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User Manual for PatchImportance 1.0: Quantifying Relative Habitat

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1. Harvest txt Int txt Loc txt MetapopOcc txt Quasi txt Ter txt Vector of 1 num V_Numberpops 1 num Exclude patches that are already identified in ranks if length ranks 0 V_Numberpops lt V_Numberpops ranks Loop through replicate simulations to include an additional patch for y in 1 length V_Numberpops 1 Read in the original PVA input file to reference lines inputFile lt readLines mpFile n 1 Find the line that specifies the number of stages modeled N_stages lt scan mpFile what list skip 9 nlines 1 quiet TRUE N_stages lt as numeric N_stages 1 Read the batch txt file used to create the RAMAS Metapop batch file Start lt readLines batch txt Update the input file name filename lt paste rep _ y mp 4 sep Create the RAMAS Metapop batch file operating system dependent ifelse Platform 0S type windows batch_rep lt paste Start 1 Start 2 Start 3 Start 4 rep y mp Start 5 sep batch rep lt paste Start 1 Start 3 Start 4 rep_ y mp Start 5 sep Write the RAMAS Metapop batch file write batch rep file batch file bat append TRUE Ensure results files correspond to appropriate input files write paste rename Abund txt Abund y txt sep batch file bat append TRUE write paste rename FinalStageN txt FinalStageN y
2. RAMAS Metapop file name mpFile seaotter mp Number of years nYr 100 Number of replications per iteration nRep 50 Number of iterations nlter lt 200 Save simulation output doSave TRUE RAMAS Metapop drive letter if using WINE wineDrive lt Z HHHHHHHAHHHAHHHHAHHHAHHHAAHHHAAHAHAHHE End user defined variables HHHHHHHAHHHAHHHHAHHHHHHHAAHHHAAHAHAHHE Remove files directories from previous runs unlink x c Abundance pdf Persistence pdf RelativeImportance pdf ranks txt pProbs txt nAbunds txt Relativelmportance csv pbs std OutputData recursive TRUE Create a directory to hold output data only used if doSave dir create path OutputData Get the required files operating system dependent ifelse Platform 0S type windows reqFiles lt c mpFile batch txt reqFiles lt c mpFile batch txt beforeMP afterMP Check if there are missing files and error if they are missing if all reqFiles in list files If so stop stop Ensure the working directory has the required files call FALSE End if there are missing files Ensure inputs are integers that satisfy constraints nYr lt as integer nYr 0 5 if nYr lt 1 nYr gt 5000 Get offending value nYrSt lt nYr 30 111 13 15 17 19 21 23 125 27 29 131 33 135 37 139 41 43 4
3. UTM easting km Figure 6 Median relative importance of British Columbia sea otter habitat patches nlter 200 iterations Geographic coordinates are projected in Universal Transverse Mercator UTM zone 9 in kilometres km The grey polygon indicates the current distribution e g area encompassing patches with non zero initial abundance Nichol et al 2009 is via Pop 1 to Pop 7 Spatial planning initiatives attempting to increase the probability of BC sea otter metapopulation persistence and metapopulation EMA may maximize their impact by protecting the most important patches or areas with clusters of important patches Coast wide spatial planning initiatives for BC sea otters may also benefit by using 16 habitat suitability maps that capture habitat characteristics on Haida Gwaii Other factors to guide the selection of protected area size and shape include the ability to monitor and enforce regulations McLeod et al 2009 ecological interactions e g prey dynamics and social political and economic constraints Ak akaya et al 2007 Generally patches with non zero initial abundance tend to be more important for sea otters than patches that are initially unoccupied Table 2 For example the 17 most important patches were initially occupied for these patches larger patches i e larger AO which supports a higher abundance tend to be more important than smaller patches Importance values for the remaining 63 patch
4. catastrophe multipliers write inputFile Line Constraints Line Constraints N stages 3 3 file filename append TRUE Write Initial Abundance matrix write table Initial Abundances filename append TRUE col names FALSE row names FALSE Read and write in the information from the stages menu write inputFile Line Constraints 1 N stages 3 3 num Line_Constraints N stages 3 3 num 5 N_stages file filename append TRUE Ensure there is no population management modeled write O pop mgmnt file filename append TRUE Write a generic extinction threshold of zero write O file filename append TRUE Write a generic explosion threshold of zero write O file filename append TRUE Write the timestep datum as specified in the original input file Mgmnt grep mgmnt inputFile perl TRUE N_Mgmnt lt scan mpFile what list skip Mgmnt 1 nlines 1 quiet TRUE N_Mgmnt lt as numeric N Mgmnt 1 write inputFile Mgmnt N Mgmnt 1 2 file filename append TRUE Write end of file write End of file file filename append TRUE End y loop over V Numberpops Run the RAMAS Metapop batch file operating system dependent if Platform 0S type windows 1 system batch_file bat wait TRUE show output on console FALSE else 1 system paste getwd beforeMP sep Platform file sep wait TRUE system paste wine wineconsole win
5. 1 1 Constant correlation if no distance function specified if sum Correlation_matrix na rm TRUE length Correlation_matrix 1 amp sum C_parameters lt 0 1 Correlation_matrix lt matrix runif 1 0 1 nrow Npops ncol Npops else If there are correlation parameters Adjust correlations according to new distances among patch pairs Correlation matrix lt C_parameters 1i exp Pairwise_distance C_parameters 3 C_parameters 2 Ensure diagonal elements on the correlation matrix are 1 diag Correlation_matrix lt 1 Constrain individual elements between O and 1 Correlation_matrix Correlation_matrix lt 0 lt 0 0 Correlation_matrix Correlation_matrix gt 1 lt 1 0 Ensure correlation coefficients are rounded to 6 decimal places Correlation_matrix lt round Correlation_matrix digits 6 End if Npops 1 Add column of at the end of each rows Correlation_matrix lt cbind Correlation_matrix rep Npops deparse level 0 Remove the selected patches from the Initial Abundances matrix if m num ifelse N_stages gt 1 Initial_Abundances lt Initial_Abundances Pops_removed Initial_Abundances lt Initial_Abundances Pops_removed Create an interim replicate simulation file pref mp write inputFile 1 6 file filename append FALSE Write the number of stochastic runs within each replicate simulation write nRep file filename append
