Population Analyses
Contents
1. 103 21 13 11 08 06 06 00 82 36 26 24 15 18 04 15339 22 21 16 08 TO9S 38 31 15 013 113 64 29 22 124 45 22 95 25 38 962 702 1132 1201 1199 1155 1131 906 353 2 Below are data that mv graduate students and I collected on muskrat populations on the Mississippi River Pool 9 The first matrix below is recoveries of Males and group 2 is Females Clark 1987 analyzed these data using the S amp f parameterization in ESTIMATE But using th use the S amp r parameters to separate the encounter process r Dead Recoveries option in MARK you can from the survival process S and thereby consider a greater Consider whether there are differences in survival and recovery rates between sexes and among the years variety of models Notice that releases wer done for 4 years and recovery for 5 ie years Can you run the original S amp f parameterization in MARK with these data Estimate the S amp r parameters and interpret the results How can you do goodness of fit testing in this framework 65 9 1 86 14 117 32 7 1 7S c19 112 204 240 301 GOGO O O O OJsHLO Population Analvsis Fall 2005 21 Homework 7 The data given below from a telemetry study of wintering black ducks were analyzed by Pollock et al Biometrics using failure time approaches The example is distributed with MARK as a known fate example It is an excellent example to use2. EE hvpothesis using a PIM modified bv a Design Matrix For confidence vou might build the F N hvpothesis using just PIMs then see if vou can get the same results using PIM and DM coding Is there more than one wav to visualize the DM coding depending on whether you start with a global model or a reduced model Population Analvsis Homework 6 survival lations as well as other animals Fall 2005 19 Band recoveries have been widelv used for estimating and the approaches have been applied to The British Trust for rates of birds fish popu Ornithologv uses related methods limited from ringing adults MARK provides two Recoveries Brownie et al Dead Recov studies birds banded as adults onlv or birds referred to in class as the although statisticallv more Ana structures m r ries the f are older programs called parameterization that are These can be downloaded from The data below are for mal MATE and BROWNIE EST usef the Patuxent web page lyses can be conducted on banded both as young and for these analyses parameteriza parameterization for the S ul for goodness of fit testing Dead tion and There amp f lards banded as both adults and voung in
3. the San Luis Vallev of Col orado distributed with MARK Brownie inp these data are an example Xou can use the Brownie dbf database to give a thorough explanation of the model comparisons and parameter estimates Examine the models in the Brownie dbf database and explain how the MARK notation corresponds to the original model designations in Brownie i e what is equivalent to model H You 1ll note that the best model reported in Brownie dbf is modified by random effects trace Search the MARK documentation to see if you can discover the concepts of variance components that underlie conclusions about differ this model neces betw Finally talk about your n parameters for adults and young You might take a look at the PI young Be sure that you understand the accounting parameters San Luis Valley Mallards Page 92 Brownie et al encounter occasions 9 groups 2 glabel 1 Adults glabel 2 Young recovery matrix group 1 10 13 06 01 01 03 01 02 O00 58 21 16 15 13 06 O1 017 DA 39 235 18 LL 1006 44 21 22 09 09 03 55 39723 1 12 66 46 29 18 101 59 30 97 22 21 231 649 885 550 943 1077 1 recovery matrix group 2 83 35 18 16 06 08 05 03 O1 r 250 938 312 IM s for the adults and of all the 1985 Population Analvsis Fall 2005 20
