consistent terminology and by describing the features that characterize the application of the PVA approach to con
365. wly from population bottle ECOLOGICAL BULLETINS 48 2000 necks Moreover of the few PVA models which consider genetic effects e g INMAT Mills and Smouse 1994 VORTEX Lacy 2000 and see Menges 2000 for referenc es on plant PVAs usually an assumption is made that individuals at the start of the population projection are all unrelated and noninbred Thus we may under appreciate existing or imminent genetic problems in populations which have already lost much genetic variation For exam ple early analyses of the remnant population of the Florida panther Felis concolor coryi assumed that prior inbreeding would not diminish reproductive rates Seal and Lacy 1989 even though a majority of the males had only one or no functional testicles Seal et al 1992 Golden lion tamarins Leontopithecus rosalia rosalia are now restricted to very small remnants of the original Atlantic coastal forest of Brazil have been reduced to a population of ca 350 an imals and scattered smaller populations Ballou er al 1998 have low genetic diversity Forman et al 1986 and show significant depression of juvenile survival when inbred Dietz et al 2000 Thus any PVA models that as sume tamarins presently have adequate genetic diversity may project perhaps incorrectly that the population could lose much more variation before genetic problems began to reduce population viability PVA modeling of small population processes As illustrated in the
366. x Min plot shows the range of results for each tested variable averaged across the values of all other tested variables A point is placed at the result for the base scenario but note as in the above graph that the ranges tested may not be symmetrical around the base in terms of the parameter values and or in terms of model results and the base may not even have been included within a range that was tested In a Max Min plot the variables with the longest lines had the greatest effect on results For all the sensitivity test results however it is important to recognize that the results for each variable and even which variables have the biggest impact over their tested ranges depends the ranges of values examined for all the variables and perhaps even on the other input variables that were not varied in the ST Due to interactions among factors adding more variables to an ST can change the picture you get of which variables are the most important drivers of population dynamics Perhaps the best approach to ST is to include every uncertain variable tested across its range of uncertainty This can easily generate a massive number of scenarios in an ST Analysis but the numbers can be more manageable if you use Latin Hypercube Sampling Also after a preliminary ST maybe with not enough samples to get precise results show that some variables seem to have very little effect more thorough sensitivity testing might proceed with that subset of vari
367. y Lacy R C 2000 Considering threats to the viability of small populations using indi vidual based models Ecol Bull 48 39 51 As wildlife populations become smaller the number of interacting stochastic processes which can destabilize the populations increases genetic effects inbreeding and loss of adaptability and instability of the breeding structure sex ratio imbalances unstable age distribution and disrupted social systems can decrease population growth and stability Recent analyses have shown that some populations can be very sensitive to these sto chastic processes at larger population sizes than had been suggested previously and often in unexpected ways Interactions among processes can reduce population viability much more so than would be assumed from consideration of isolated factors For exam ple in monogamous species random fluctuations in sex ratio will depress the mean number of breeding pairs in populations with as many as 500 adults At low population densities individuals may not be able to find mates or may not encounter individuals sufficiently unrelated to be accepted as suitable mates Inbreeding depression of demo graphic rates can become a significant contributor to population decline in populations with several hundred individuals even if genetic problems are not the primary threat Most models of genetic decay in small and fragmented populations assume demograph ic stability However when the incre
368. y a year and iteration Y R 1 in which no catastrophe for any age occurs Multi year catastrophes RATE 50 20 SRAND Y 2 R 100 lt 0 oe The catastrophes have a 2 year impact 90 0 F because the seed value is converted to an 80 0 L integer giving pairs of subsequent years the o 700 same random number The frequency per year amp eae is 10 so that the frequency of an onset of a fs 2 year catastrophe is 5 aon 5 40 0 J o E 30 0 4 A 20 0 10 0 0 0 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 19 Multi year catastrophes with a decreased impact in year 2 20 21 RATE 50 10 SRAND Y R 100 lt 0 05 8 SRAND Y 1 R 100 lt 0 05 The second seed is the same as the first seed from the previous year Thus the catastrophe has a lesser impact severity 0 84 rather than 0 80 in the second year This approach can also be used to model catastrophes which impact survival in one year using a function with an expression like that in the first brackets above and fecundity in the second year using a function containing the expression in the second set of brackets Note that in example 18 catastrophes always start in even numbered years while in this example catastrophes can begin in any year Random variation across years Demographic Rate 50 0 r r r r r r r r r 40 0 F A 35 0 30 0 25 0 20 0 15 0 10 0 5 0 F 0 0 0
369. y dependence with an equation that specifies the proportion of adult females that reproduce as a function of the total population size Normally the proportion of females breeding would decrease as the population size becomes large In addition it is possible to model an Allee effect a decrease in the proportion of females breeding at low densities due for example to difficulty in finding mates The table that is provided to help you build a model of density dependent breeding creates a function of a form that has often been used to represent density dependence in vertebrates If you use this table then the function that you specify will be transferred to the first data entry box for breeding on the next page You can further edit the function there or enter any other function for density dependence Density dependence in any other parameter in VORTEX e g mortality or dispersal can also be specified by functions but the density dependence in reproduction is provided here because that is often thought to be a parameter that is particularly sensitive to population density The equation that VORTEX uses to model density dependence is N N A P N PO PO PEK YD in which P N is the percent of females the breed when the population size is N P K is the percent that breed when the population is at carrying capacity K to be entered later and P 0 is the percent of adult females that breed at low densities when there is no