6. We demonstrated our analysis by ranking the relative importance of BC sea otter patches based on their influence on Ppers and resolved ties by considering their in fluence on Nyi However the PatchImportance code could be customized to suit individual requirements by considering alternative statistics modifying our R code and by incorporating other conservation tools 6 1 Alternative statistics and modifications The PatchImportance code could quantify patch importance according to alterna tive statistics such as N AO EO percent decline probability of quasi extinction e g quasi extinction threshold 100 individuals or time to extinction Ak akaya 2005 The code could be modified to consider additional statistics which could break patch importance ties instead of selecting a patch at random Users could incorporate the aforementioned changes in the statMat matrix It is noteworthy that patch importance 20 Table 3 Patches required for metapopulation expected minimum abundance gt 750 female British Columbia sea otters Patches are ordered from top to bottom by the per centage of the nIter 200 iterations that required the patch l and then by median relative importance not shown Also indicated is whether the patch was initially oc cupied No gt 0 Metapopulation statistics female metapopulation abundance N area of occupancy AO as patch area number of patches NP and extent of occurrence EO as minimum convex p
7. lt rep 0 num Pop_vector lt rbind Pop_vector rep 0 num Read in the dispersal matrix if it is there if Nrows_dispersal_matrix gt 0 Dispersal_matrix lt matrix scan mpFile sep nlines Correlation Migration 3 skip Migration 2 quiet TRUE ncol Correlation Migration 2 byrow TRUE Remove the last column NAs Dispersal matrix lt Dispersal_matrix ncol Dispersal matrix else Otherwise create an empty one Dispersal matrix lt matrix 0 num num HB ed Read in the correlation matrix or create one D autofill lt as logical scan mpFile what list skip Correlation 1 nlines 1 quiet TRUE if any D autofill Correlation matrix lt matrix 0 num num else Correlation matrix matrix NA num num corDat lt scan mpFile sep quiet TRUE nlines num Skip Correlation 2 Correlation matrix upper tri Correlation matrix diag TRUE na omit corDat Correlation matrix lower tri Correlation matrix diag TRUE lt na omit rev corDat Read in the stage specific initial abundances Initial Abundances lt matrix scan mpFile nlines num quiet TRUE Skip Line Constraints N stages 3 3 ncol N_stages byrow TRUE Get the line on which the number of stages matrices is listed Line N stage matrices lt grep stage matrix inputFile perl TRUE Read the stage and standard deviation matrices and their description
8. mpFile sep quiet TRUE Skip Line N stdev matrices i 1 i 1 N_stages nlines 1 what list Stdev matrices il lt matrix scan mpFile quiet TRUE Skip Line N stdev matrices 1 i 1 i 1 N_stages nlines N stages N stages N stages byrow TRUE Assign 1 when patch is removed 0 when patch is retained Pops_removed lt sort V_Numberpops y decreasing TRUE if m num ifelse y 1 Pop vector Pops removed lt 1 Pop vector y Pops removed lt 1 Remove the selected patches from the patch dataframe if m num pop lt pop Pops_removed Remove selected patches from the dispersal matrix if m num Dispersal_matrix lt Dispersal_matrix Pops_removed Pops_removed if Npops 1 1 Read in the dispersal distance parameters M_parameters lt scan mpFile skip Migration 1 1 nlines 1 sep quiet TRUE Create a matrix of pairwise geographic distances Euclidean Pairwise_distance lt matrix 0 Npops Npops for i in 1 Npops for j in 1 Npops Pairwise_distanceli j lt sqrt popli 2 poplj 21072 popli 3 poplj 31 2 D Y Dispersal if M parameters 1 0 Get dispersal and constrain Dispersal matrix lt M parameters i1 exp Pairwise distance M parameters 3 M_parameters 2 if M parameters 4 O Dispersal matrix Pairwise distance gt M parameters 4 lt 0 Constrain between O and
9. which could inform critical habitat identification or other spatial planning initiatives 21 Second our code could be modified to incorporate prior knowledge regarding the ability or desire to protect specific patches For example some patches may be harder to protect due to their proximity to urban areas while other patches may be easier to protect due to their proximity to existing protected areas e g via expansion Alternatively the presence of multiple species at risk in some patches may support their inclusion in protected areas e g key biodiversity areas Langhammer et al 2007 Finally the PatchImportance code could be used to evaluate the relative influence of patch quality by modifying patch characteristics e g carrying capacity links be tween habitat attributes relative fecundity relative survival For example consider a situation in which individuals in protected patches benefit from increased fitness e g greater habitat quality leads to greater fecundity compared to unprotected patches For this approach the PatchImportance algorithm could be adjusted to include every patch in the metapopulation and iteratively increase habitat quality one patch at a time Important patches would maintain their artificially increased fitness benefits to simulate their inclusion in a network of protected areas 6 2 Incorporating additional conservation tools The PatchImportance code could be used in conjunction with other c
10. 0 2 of ties were broken by selecting a patch at random That is to say none of the sea otter patch ranks in our metapopulation model were determined by solely considering the probability of metapopulation persistence The high probability of persistence is not entirely unexpected because extinction risks 13 for population models tend towards either zero or one over a wide range of parameter values McCarthy and Thompson 2001 There are at least two explanations for the consistent high probability of BC sea otter metapopulation persistence 1 model parameters inadvertently over estimate persistence or 2 persistence is assured even with very few patches Of these two explanations we believe that our BC sea otter metapopulation model may be inadvertently over estimating persistence because of one or more overly optimistic parameter values For example parameter values based on data collected during a phase of rapid population growth could be overly optimistic which could be relevant to this analysis Also our Beverton Holt model of density dependence assumes compensatory dynamics which means that populations tend to increase towards carrying capacity Although the probability of BC sea otter metapopulation persistence is always equal to 1 0 in our case study some example metapopulations have a different relationship For example consider the BC herring sample file available with the RAMAS Metapop installation PacificHerring mp based on