4. Now run CAPTURE C Capture99 directory and POPULATION EST MAT adequate to obtain precision and rob by Start Programs Then input file o your output file ON Consider CLOSURE Interpret th results a reasonable estimate of N ustness of the model selected MSDOS Prompt at the prompt type CAPTURI MO n XY formats to Change to the DEL m E i vour SELECTION Was the survey considering bias 2 Next go on to see how well you understand underlying model structure by rerunning these same analyses with MARK you a quick lesson on starting MARK and show you the parameter PIM information matrix that will work for M 0 In M 0 I ll give there Population Analvsis Fall 2005 8 is one nuisance parameter p and N that vou ll estimate But MARK includes a parameter for recapture c to enable vou to model behavior and hetereogeneitv You should recognize that when there is no time or behavioral response p c for all times So the PIM s for M 0 look like PIM for p capture probability d i Bel oe L 1 PIM for c recapture probabilitv gt ky Sh ah le E E PIM for N 2 Write a couple of sentences explaining how the above PIM s reflect the model M O Run the model and see how the results compare them with CAPTURE Now construct PIM s for the Darroch mo
5. 1985 JWM 49 668 674 Heisey has developed has been widely used to analyze ICROMORT runs on in AECL611 MICROMOR fore beginning this assignment read Heisev and Fuller er on cottontail rabbits by Trent and Rongstad HF will R which they cite iss and you will be analyzing some data which Begin by simply running MI ROMORT to get a gram It s pretty simple to use if tle obtuse the first time through MICROMOR All of your work can be irt the program There is a user s manual ve the machine The first time led RABBIT SYS that is f a given on page 468 of ice bar to go to the next menu in the subdirectorv their paper Get to done h ti you run analyses After reading When you get to the Next 1974 D HF 23 and the program BM PC compatibles and and the JWM 38 469 472 feel for the you have been through it but a the subdirectory by typing type for MICROMORT in the cabinet read the system file This is TR s original the data hit the ISPLAY OPTI MORT lu you can change the printing options and then proceed to the ilysis M cefully if you decide to print ithing the first time through the analysis 9king at the quantities and comparing them with TR Now comes the real fun ilyses Below are some data for male and f re adapted
6. There is an emphasis on learning by doing through the homework problems REQUIR iD TEXT There is now a great text that covers the material in 611 and beyond Williams B K J D Nichols and M J Conroy 2002 Analysis and management of animal populations Academic Press 99 this book is one stop shopping for population analyses I strongly recommend that you purchase this book will also make available the pdf version of the manual Program MARK a gentle introduction Evan Cooch and Gary White Population Analvsis Fall 2005 2001 that can also be downloaded from Evan s web site http www phidot org software mark docs book It includes some of the conceptual material that we will cover as well as the practical applications of using the MARK softwar manv assigned readings from texts other manuals and the primarv literature e There will be We will plan the relative emphasis on the topics below as we see where our interests take us TOP IC OUTLINE ntroduction to population analvsis Li A Population dvnamics birth and death rates of growth and trends B What are you interested in Statistical concepts and tools A Sampling estimation of Precision bias confidence intervals Sampling and process error Power effect size J Jaw APPROX DATES A
7. as an introduction to survival analyses using PROCs FETEST LIFEREG and PHREG in SAS Hatch year refers to birds that were radioed during their first winter Days is the number of days to death or censoring ci l for death and ci 0 for censoring Condition refers to a condition index weight in g wing length in mm Hatch year birds After hatch year birds Days fone Condition Days GI Condition 06 0 4 286 02 1 4 188 07 1 4 394 06 0 4 500 14 0 4 275 13 1 045 22 1 3 992 16 0 240 26 1 4 576 16 1 4 115 26 1 3 730 17 0 5x259 2q 1 4 226 17 1 4 167 29 1 G ANA NO 20 0 4 118 32 1 35802 21 1 4 096 34 1 2741 28 0 4 873 34 1 348 32 0 4 529 37 1 4 596 41 1 3 818 40 T 3 964 54 0 4 632 1 078 57 0 4 684 49 0 4 216 63 0 4 982 56 0 4 007 63 0 4 704 56 0 4 556 63 0 3 818 Du 0 4 601 63 0 4 555 58 0 4 154 63 0 4 111 63 0 4 088 63 0 4 222 63 0 4 351 63 0 4 552 63 0 4 604 63 0 4 373 63 0 4 361 63 0 3 874 63 0 4 487 63 0 4 218 63 0 3 887 63 0 4 243 Analyze the data using both the Kaplan Meier product Population Analvsis Fall 2005 22 limit non parametric estimator and also the life table method available in SAS LIFETEST The first part of the code does th analvses You can learn about LIFETEST in Introductory Examples in the Lifetest Documentation Help Sample Programs or i