370. y population declines in some areas would be offset by growth elsewhere In PVA models consideration should be given to whether the amount of environmental variation in the sys tem should change with range contraction and expansion Unfortunately data on variation in demographic rates are woefully inadequate for almost all species Usually we have no more than crude guesses as to the magnitude of envi ronmental variation for use in population viability analy ses There would be considerable value in a compilation of data across species which would allow generalizations con cerning the typical magnitude of fluctuations in demo graphic rates for species with various life histories trophic guilds and habitat types Figures 3 and 4 show two examples of fluctuations in natural populations that contrast markedly in the extent to which they are impacted by environmental variation The population trend for whooping cranes during recovery from a near extinction shows the reduced relative fluctua tions in numbers as the population increased in size Cranes form long term monogamous pair bonds they re turn to nesting sites for a number of years they have low fecundity and they are very long lived Hence they would ECOLOGICAL BULLETINS 48 2000 Fig 3 Number of whooping cranes arriving each winter at E the Aransas National Wildlife 2 160 Refuge Texas Data from Mi 5 rande et al 1991 g 140 D L 41207 o b 3 100 w
371. y sophisticated models will also become more specific to the individual taxa and environments under study PHVA workshops must incorporate consideration of the assumptions of the PVA model used and the biases or limitations in interpretation that could result PHVAs consider only those threatening processes of which we have knowledge for which we can develop algorithms for modeling or other methods for analysis and for which we have some data As a result it is likely that PVAs will underestimate the vulnerability of most populations to extinction and that PHVA workshops will be less comprehensive than is desirable We need always to be cognizant of the limits of our understanding of wildlife populations and to include appropriate margins for error in our conservation strategies PVA is by definition an assessment of the probability of persistence of a population over a defined time frame Yet persistence of a population while a necessary condition for effective conservation of natural systems is often not sufficient Prevention of extinction is the last stand of conservationists but the goals should be higher conservation of functional biological communities and ecosystems PVA usually ignores the functional role of a species in a community but a PHVA workshop should consider much more than the prevention of the final biological extinction of the taxon A species such as the American Bison Bison bison can be functionally extinct in terms o
372. y times to generate the distribution of fates that the population might experience VORTEX is an individual based model That is it creates a representation of each animal in its memory and follows the fate of the animal through each year of its lifetime VORTEX keeps track of the sex age and parentage of each animal Demographic events birth sex determination mating dispersal and death are modeled by determining for each animal in each year of the simulation whether any of the events occur VORTEX requires a lot of population specific data For example the user must specify the amount of annual variation in each demographic rate caused by fluctuations in the environment In addition the frequency of each type of catastrophe drought flood epidemic disease and the effects of the catastrophes on survival and reproduction must be specified Rates of migration dispersal between each pair of local populations must be specified Because VORTEX requires specification of many biological parameters it is not necessarily a good model for the examination of population dynamics that would result from some generalized life history It is most usefully applied to the analysis of a specific population in a specific environment In the program explanation that follows demographic rates are described as constants specified by the user Although this is the way the program is most commonly and easily used VORTEX does provide the capability to specify m
373. years and older Note that although it can be 350 tedious any rate function can be modeled by 2 30 0 specifying the rate for each interval of the 25 0 dependent variable gt 2001 5 15 0 10 0 5 0 1 0 0 0 10 20 30 40 50 60 70 80 90 100 Age Years 12 Cyclical response 13 14 RATE 50 10 SIN PI Y 5 Here the rate fluctuates between 40 and 60 according to a sine wave with a 10 year periodicity Regular pulses of a higher rate RATE Y 8 0 20 30 Background rate of 30 jumps to 50 every 8th year Note that the order of operators was left to the VORTEX default left to right This is not a safe practice but it does work in this case Pulses of longer duration RATE Y 8 lt 3 20 30 The rate jumps to 50 for a 3 year time span every 8th year In this case parentheses were used wisely to be sure that the intended order of operators was followed Demographic Rate Demographic Rate Demographic Rate 126 30 0 10 0 0 0 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 50 0 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 5 0 F 0 0 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 50 0 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 f 5 0 F 0 0 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 15 16 17 18 Random pulses catastrophes RATE 50 20 SRAND
374. zation and Transition functions if necessary to the values you intend for each population Make sure that you remember to set the PS variables for each population and then re check EF them all before moving on to further data input It is easy too easy to forget to set the PS variables for the populations after the first one Individual State IS Variables VORTEX also provides the user with the option of creating any number of Individual State variables that define characteristics of individuals These state variables may represent any feature of the organism that can be specified or coded by a numeric value For example dominance status might be encoded as Dominant 1 0 Subdominant 2 0 and Subordinate 3 0 Or a state variable might be used to represent some measure of body condition Or two state variables might be used to track the x and y coordinates of each individual s location on a landscape 31 To create one or more individual state variables click the Add button for each variable you will be creating For each variable you then enter into the table a label which can be any text that will help you to remember what parameter you were representing For each IS variable you need to enter three functions or constants to define a an initialization function Init fn the starting value for each individual at the beginning of the simulation b a birth function Birth fn the value for each newborn individual

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