11. 0 513 6 5 17 4427 3486 23871 Pop 10 No 0 487 10 8 18 4437 3494 42849 Pop 74 Yes 0 481 8 6 19 4445 3500 43711 Pop 44 No 0 481 179 141 20 4624 3641 56644 17 Table 2 continued Cumulative Patch M gt 0 z N AO NP N AO EO Pop5 No 0 475 398 313 21 5022 3954 73779 Pop 78 No 0 475 113 89 22 5135 4043 78047 Pop 73 Yes 0 468 14 11 23 5149 4054 78047 Pop 51 No 0 468 264 208 24 5413 4262 78047 Pop 19 No 0 468 173 136 25 5586 4399 78047 Pop 79 No 0 468 10 8 26 5597 4407 95817 Pop 41 No 0 462 54 43 27 5651 4450 103154 Pop 21 No 0 462 151 119 28 5802 4568 104203 Pop 1 No 0 462 17 14 29 5819 4582 107619 Pop 29 No 0 456 43 34 30 5862 4616 107619 Pop 33 No 0 456 97 76 31 5959 4692 107619 Pop 42 No 0 449 21 16 32 5980 4709 108344 Pop 65 No 0 449 10 8 33 5990 4716 108344 Pop 72 Yes 0 443 4 4 34 5994 4720 108344 Pop 49 No 0 443 193 152 35 6187 4872 108344 Pop 13 No 0 443 49 38 36 6236 4910 130582 Pop 36 No 0 443 T 5 37 6243 4916 130582 Pop8 No 0 430 9 7 38 6252 4922 130866 Pop3 No 0 430 117 92 39 6368 5014 131532 Pop 52 No 0 430 6 4 40 6374 5019 131532 Pop 40 No 0 430 150 118 41 6524 5137 131532 Pop 18 No 0 430 271 213 42 6794 5350 131532 Pop 31 No 0 430 3 2 43 6797 5352 131532 Pop7 No 0 430 105 83 44 6903 5435 131532 Pop 39 No 0 430 135 106 45 7038 5542 131532 Pop9 No 0 430 1467 1155 46 8505 6697 131532 Pop6 No 0 424 103 81 47 8607 6778 134550 Pop 45 No 0 424 46 36 48 8653 6814 135828 Pop 58 No 0 424 76 60 49 8729 6873 135828 Pop 37 No
12. 1 Dispersal matrix Dispersal matrix lt 0 0 0 Dispersal matrix Dispersal matrix gt 1 1 0 else Otherwise sample dispersal from a random uniform 34 371 373 375 377 379 381 383 385 387 389 391 393 395 397 399 401 403 405 407 409 411 413 415 417 419 421 423 425 427 429 431 433 435 Dispersal_matrix lt matrix runif i O 1 nrow Npops ncol Npops Set diagonal to zero diag Dispersal_matrix lt 0 Enforce a maximum total dispersal rate of 1 from each patch colSumi lt sum Dispersal_matrix 1 if colSumi gt 1 Dispersal_matrix lt Dispersal_matrix colSumi Keep track of dispersal rates for calculating statistics Lower_logical lt lower tri Dispersal_matrix Round values in the dispersal matrix are rounded to 7 decimal places Dispersal_matrix lt round Dispersal_matrix 7 Add the extra column of at the end of each matrix row for writing to the replicate simulation input file Dispersal_matrix lt cbind Dispersal_matrix rep Npops deparse level 0 End if Npops 1 Remove the selected patches from the correlation matrix if m num Correlation_matrix lt Correlation_matrix Pops_removed Pops_removed Read in the correlation distance function parameters C_parameters lt scan mpFile skip Correlation 1 1 nlines 1 sep quiet TRUE if Npops
13. 18 4 1002 1013 doi 10 1111 j 1523 1739 2008 01066 x Curtis J M R and Naujokaitis Lewis I R 2008b Source code for the program GRIP 1 0 Generation of Random Input Parameters URL http esapubs org archive appl A018 033 suppl 1 htm Ecological Archives A018 033 S1 Supple ment Diamond J M 1975 The island dilemma Lessons of modern biogeographic studies for the design of nature reserves Biological Conservation 7 2 129 146 doi 10 1016 0006 3207 75 90052 X Dickins D F 1995 The double hull issue and oil spill risk on the Pacific West coast Technical report Ministry of Environment Lands and Parks URL www env gov bc ca Dudley N ed 2008 Guidelines for applying protected area management categories International Union for Conservation of Nature Gland Switzerland URL www iucn org about union commissions wcpa Dwernychuk L W and Boag D A 1972 Ducks nesting in association with gulls An ecological trap Canadian Journal of Zoology 50 5 559 563 doi 10 1139 z72 076 Fagan W F Fortin M J and Soykan C 2003 Integrating edge detection and dy namic modeling in quantitative analyses of ecological boundaries BioScience 53 8 730 738 doi 10 1641 0006 3568 2003 053 0730 IEDADM 2 0 CO 2 Fahrig L 2001 How much habitat is enough Biological Conservation 100 1 65 74 doi 10 1016 S0006 3207 00 00208 1 Fu C Wood C C and Schweigert J 2004 Pacific herring Clupea pallasi in Canada Gen
14. 2 Two one line files are required to convert end of line characters from unix to dos beforeMP a and dos to unix afterMP b when running PatchImportance on non Windows operating systems using WineHQ WPD 2010 a unix2dos mp b dos2unix mp nYr Number of years to project the metapopulation and quantify patch importance Note that nYr over rides the number of years specified in mpFile Value integer satisfying the constraint 1 lt nYr lt 500 Ak akaya 2005 nRep Number of replications per iteration Note that nRep over rides the number of replications specified in mpFile Value integer satisfying the constraint 4 lt nRep lt 10000 Ak akaya 2005 nIter Number of iterations Users must determine the number of iterations re quired for example the minimum number required to achieve consistent patch importance and variability estimates Value integer satisfying the constraint niter gt 1 doSave Whether output simulation data should be saved to the hard disk Set to TRUE to save output data set to FALSE to skip this step If doSave users must ensure that sufficient hard disk space is available to save the large number of RAMAS Metapop input and output files Subsection 4 3 Value logical wineDrive Drive letter indicating the location of the RAMAS Metapop exe cutable Note that this is only required on non Windows operating systems using WineHQ Value character e g C The analysis w
15. 259 261 263 265 267 269 271 273 275 277 279 281 283 285 287 289 291 293 295 297 299 301 303 305 batch_file bat append TRUE Get the line number in the input file that has Migration on it Migration lt grep Migration inputFile perl TRUE Get the line number in input file that has Correlation on it Correlation lt grep Correlation inputFile perl TRUE Calculate the number of rows in the dispersal matrix Nrows_dispersal_matrix lt Correlation Migration 3 Get the line number in the input file that has Constraints Matrix Line_Constraints lt grep Constraints inputFile perl TRUE Sample a new number of patches based on the original number Npops lt m Calculate the number of patches that need to be added Diff lt num Npops Get the first line of the population dataframe and subtract 1 firstNpop lt grep Pop firstltemMP perl TRUE 1 1 Read in the patch dataframe pop lt read table mpFile skip firstNpop sep nrow num Read in the total number of individuals in the original patches to calculate decline at t 100 and t 20 Total_N_original lt sum pop V4 Create patch names for all patches pop Vi lt as character 1 num Write patch names PopNames lt as list paste pop 1 num sep Matrix to keep track of which patches are included ifelse y 1 Pop_vector