8. consider the sam case of a three capture survey On occasion 1 we mark and release n 100 individuals and then recapture them on occasions 2 and 3 The possible recapture histories are Xoo Xio Xo Xu Assuming that the recapture probability is different on occasions 2 and 3 i e Po Pp write the expressions for the probability of each outcome i e P Xg etc and then writ th xpression for the set of all outcomes the likelihood function Suppose that we have some prior experience capturing these animals and we think that p 0 20 and p 0 10 For each capture survey case below calculate the value of the likelihood for the two sets of observations below Case 1 Case 2 Xoo 80 40 X10 12 40 Xo1 be l 0 Xi kar al 0 For which case are the values of p and p that we picked more likely given these two sets of observations Can you roughly estimate the likely values of the parameters from the observations Population Analvsis Homework 2 1 Attached is an X matrix squirrels Fall 2005 from a recapture studv of fox The first part of vour assignment is to estimate population size Burnham 1991 using the most recent version of CAPTURE99 generally find it easiest to run prompt and store my files and work in a directory C Capture99 106 You can use you start with CAPTURE more straightfor
9. from the figure on page 469 of TR F solidify the concepts we have discussed in have adapted from TR tO ONS ICROMORT produces a large output so be sure to select options recommend that you not print rather spend your time creating your own data set and running emale cottontails which Population Analvsis Fall 2005 24 MORTALITIES SS NTERVAL DAYS RADIODAYS FOX OTHER es Mar Apr 61 380 2 0 May Jun 61 460 0 1 Jul Aug 62 665 0 0 Sep Oct 61 945 0 2 Nov Dec 61 850 3 0 Jan Feb 59 372 3 1 ales Mar Apr 61 310 1 0 May Jun 61 42 0 2 Jul Aug 62 410 1 0 Sep Oct 61 790 3 1 Nov Dec 61 700 4 2 Jan Feb 59 420 1 0 Data entry is accomplished by the following steps jin by space bar swer the series of questions about classes intervals etc the DATA MANIPULATIONS OPTIONS select 1 for Subject Classes and give ves to the old classes reat this step selecting 2 for Rate Parameters and 3 for Time jervals males nter the lengths of intervals on one line followed bv turn reat for total deaths from cause 1 and cause 2 reat the entry similarly for females b At this point you have an option you can proceed with ilysis or save the data set I recommend that you save the data set as sur initials SYS This preserves your labels and allows you to reuse gt data later when you wish to pool If you continue analysis your els won t be as clear but calcu
10. Population Analvsis Fall 2005 1 Population Analyses EEOB AEcI 611 Fall Semester 2005 Scheduled meetings MW 12 Room 231E Bessey T 11 1 Room 231E Bessey INSTRUCTOR Dr Bill Clark Office 233 Bessey Phone 294 5176 email wrclark iastate edu AEcl 611 is evolving in response to very rapid changes in the field of population analyses changes in quantitative ecology courses at Iowa State and changes in student backgrounds and needs The overall objective of the course is to integrate estimation of parameters such as population density and survival rate with important questions in population ecology The emphasis in AEcl 611 is on understanding the statistical basis of various analytical techniques applying techniques to data on taxa including insects plants and all kinds of vertebrates and developing proficiency with current software like MARK PopTools and MATLAB PREREQUISITES The catalog prerequites for AEcl 611 are AEcl 312 Ecology Stat 401 Stat for Research and a course in calculus You will be expected to understand concepts of statistical inference to be able to execute a regression xi and Z tests and to use minimal concepts from calculus We will make substantial use of software on PC s including MARK SAS DISTANCE and others We ll often use the recitation session to get you started with homework problems and software
11. R SAS MARK C Proportional hazards applications Thanksgiving holiday week Nov 21 25 VI Distance sighting methods A Line transects Buckland et al 1992 Nov 28 30 DISTANCE VII Loose ends Dec 5 7 23 annual course evaluations Dec 15 COURSE GRADING Mid term Exam Final Exam 30 Q Homework 30 Class discussion 30 approximately mid term finals week including orals approximately one assignment per week 10 Population Analvsis Fall 2005 Homework 0 1 y 2x Plot y x and find dy dx 2 y 1 2x 3 x Find dy dx 3 y 3x 5 2x47 Find dy dx 4 y e Find dy dx 53 y ae Find dy dx plot y x and dy dx 6 y In x Find dy dx he y ln l x Find dy dx 8 In x y 9 In x y 10 n x Eix f N dN dt 0 015 N 2 Plot f N find and plot f N 12 Ne Me Find dN dt if N N at t 0 13 W a l e Find dW da dW db and dW dt 14 K T be Find dN dt I5 jit x 16 dx 1 x for a l and b 0 25 Population Analvsis Fall 2005 Population Analvsis Fall 2005 6 Homework 1 For a review of statistical concepts related to estimation and mark recapture complete problems 4 5 6 8 9 10 11 12 13 14 15 16 19 20 and 22 at the end of Chapter 2 in White et al 2 To follow up on Dave Otis example of the multinomial extension of the simple binomial probability distribution
12. capture data with both death and immigration stochastic model Biometrika 52 225 247 Jolly G M 1979 A unified approach to mark recapture stochastic model exemplified by a constant survival rate Population Analvsis Fall 2005 1 3 model pages 277 282 in R M Cormack G P Patil and D S Robson eds Sampling biological populations Statistical Ecology Ser 5 Internat Coop Publ House Burtonsville MD specialized models that led to great expansion on the original goals of estimation of N Jolly G M 1982 Mark recapture models with parameters constant in time Biometrics 37 301 321 Pollock K H 1975 A k sample tag recapture model allowing for unequal survival and catchability Biometrika 62 577 583 Pollock K H 1981 Capture recapture models a review of current methods assumptions and experimental design pages 426 435 in C J Ralph and J M Scott eds Estimating the numbers of terrestrial birds Stud Avian Biol 6 Pollock K H 1981 Capture recapture models allowing for age dependent survival and capture rates Biometrics 37 521 529 this paper was the basis for the development of JOLLYAGE Pollock K H 1982 A capture recapture sampling design robust to unequal catchability J Wildl Manage 46 752 757 this is the robust design paper Kendall has extended these methods considerably Seber G A F 1965 A note on the m
13. causes other than trapping d Assume that all of the trapping occurred during the 6th and 7th month after peak birth period of the cohort Write an expression for the cohort size at the beginning of the next year N in terms of the initial cohort size instantaneous mortality rates and time 2 Imagine a year of an animal s life divided into n equal time intervals and the quantity Z n the fraction of the population of 10 000 that die in each interval For Z 2 8 and a n 50 b n 500 c n 1000 calculate to 3 decimal accuracy the annual mortality rate from an expression of the numbers dying in each interval Compare each calculated value to the value of A derived directly from the instantaneous rate 853 For t 30 months and a corresponding finite mortalitv rate of 0 69 calculate the corresponding instantaneous rate Now calculate the correct instantaneous rate for a t 15 months b t 3 months c t 6 5 months directly from the instantaneous rate Can you write a general relationship between the instantaneous rates over time t and t 4 A bird s life is divided into the following life history stages with corresponding finite survival rates nestling s 0 75 lst 2 weeks fledgling s 0 60 next 6 weeks juvenile s 0 80 10 months adult s 0 90 next year aarp Population Analvsis Fall 2005 16 Calculate the finite survival over the first 2 vears of l
14. del M t and Zippin model M b and run those in MARK Interpret the model selection for these 3 models and compare the estimates and confidence limits obtained from MARK with those obtained from CAPTURE CAPTURE RECAPTURE OF FOX SQUIRRELS ID X MATRIX y 110010 0 2s Te 1 4 0 O 3 Ar dr LA 4 1 1 1 1 1 5Ssdedui 1 0 3 6 LLLA 1 TA hl 0 4 0 0 0 811011 1 90110 0 0 0 0 10 01001 0 11010003110 1 12 0 Q 21 17070 13010000000 0 14 O 1 1 0 1 1 150010 000 0 0 16 0 0 1 0 0 0 0 0 170031001 0 1 180011 1 19 001 0 20001000 0 0 0 21001 1001 1 2200310001 29 0 00 0 1 24 0 0 0 25 0 0 0 000 0 0 Fall 2005 Population Analvsis 0 0 0 0 0 0 0 0 1 26 0 0 0 0 27 0 0 0 0 28 0 0 0 0 29 0 0 0 0 30 000 0 0 3 0 0 0 0 32 0000 0 0 33 00000 0 34 00000 0 0 35 00000 0 0 36 00000 0 0 37 00000 0 0 38 000000 0 0 0 39 00000000 0 400000000 0 0 Population Analvsis Fall 2005 10 Population Analvsis Fall 2005 lol Homework 3 Here are some small mammal trapping data that were collected in Wvoming bv Terrv Hingtgen and mvself see Hingtgen and Clark 1984 J Wildl Manage 48 1255 1261 The goal of this homework is simply to analyze another data set using program CAPTURE f