16. Briefly Conefor Sensin ode quantifies patch importance based on landscape connectivity indices using graph structures to represent patches and connections between patches i e corridors For example quantifying importance based on connectivity might identify patches Pop 1 and Pop 7 as important because they are critical to populating Haida Gwaii Because Conefor Sensinode is fast to implement PatchImportance could run Conefor Sensinode via a batch file to calculate connectivity statistics which might resolve 22 patch importance ties 7 Conclusions Identifying the most important habitat patches using a quantitative statistic is crit ical to designing protected areas when it is not feasible to protect the entire area of occupancy We demonstrated our simulation approach to ranking patches according to their impact on metapopulation persistence and minimum abundance using the BC sea otter metapopulation as a case study In this context the inclusion of important patches causes the probability of metapopulation persistence or metapopulation EMA to increase more than the inclusion of less important patches Our PatchImportance tool could be applied to BC sea otters and other species to provide science based advice for spatial planning initiatives in BC Further users could modify our code to provide science based advice on related conservation questions and couple PatchImportance with other existing software 8 Acknowledgements The
17. X dat2 MARGIN 2 FUN quantile probs 0 975 699 col black lwd 1 Turn the device off 701 dev off 703 Plot expected minimum metapopulation abundance pdf height 6 width 6 file Abundance pdf 705 Set up the plot area par mar c 3 6 3 5 1 5 0 1 707 Determine the upper range upper95 lt apply X dat3 MARGIN 2 FUN quantile probs 0 975 709 Plot the median plot x 1 num y apply X dat3 MARGIN 2 FUN median lwd 3 type l 711 ylim c 0 max upper95 ann FALSE mtext side 1 line 2 5 Number of patches cex 1 25 713 mtext side 2 line 2 5 Metapopulation expected minimum abundance cex 1 25 715 mtext side 3 line 0 5 paste RAMAS Metapop file mpFile sep cex 1 25 717 Add 50 polygon polygon x c i num num 1 border NA col rgb 0 0 0 0 35 719 y c apply X dat3 MARGIN 2 FUN quantile probs 0 25 rev apply X dat3 MARGIN 2 FUN quantile probs 0 75 721 Add 95 lines lines x 1 num y apply X dat3 MARGIN 2 FUN quantile probs 0 025 723 col black lwd 1 lines x 1 num y upper95 col black lwd 1 725 Turn the device off dev off 727 Return each patch s relative importance 729 return list stats relImp imps mati probs mat2 abunds mat3 End CalcPatchImp function 731 Calculate and plot relative patch importance 733 patchImp lt CalcPatchImp dati read table file ranks txt sep dat2 read table file pProb
18. authors thank K Kinnersley for facilitating their use of the High Performance Computing cluster at the Institute of Ocean Sciences as well as I R Naujokaitis Lewis and B Davis for technical support Funding support was provided by Fisheries and Oceans Canada s National Species at Risk Programme 23 References Ak akaya H R 2005 RAMAS GIS Linking spatial data with population viability analysis Applied Biomathematics URL www ramas com ramas htm User manual for version 5 Ak akaya H R Mills G and Doncaster C P 2007 The role of metapopulations in conservation In D W Macdonald and K Service eds Key topics in conservation biology chap 5 64 84 Blackwell Publishing ISBN 978 1 4051 2249 8 Anderson C M and LaBelle R P 2000 Update of comparative occurrence rates for offshore oil spills Spill Science and Technology Bulletin 6 5 6 303 321 doi 10 1016 51353 2561 01 00049 4 Battin J 2004 When good animals love bad habitats Ecological traps and the conservation of animal populations Conservation Biology 18 6 1482 1491 doi 10 1111 j 1523 1739 2004 00417 x Bivand R 5 2011 spdep Spatial dependence Weighting schemes statistics and mod els URL http CRAN R project org package spdep With contributions by M Altman L Anselin R Assun o O Berke A Bernat G Blanchet E Blankmeyer M Carvalho B Christensen Y Chun C Dormann 5 Dray R Halbersma E Krainski P Legendre N Lewin
19. few patches are added to the metapopulation The presence of patches which reduce metapopulation EMA may indicate that there are sink populations which have negative population growth rates e g deaths exceed births Sink populations are in contrast to source populations which have positive pop ulation growth rates Although population sinks may reduce abundance their existence is not necessarily detrimental to metapopulations because sinks can increase connectiv ity between source populations or buffer against catastrophes Akcakaya et al 2007 Additionally patches that currently act as sinks due to the prevalence of low quality 14 RAMAS Metapop file PacificHerring mp RAMAS Metapop file PacificHerring mp 1 0 0 8 4e 05 3e 05 1 0 6 0 4 2e 05 1 0 2 Probability of metapopulation persistence 1e 05 Metapopulation expected minimum abundance 34 Eg T T T T T 2 T T T T T 1 2 3 4 5 1 2 3 4 5 Number of patches Number of patches a Probability of metapopulation persistence b Metapopulation expected minimum abun Pers dance Nyin Figure 5 Relationship between the number of habitat patches and the two metapopu lation statistics used to quantify relative patch importance for British Columbia herring Thick lines indicate medians grey polygons indicate 50 percentile ranges and thin lines indicate 95 percentile ranges nIter 100 iterations habitat could become sour
20. la m tapopulation Toutefois la d termination des parcelles importantes pose des difficult s et il est possible que certaines parcelles importantes soient actuelle ment inoccup es ce qui rend leur rep rage encore plus compliqu Pour aider rep rer les parcelles potentielles pour servir la protection nous avons con u PatchImpor tance un outil qui quantifie l importance relative de chaque parcelle en fonction de son influence sur les chances de survie de la m tapopulation et des attentes concer nant l abondance minimale de la m tapopulation Nous faisons une d monstration de notre analyse en utilisant la m tapopulation de la loutre de mer Enhydra lutris de la Colombie Britannique comme tude de cas vi 1 Motivation One common approach to increasing the probability of persistence for species at risk of extinction is to protect areas of suitable habitat e g parks reserves no take zones Dudley 2008 In Canada species listed under the Species at Risk Act benefit from the protection of critical habitat defined as the habitat required for species survival or recovery SARA 2011 Critical habitat does not typically encompass the entire area of occupancy AO i e every habitat patch exceptions include cases when habitat availability limits species persistence and recovery or when data limitations preclude otherwise Hatfield 2009 When available habitat does not limit species persistence and recovery a subset of sui