15. ework 3 fox squirrels but only use the data for days 1 5 Calculate the entries for a Jolly trellis using the outline given by Blower et al that gave you Then calculate the population size survival and gain birth for all days for which this is possible Note that capital letters indicate both the date and number of captures and releases Each recapture entry ie aj has its occasion of release above and its occasion of recapture to the left In addition to the introduction to MARK and the associated bibliographies I have included other references that I find useful These might be considered foundation references Arnason A N and L Baniuk 1978 POPAN 2 A data maintenance and analysis system for mark recapture data Chas Babbage Research Centre St Pierre Manitoba this original manual is a very good source of details on Jolly Seber methods Carothers A D 1971 An examination and extension of Leslie s test of equal catchability Biometrics 27 615 630 methods for testing assumptions about capture heterogeneity using taxi cabs in London Carothers A D 1973 The effects of unequal catchabilitv on Jollv Seber estimates Biometrics 29 79 100 Cormack R M 1972 The logic of capture recapture estimates Biometrics 28 337 343 a tough paper to read but a foundation paper Jolly G M 1965 Explicit estimates from capture re
16. ife plot a survivorship curve and compare that curve to a plot of the mortality pattern if you assume a constant rate over the entire 2 year span Da Given below are population estimates and standard errors for muskrats on the Upper Mississippi River derived using closed capture methods i e Otis et al Trapping survevs were 5 davs long conducted simultaneously in 2 habitats and centered on the dates given Habitat A Habitat B 15 April Os Sea 10 10 23 15 Sept 3 6 0 6 OD HH O62 a Plot the population estimates with 95 confidence interval error bars b Calculate a z statistic to compare the April population estimates between habitats A and B Cis Calculate estimates of survival over the interval Compare these statistically using a similar z statistic Population Analvsis Fall 2005 17 Homework 5 To learn the basics of MARK for analyzing survival data you will analyze the dipper data presented in Lebreton et al 1992 For the CJS models presented in Lebreton you could use JOLLY for some of the basic analyses but you could not model the combinations of sex specific time specific and more complex relationships with flooding that were presented Remember that dippers were marked and recaptured for 7 consecutive years along the streams where they breed generally in mated pairs resulting in 6 intervals between occasions The 2 sexes are treated as 2 groups and tests can be c
17. in the year that the initial xort goes to extinction a For each case is the population increasing or decreasing ww do the estimates of mortality obtained from the age structure ipare with the values you know to be true from your inputs b What is the direction and magnitude of bias involved in imating the rates from the age structure in each case What sumption must be met when estimating mortality rates from the age cucture when using time specific samples Comment on the process of yositing samples from many years as is commonly done in game lagement Analvticallv show that q will be an unbiased estimate of the ie rate a when A 1 given that a the actual mortality rate of age class x to x 1 qx the estimated mortality rate from life table analysis and A lyen lxgt the finite growth of the population