21. txt sep batch file bat append TRUE write paste rename Harvest txt Harvest y txt sep batch file bat append TRUE write paste rename HarvestRisk txt HarvestRisk y txt sep batch file bat append TRUE write paste rename IntExpRisk txt IntExpRisk y txt sep batch file bat append TRUE write paste rename IntExtRisk txt IntExtRisk y txt sep batch file bat append TRUE write paste rename IntPerDec txt IntPerDec y txt sep batch file bat append TRUE write paste rename LocalOcc txt LocalO0cc y txt sep batch file bat append TRUE write paste rename LocExtDur txt LocExtDur y txt sep batch file bat append TRUE write paste rename Metapop cc txt MetapopOcc_ y txt sep batch file bat append TRUE write paste rename QuasiExp txt QuasiExp y txt sep batch file bat append TRUE write paste rename QuasiExt txt QuasiExt y txt sep batch file bat append TRUE write paste rename TerExpRisk txt TerExpRisk y txt sep batch file bat append TRUE write paste rename TerExtRisk txt TerExtRisk y txt sep batch file bat append TRUE write paste rename TerPerDec txt TerPerDec y txt sep 32 241 243 245 247 249 251 253 255 257
22. 0 424 29 23 50 8758 6896 135828 Pop 64 No 0 424 2 1 51 8760 6897 135828 Pop 15 No 0 424 43 34 52 8803 6932 138302 Pop 80 No 0 424 88 69 53 8891 7000 153759 Pop 71 Yes 0 424 10 8 54 8900 7008 153759 Pop 60 No 0 418 101 80 55 9001 7088 153759 Pop 20 No 0 418 50 39 56 9051 7127 153759 Pop 4 No 0 418 375 295 57 9426 7422 153759 Pop 16 No 0 411 26 20 58 9452 7442 154438 Pop 77 No 0 411 682 537 59 10134 7980 154438 18 Table 2 continued Cumulative Patch M gt 0 z N AO NP N AO EO Pop 53 No 0 411 936 737 60 11070 8716 154438 Pop 25 No 0 405 350 276 61 11420 8992 154438 Pop 23 No 0 405 1 1 62 11421 8993 154438 Pop 50 No 0 405 26 21 63 11448 9014 154438 Pop 28 No 0 405 27 22 64 11475 9036 154438 Pop 24 No 0 399 17 14 65 11492 9049 154438 Pop 66 No 0 399 107 84 66 11600 9134 154438 Pop2 No 0 399 30 23 67 11629 9157 154498 Pop 22 No 0 392 33 26 68 11662 9183 154498 Pop 59 No 0 392 14 11 69 11676 9194 154498 Pop 61 No 0 392 781 615 70 12457 9809 154498 Pop 27 No 0 392 4 4 71 12462 9812 154498 Pop 12 No 0 386 T 6 72 12469 9818 154498 Pop 17 No 0 386 14 11 73 12483 9829 154498 Pop 35 No 0 386 47 37 74 12530 9866 154498 Pop 43 No 0 380 80 63 75 12610 9929 154498 Pop 26 No 0 380 95 75 76 12704 10004 154498 Pop 54 No 0 380 217 171 77 12921 10174 154498 Pop 48 No 0 367 72 56 78 12993 10231 154498 Pop 14 No 0 367 1 1 79 12994 10232 154624 Pop 11 No 0 329 20 16 80 13014 10247 154893 5 5 Setting conservation targets Patch importance values co
23. 5 47 49 51 153 55 157 59 61 163 65 69 71 73 175 Reset to allowed value ifelse nYr lt 1 nYr lt 1 nYr lt 500 Warning warning Bad value variable nYr changed from nYrSt to nYr call FALSE nRep lt as integer nRep 0 5 if nRep lt 4 nRep gt 10000 1 Get offending value nRepSt lt nRep Reset to allowed value ifelse nRep lt 4 nRep lt 4 nRep lt 10000 Warning warning Bad value variable nRep changed from nRepSt to nRep call FALSE nlter lt as integer nlter 0 5 if nlter lt 1 Get offending value nIterSt lt nIter Reset to allowed value nlter lt 1 Warning warning Bad value variable nIter changed from nlterSt to nlter call FALSE Get the first item from each line in the original mp file firstItemMP lt scan file mpFile skip 0 sep what character quiet TRUE flush TRUE blank lines skip FALSE Count the number of patches ignore the header and after the pop matrix CountPatches lt function dat Get lines corresponding to patch names vec lt grep Pop dat perl TRUE Ignore the first 6 lines the header vec lt vec vec gt 6 Get the first number and build a sequence of length vec seqVec lt seq from vec 1 by 1 length out length vec Count the number of elements that match nMatch lt length wh
24. 5 677 679 681 683 685 687 689 691 693 695 prob75 apply X mat2 MARGIN 1 FUN quantile probs 0 75 0 75 prob975 apply X mat2 MARGIN 1 FUN quantile probs 0 975 0 975 Threshold abundance abun025 apply X mat3 MARGIN 1 FUN quantile probs 0 025 0 025 abun25 apply X mat3 MARGIN 1 FUN quantile probs 0 25 0 25 abunMed apply X mat3 MARGIN 1 FUN quantile probs 0 5 Median abun75 apply X mat3 MARGIN 1 FUN quantile probs 0 75 0 75 abun975 apply X mat3 MARGIN 1 FUN quantile probs 0 975 0 975 Get the order of importance by median then 95th percentile range impOrd lt order relImp impMed relImp imp975 relImp imp025 Order by the relative importance relImp lt relImp impOrd Write to a csv write table relImp file RelativeImportance csv col names TRUE sep row names FALSE append FALSE Plot relative patch importance pdf height 9 75 width 8 file RelativeImportance pdf Set graph area par oma c 0 1 5 0 0 mar c 3 55 3 1 75 0 1 Plot using a Cleveland dot plot dotchart x rellmp impMed labels rellmp patch pch 19 cex axis 1 cex 0 7 xlim c 0 1 ann FALSE Labels mtext side 1 line 2 35 Relative importance mtext side 2 line 3 35 Patch name mtext side 3 line 0 5 font 2 paste RAMAS Metapop file mpFile sep Vertical line at 0 5 abline v 0 5 lwd 1 lty dashed Start lo
25. BC sea otters seaotter mp are available from the authors upon request We can also provide electronic copies of the batch file batch txt Listing 1 and the two end of line conversion files beforeMP and afterMP Listing 2 Quantifying the relative importance of the 80 BC sea otter patches requires significant time metapopulations with fewer patches are faster to implement For example the BC herring sample file available with the RAMAS Metapop instal lation PacificHerring mp has five patches based on Fu et al 2004 Note that BC herring patch names must follow the GRIP naming convention Subsection 4 1 Listing 3 The PatchImportance code PatchImportance R version 1 0 is written in the programming language R RDCT 2011 L AHHHHAHAHMHAHHAMMHHAAAMAMHHAAAMMHHAAAMMAHHAAAMMAHAAMMMMAHAMMAHAAAMMHHAAAMHHHAAAHHHAE 3 Authors Janelle M R Curtis and Matthew H Grinnell Affiliation Pacific Biological Station Fisheries and Oceans Canada 5 Research group Conservation Biology Section Janelle M R Curtis Contacts e mail janelle curtis dfo mpo gc ca tel 250 756 7157 7 e mail matt grinnell dfo mpo gc ca tel 250 756 7326 Project Quantify patch importance based on metapopulation persistence 9 and minimum abundance Code name PatchImportance R 11 Code version 1 0 Date started 2008 04 01 yyyy mm dd 13 Date finished 2012 02 20 yyyy mm dd 15 Goal Quantify the relative importance of habitat patches based on thei