18. lations will still be correct on If you saved your data start again by Reading the data gt the list models option to see the data Toggle the variances and relations matrices off to avoid volumes of output You can always get m later if you want them Ons Analyze the full model data Are there significant ferences in survival between months Construct z tests to determine certain months can be pooled TR might be of some use in deciding it is reasonable to try Are there differences between sexes Can you gt l sexes into one category of rabbits What can you say about the ferent causes of mortality Are these significantly different Use Population Analvsis Fall 2005 25 pooling options to combine categories intervals classes rates re this appropriate Work toward developing the simplest model that is the data How do you test between models Can you do it Population Analvsis Fall 2005 26 iework 10 Construct a cohort shrinkage table using vour favorite ceadsheet starting with 500 animals of age 0 in year 1 Minimum seding age is 1 year and productivity is 2 young female year with a 1 1 ratio at birth Do this for 2 cases Case I with Annual mortality 60 and Case with Annual mortality 40 Estimate the the age specific mortality rates and the ghted average annual mortality obtained from a life table analysis istructed from a time specific sample
19. n Allison s documentation for survival analyses with SAS a The code produces plots of both the survival distribution and the log log survival for each strata Please interpret thes diagnostic plots b Please interpret the tests of equality of survival between hatch year and after hatch year ducks c Examine the use of the condition index as a covariate to test whether there is a relation between condition and the survival of birds d Interpret the life table analysis that used intervals of 10 days Be sure to plot the hazard function What is the mathematical and ecological interpretation of the hazard function e After studying the output for the two age groups modify the code to run an analysis with the age groups combined f Now examine the estimates produced by MARK in the file KAPMEIER INP These analvses are for both age groups combined How do thev compare to the estimates produced in LIFETEST and to those published by Pollock et al 1989 Finally consider the last part of the SAS code generated by PROC PHREG This does proportional hazards modeling Please interpret the proportional hazards model parameter estimates and the risk ratios Population Analvsis Fall 2005 iework 8 methods of JROMORT that cvival data lave instal Heisey and Fuller M in recent years led MICROMORT
20. ocusing on estimating density rather than population size Tr The data set is called WYOM DAT and I have included the input format The data file includes lots of extra information that might be typically collected in a field study For example note that there are additional fields of data as well as the capture histories Columns 1 6 give the date 7 the grid code 8 11 the animal id 12 13 the species code 14 20 sex age weight and reproductive condition and 21 26 the trapping occasion x coordinate and y coordinate This last set of 6 columns is repeated 9 times for all trapping occasions 2 Write a CAPTURE program designed to consider model selection and estimation of density The overall grid was 14 x 14 traps spaced 15 meters apart Consider how estimation might be affected by the model chosen and the number of subgrids specified Check for closure uniform density and estimate density Interpret the results Population Analvsis Fall 2005 12 Homework There is now a huge literature on using recapture data to estimate parameters of open populations that started with Cormack Jolly and Seber in the mid 1960 s To get a intuitive feel for the Jolly Seber analysis I constructed this assignment to calculate a J S by hand following the procedures that researchers used before modern software T Use the X matrix you used in Hom
21. onstructed for differences between groups The encounter histories file is of the form LLLLL and is Program Files Mark Examples Dipper inp which is distributed with MARK Review the Cooch and White Gentle Intro if you need help on getting started with MARK again a The results data base Dipper dbf is distributed with the Mark examples and you can use it as a reference as you proceed with these analyses But want you to start from the raw input data to learn about the analyses So make a personal copy of Dipper inp on a zip disk Call it something vou ll remember like Dipwrc inp I used my initials Fire up MARK and click File New to get started First you ll select the Data Type in this case Recaptures only b Give your analysis a catchy title like Homework 6 Dipper WRC c Find the vour inp file on the zip disk bv using the Select File option vou ll note that MARK writes dbf and fpt files to vour zip disk or wherever vou tell it to find dippv inp Notice that vou can also View the input file from this menu The ip disk will become the working directorv for all MARK files When vou run a New analvsis with MARK it creates files called DIPWRC DBF DIPWRC FPT DIPWRC CDX in the directorv For future reference note that DIPWRC INP is an ASCII file that could have been created with WORDPAD or another text editor When creating yo
22. predefined models provides the best fit Compare your results with the analyses presented in Lebreton et al 1992 Answer these questions Does the global model fit the data Use RELEASE tests and bootstrap goodness of fit to answer this question Is there evidence of sex specific effects on parameters Is there evidence of time specific effects on parameters How do you run a Likelihood ratio tests between 2 models How do you know if and when you are over fitting the data What is the danger of testing hypotheses suggested to you by the data What is the difference between apparent survival f and survival S without Emigration E How could you detect if animals had emigrated from the study area think about model tests above Given the time variation suggested by the discussion in Lebreton et al are you surprised that models with time variation did not fit the data particularly well For a model with time effects plot M t vs t You can do this by Output gt Specified Model gt Interactive Graphics and selecting the correct parameters to plot of course you have to think about which model to specify and which parameters to select Given the conclusions of Lebreton et al about the time specific effects of flooding and the plot you just made can you envision how to model these effects with either PIMs or PIM s combined with Design matrices Concentrate on modeling the flood noflood
23. the data from i 11 14 bu JOLLY BUG originally distributed as JLVEXMP3 is data on male butterflies sampled in Colorado but of a species unknown to me These data were originally used by Jolly 1982 as an example Gl also want you to run JOLLYAGE e For an age structured problem we will use the data on northern pike given in Pollock et al 1990 The input file on the disk is PIKE ENG originally JAGEXMPL and was originally published by Pollock and Mann 1983 d There is another example on the disk called MARSHY BC originally JAGEXMP2 that is age structured data on Canada geese analyzed by Pollock 1981b Run this example too Population Analvsis Fall 2005 15 Homework 5 Teg Assume that the mortality rates for the following problems are constant in time a With a starting cohort of 1000 young muskrats find the overall mortality rates both finite and instantaneous if after 1 year 150 remain alive Express these rates on a yearly and monthly basis b Trappers are known to have trapped 600 of the animals that died in part a above Assuming that this report accounts for all trapping deaths what was the mortality rate of muskrats due trapping Again express finite and instantaneous rates on a yearly and monthly basis c Given no other information what is your best estimate of mortality rates due to natural causes all
24. ug 22 Maximum likelihood and information criteria Labor Day Holiday Mark release recapture recovery methods A Estimating population size of Closed Populations Sep 1 Binomial sampling multinomial models Sep 2 Otis et al 1978 CAPTURE amp MARK 3 Indices and Minimum N alive B Open populations estimation of N 1 Intro Jolly Seber Pollock et al 1990 Sep JOLLY JOLLYAGE Clark gone to TWS C Estimating survival b 1 Jolly and survival Sep Oct 2 Live recaptures Cormack Jolly Seber Lebreton et al 1991 JOLLY MARK D Extensions of CJS framework with MARK 1 Using MARK PIM s and Design Matrices Oct 2 Adding explanatory covariates 3 Estimating movements separating into S and yw Hestbeck et al 4 Estimating recruitment and rates of growth A Pradel et al Oct Aug 23 31 parameters and modeling 17 19 Oct 24 Oct 25 26 31 Population Analvsis Fall 2005 3 5 Robust design combining closed and open models Nov l 2 6 Dead recoveries Brownie et al 1978 Nov 7 8 MARK ESTIMATE BROWNIE 7 Resighting combining live and dead Barker s models IV Observations of failure times resampling methods estimating survival S or b A Nest success models Mayfield 1961 MARK Nov 9 16 B Failure time methods Kaplan Meier STAGGE