26. Fu et al 2004 We used PatchImpor tance to quantify the relative importance of the five BC herring patches with the following parameters nYr 100 years nRep 200 replications and nIter 100 it erations results not shown Our analysis suggests that the median probability of BC herring metapopulation persistence is low but increases from 0 225 to 0 335 as more patches are included in the metapopulation Figure 5a We also show the relationship between the number of patches and median metapopulation EMA which increases from 140 868 to 369 727 herring as more patches are included in the metapopulation Figure 5b 5 3 Metapopulation expected minimum abundance The relationship between BC sea otter metapopulation EMA and the number of patches can be broken up into three zones based on the number of patches in the metapopula tion between 1 and 4 patches between 5 and 60 patches and between 61 and 80 patches Figure 4b Initially median metapopulation EMA is low but increases rapidly to ap proximately 920 females as important patches are added to the small metapopulation This zone of rapid increase in median metapopulation EMA is followed by a zone of di minishing marginal gains and wide variability as the number of patches approaches 60 The addition of these less important patches causes median metapopulation EMA to increase to about 1 280 females Finally median metapopulation EMA declines slightly to about 1 160 females as the last
27. Koh H Li J Ma G Millo W Mueller H Ono P Peres Neto G Piras M Reder M Tiefelsdorf and D Yu R package version 0 5 43 Clarke C L and Jamieson G S 2006a Identification of ecologically and biologically significant areas in the Pacific North Coast Integrated Management Area Phase I Identification of important areas Canadian Technical Report of Fisheries and Aquatic Sciences 2678 Fisheries and Oceans Canada URL www dfo mpo gc ca libraries bibliotheques tech eng htm Clarke C L and Jamieson G S 20066 Identification of ecologically and bi ologically significant areas in the Pacific North Coast Integrated Management Area Phase II Final report Canadian Technical Report of Fisheries and Aquatic Sciences 2686 Fisheries and Oceans Canada URL www dfo mpo gc ca libraries bibliotheques tech eng htm COSEWIC Committee on the Status of Endangered Wildlife in Canada 2007 COSEWIC assessment and update status report on the sea otter Enhydra lutris in Canada Technical Report Canadian Wildlife Service and Environment Canada URL www sararegistry gc ca status COSEWIC Committee on the Status of Endangered Wildlife in Canada 2010 COSEWIC s assessment process and criteria URL www cosewic gc ca Approved April 2010 Retrieved 1 March 2011 24 Curtis J M R and Naujokaitis Lewis I R 2008a Sensitivity of population viability analysis to spatial and nonspatial parameters using GRIP Ecological Applications
28. TRUE Write the number of time steps write nYr file filename append TRUE write inputFile 9 28 file filename append TRUE Write what happens when population size falls below local threshold write count in total file filename append TRUE write inputFile 30 firstNpop file filename append TRUE Write the new population dataframe write table pop file filename append TRUE sep row names FALSE 35 437 439 441 443 445 447 449 451 453 455 457 459 461 463 465 467 469 471 473 475 477 479 481 483 485 487 489 491 493 495 497 499 col names FALSE na quote FALSE Write Migration on a line write Migration file filename append TRUE Write the line after Migration write TRUE file filename append TRUE Write Dispersal_distance function parameters write inputFile Migration 2 file filename append TRUE Write Correlation write Correlation file filename append TRUE Write the line after Correlation write TRUE file filename append TRUE Write Correlation_distance function parameters write inputFile Correlation 2 file filename append TRUE Write the stage and standard deviation information write inputFile Line_N_stage_matrices Line_Constraints 1 file filename append TRUE Write the Constraints Matrix relative dispersal indices and
29. Technical Reports of the Fisheries Research Board of Canada Numbers 457 714 were issued as Department of the Environment Fisheries and Marine Service Research and Development Directorate Technical Reports Numbers 715 924 were issued as Department of Fisheries and Environment Fisheries and Marine Service Technical Reports The current series name was changed with report number 925 Rapport technique canadien des sciences halieutiques et aquatiques Les rapports techniques contiennent des renseignements scientifiques et techniques qui constituent une contribution aux connaissances actuelles mais qui ne sont pas normalement appropri s pour la publication dans un journal scientifique Les rapports techniques sont destin s essentiellement un public international et ils sont distribu s cet chelon II n y a aucune restriction quant au sujet de fait la s rie refl te la vaste gamme des int r ts et des politiques de P ches et Oc ans Canada c est dire les sciences halieutiques et aquatiques Les rapports techniques peuvent tre cit s comme des publications part enti re Le titre exact figure au dessus du r sum de chaque rapport Les rapports techniques sont r sum s dans la base de donn es R sum s des sciences aquatiques et halieutiques Les rapports techniques sont produits l chelon r gional mais num rot s l chelon national Les demandes de rapports seront satisfaites par l tablissement auteur dont le nom