25. ultiple recapture census Biometrika 52 249 259 Population Analvsis Fall 2005 14 Homework 4 This assignment is a first step in learning about estimation of vital parameters under the open models of Jollv Seber The analvses will be conducted using readilv available PC software JOLLY and JOLLYAGE For the basic Jolly Seber single age models you can use JOLLY For age structured analyses we will use JOLLYAGE Both programs are now available over the internet at http www mbr pwrc usgs gov software html These programs are very simple to use and provide estimates of capture probability population size survival and recruitment Similar models focusing on estimation of survival or more complex analyses have been programmed into MARK All citations herein can be found in Pollock et al 1990 JOLLY and JOLLYAGE The program and example files for JOLLY are on the disk Take a look at the data sets using an ASC editor like NOTEPAD to get the feel for the format of the input You might also look at ROBUST DES distributed as JLYEXMPL which is Microtus data from the robust design example that we will look at in class Please run the following two examples using JOLLY and interpret the results a SQUIRREL GRY is data on grey squirrels that are discussed in Pollock et al 1990 Table 4 3 Consider the full data set but take a critical look at
26. ur own files don t forget to end each input line with d Select vour file and be prepared to enter the number of encounter occasions number of groups remember this file has males and females coded as 2 groups and give some labels for the groups Once evervthing is set click OK e The next thing vou ll see is a PIM chart for group 1 Q s Look at the PIM charts for the Q s and p s These PIMs correspond to the model g t and p g t You can view the other PIM charts by using the PIM menu in the top banner There are other menus there that you will want to learn to use including Design Run Tests Output and Help Population Analvsis Fall 2005 18 Assigment Explain how the default PIM coding corresponds to the g t p g t model Whv are there 4 sub tables to the PIM and 24 parameters Now write a PIM for parameters that corresponds to the default CJS model of M t p t with no differences in groups sex Write another PIM for the model that corresponds to JOLLY Model B and p t How does this compare to the PIM for Q t and p Finally write the PIM for and p Assigment Next find the Run button and select Run Predefined Models You ll have to select models to run You can run all the models with PIM coding These will correspond to the models for which you made PIMs plus others Determine which of the
27. ward As with most software input file squirrel data in the Capture99 directory called CAPTIN the structure of the X matrix the input line skip a space I ve stored the data that way on the MARK to analyze these data because but see Rexstad and from the MSDOS like PC s in Room suggest that model selection and estimation is CAPTURE and MARK are particular about the 10 occasions DATA X MATRIX READ INPUT DATA 11001 0 1 2 de gt Te 10 70 B da d data b DS Constructing input in X Matrix format although MARK requires that vou comment out the and include a group number and xercises vou will input Wi or each line In ithin the X Matrix FORMAT A2 1X 10 F1 0 1X later convenient form called NON XV matrix rather than the f have included an electronic version of the fox Notice fox format of the data and the format of The first two characters are the animal ID then repeat the X matrix captures l captured then E ror is good practice for MARK ID use no spaces r See Rexstad and Burnham or Appendix A of White et al at the end data in a more ully specified X for an explanation of Non XY as a way to organize your data For practice make a file in both X Matrix and No hand in as part of this homework
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