30. User Manual for PatchImportance 1 0 Quantifying Relative Habitat Patch Importance Based on Metapopulation Persistence and Minimum Abundance M H Grinnell and J M R Curtis Fisheries and Oceans Canada Science Branch Pacific Region Pacific Biological Station 3190 Hammond Bay Road Nanaimo BC V9T 6N7 2012 Canadian Technical Report of Fisheries and Aquatic Sciences 2977 Fisheries and Oceans P ches et Oc ans il LH fe i Canada Canada Canada Canadian Technical Report of Fisheries and Aquatic Sciences Technical reports contain scientific and technical information that contributes to existing knowledge but which is not normally appropriate for primary literature Technical reports are directed primarily toward a worldwide audience and have an international distribution No restriction is placed on subject matter and the series reflects the broad interests and policies of Fisheries and Oceans Canada namely fisheries and aquatic sciences Technical reports may be cited as full publications The correct citation appears above the abstract of each report Each report is abstracted in the data base Aquatic Sciences and Fisheries Abstracts Technical reports are produced regionally but are numbered nationally Requests for individual reports will be filled by the issuing establishment listed on the front cover and title page Out of stock reports will be supplied for a fee by commercial agents Numbers 1 456 in this series were issued as
31. airwise_distance 22 patchImp 11 PatchImportance pdf 11 PatchImportance R 6 29 Persistence pdf 11 population 5 sink 14 source 14 trap 15 pProbs txt 10 R 2 6 RAMAS Metapop 6 RAMAS Patch 3 ranks txt 8 10 RelativeImportance csv 11 seaotter mp 6 29 statMat 20 wineDrive 7 WineHQ 6 41
32. al 0 900 proportion Krkosek et al 2007 Adult fecundity 0 450 proportion Krkosek et al 2007 Local oil spill probability 4 0 175 probability See footnotes Regional oil spill probability 0 029 probability See footnote Local oil spill multiplier 0 770 proportion Gerber et al 2004 Regional oil spill multiplier 0 580 proportion Gerber et al 2004 Maximum distance between suitable cells to consider them part of the same discrete patch I Minimum habitat suitability for breeding i Patches within the current distribution patches outside the current distribution had initial abundance equal to zero Yearly probabilities based on frequencies of 97 and 16 spills per 2 20 x 104 litres 1 of crude oil transported for local and regional spills respectively Anderson and LaBelle 2000 and 3 98 x 1079 1 of hydrocarbons transported annually in BC Dickins 1995 Coast wide probability of a local oil spill patch specific probability is we 0 002 Proportion of abundance remaining after the oil spill occurs included all 80 patches in our analysis to account for potential range expansion 3 2 Metapopulation dynamics We restricted our metapopulation model to females because of their importance in regulating population growth and driving population trends Tinker et al 2006 We modeled metapopulation dynamics using a stage structured model with a yearly time step Beverton Holt density dependence affected all vital rates base
33. ast of Vancouver Island is completely above 0 5 indicating that Pop 70 has a 11 RAMAS Metapop file seaotter mp Pop 69 Pop 47 Pop 76 Pop 70 Pop 67 Pop 63 Pop 57 Pop 62 Pop 38 Pop 56 Pop 75 Pop 46 Pop 30 Pop 32 Pop 68 Pop 34 Pop 55 Pop 10 Pop 74 Pop 44 Pop 5 Pop 78 Pop 73 Pop 51 Pop 19 Pop 79 Pop 41 Pop 21 Patch name at 8 0 0 0 2 0 4 0 6 0 8 1 0 Relative importance Figure 3 British Columbia sea otter habitat patches ordered by decreasing median relative importance dots and 95 percentile range horizontal lines with ticks from top to bottom nIter 200 iterations Grey rectangles indicate 50 percentile ranges Note that patch names correspond to patch numbers in Figure 1 Patch symbols initially occupied and initially unoccupied O 12 RAMAS Metapop file seaotter mp RAMAS Metapop file seaotter mp A s 1 0 1400 L 1200 0 8 1000 0 6 800 0 4 600 400 Probability of metapopulation persistence 0 2 200 0 0 0 Metapopulation expected minumum abundance females I I T I I I I T I 0 20 40 60 80 0 20 40 60 80 Number of patches Number of patches a Probability of metapopulation persistence b Metapopulation expecte
34. at Fisheries and Oceans Canada URL www dfo mpo gc ca csas Pascual Hortal L and Saura S 2006 Comparison and development of new graph based landscape connectivity indices Towards the priorization of habitat patches and corridors for conservation Landscape Ecology 21 7 959 967 doi 10 1007 s10980 006 0013 z Ralls K Eagle T C and Siniff D B 1996 Movement and spatial use patterns of California sea otters Canadian Journal of Zoology 74 1841 1849 doi 10 1139 z96 207 RDCT R Development Core Team 2011 R A language and environment for statisti cal computing URL www R project org R Foundation for Statistical Computing Vienna Austria R version 2 14 0 Rosenfeld J S and Hatfield T 2006 Information needs for assessing critical habitat of freshwater fish Canadian Journal of Fisheries and Aquatic Sciences 63 3 683 698 doi 10 1139 f05 242 SARA Species at Risk Act 2011 The Species at Risk Act An Act respecting the protection of wildlife species at risk in Canada URL www sararegistry gc ca Canada Gazette Part III Vol 25 No 3 Retrieved 30 November 2011 Saura S and Torn J 2009 Conefor Sensinode 2 2 A software package for quanti fying the importance of habitat patches for landscape connectivity Environmental Modelling and Software 24 1 135 139 doi 10 1016 j envsoft 2008 05 005 Zh Tinker M T Doak D F and Estes J A 2008 Using demography and movement behavior to predict range ex
35. by row for p in 1 nrow mati Find out which columns the patch is in get rank mati p lt which dati p arr ind TRUE col Get the probability of persistence mat2 p lt dat2 which dati p arr ind TRUE Get the incremental increase in the probability of persistence mat3 p lt dat3 which dati p arr ind TRUE End loop over patches Switch so important patches low ranks have high importance values mati lt max mati mati 1 Re scale between 0 00 and 1 00 mati lt mati min mati max mati min mati Calculate some statistics for each patch relImp data frame row names NULL Patch names patch rownames mati Relative importance imp025 apply X mati MARGIN 1 FUN quantile probs 0 025 0 025 imp25 apply X mati MARGIN 1 FUN quantile probs 0 25 0 25 impMed apply X 2mati MARGIN 1 FUN quantile probs 0 5 Median imp75 apply X mati MARGIN 1 FUN quantile probs 0 75 0 75 imp975 apply X 2mati MARGIN 1 FUN quantile probs 0 975 0 975 Probability of metapopulation persistence prob025 apply X mat2 MARGIN 1 FUN quantile probs 0 025 0 025 prob25 apply X mat2 MARGIN 1 FUN quantile probs 0 25 0 25 probMed apply X mat2 MARGIN 1 FUN quantile probs 0 5 Median 38 631 633 635 637 639 641 643 645 647 649 651 653 655 657 659 661 663 665 667 669 671 673 67
36. carbons transported in BC waters annually Dickins 1995 and 80 patches We assume that our calculated oil spill probabilities represent a baseline conditions may have changed since these data were collected and may be different for BC waters For example spill probabilities may be lower due to short transit times in BC waters or higher due to more navigational hazards and an increased volume of transported oil since the data were collected Also spill frequencies based on tankers carrying crude 5 oil do not account for spills caused by other vessels such as barges and other hydrocar bons We assumed that the occurrence of local i e patch specific and regional i e metapopulation wide oil spills in BC is uncorrelated Due to lack of data on long term effects of oil spills on sea otter fitness we modeled the optimistic situation in which catastrophes only affected abundance the year in which they occurred i e no residual effects However sea otters exposed to oil may have reduced reproductive success for more than one generation Mazet et al 2001 Our model could easily be updated to incorporate new information on residual effects 4 Implementing PatchImportance We assume that users have at least a working ability with the R statistical and graph ing programme RDCT 2011 and are familiar with RAMAS Metapop version 5 0 software Akcakaya 2005 both of which must be installed Users can run PatchIm portance on non Windows
37. ces in the future if environmental conditions change e g climate change Using metapopulation models to identify valuable and less valuable e g sink patches may be a step towards identifying ecological traps which are pref erentially selected low quality patches Dwernychuk and Boag 1972 In contrast to population sinks identifying population traps is a conservation concern because their presence can lead to metapopulation extinction Battin 2004 5 4 Spatial autocorrelation of important patches Our analysis suggests that median patch importance values exhibit significant posi tive spatial autocorrelation indicating that sea otter patches of similar importance are somewhat clustered Moran s 0 233 p 0 001 Bivand 2011 Figure 6 Impor tant patches are clustered in the current distribution on the West Coast of Vancouver Island the Goose Islands and Aristazabal Island Important patches may be under represented on Haida Gwaii in part because the habitat suitability map did not capture habitat characteristics in this area despite likely supporting a high otter abundance in the past Gregr et al 2008 Additionally otters migrating from initially occupied patches to Haida Gwaii would have had to travel through several intermediate patches which would delay their occupation the only route to Haida Gwaii from the mainland 15 6000 5800 UTM northing km 5600 Median relative habitat patch importance 5400
38. d minimum abun Ppers Note that variability e g 50 percentile dance Nyin and values mentioned in the text range overlaps the median Vertical lines 4 and 60 patches horizontal line Nuin 1000 females Figure 4 Relationship between the number of habitat patches and the two metapop ulation statistics used to quantify relative patch importance for British Columbia sea otters Thick lines indicate medians grey polygons indicate 50 percentile ranges and thin lines indicate 95 percentile ranges nIter 200 iterations stronger influence on the probability of metapopulation persistence or metapopulation EMA than the average patch The high relative importance of Pop 70 suggests that it might be more valuable to BC sea otters than other patches on the BC coast These 5 patches and the 12 other patches with median relative importance gt 0 5 were all initially occupied None of the patches have significantly lower than average patch importance values and patches with lower importance tend to have more variability e g wider 95 percentile range 5 2 Probability of metapopulation persistence In our BC sea otter case study our analysis suggests that the probability of metapop ulation persistence is always equal to 1 0 even when only one patch e g the most important patch is included in the metapopulation Figure 4a The secondary statis tic metapopulation EMA was used to break 99 8 of patch importance ties and
39. d on the abundance of all stages Ak akaya 2005 We excluded Allee effects from growth functions because it is unlikely that small otter populations are impacted by such effects Tinker et al 2008 However we set the local extinction threshold at 1 female which is the minimum patch abundance to consider the patch occupied We modeled log normal environ mental stochasticity and demographic stochasticity with a coefficient of variation of 0 1 4 Ak akaya 2005 We initialized the metapopulation model by setting abundance to 40 of carrying capacity k for the 21 patches with centroids within the current distribution in accor dance with predicted and observed population densities Gregr et al 2008 we set abundance to zero for patches outside the current distribution These 21 initially oc cupied patches supported an initial metapopulation abundance N 1785 females had an area of occupancy AO 3514 km as the sum of patch areas and an extent of occurrence EO 24732 km using the minimum convex polygon method on patch centroids IUCN 2010 COSEWIC 2010 In RAMAS Metapop patches of suitable habitat are treated synonymously as spatially structured populations linked by dispersal and modeled as a metapopulation Ak akaya 2005 As in RAMAS Metapop we define a metapopulation as a set of spatially structured interacting populations and a population as the individuals in a habitat patch Sea otters migrate between patches but
40. e minAbunList lt scan intExtRisk skip firstLine 1 quiet TRUE flush TRUE nlines 1 what list char minAbun 0 sep Then get expected minimum metapopulation abundance statMat p nAbun minAbunList minAbun End p loop over replicate simulations Bind extinction probability with information regarding included patches extDF lt data frame statMat matrix Pop vector ncol num Start vectors to hold stats could include other stats if desired popID lt vector Patch ID pPers lt vector Metapopulation persistence probability nAbun lt vector Minimum metapopulation abundance Loop over patches that haven t been identified as important for i in 1 num 1 num in ranks Get the row that include the patch pred lt subset extDF extDF i ncol statMat 0 Stop if there are too many rows if nrow pred gt 1 stop Too many rows in pred call FALSE Get statistics popID i lt i Patch ID pPers i lt 1 pred pExt Probability of metapop persistence nAbun i lt pred nAbun Minimum metapopulation abundance End i loop over patches Get a table of patch ID and statistics impMat lt na omit data frame popID popID pPers pPers nAbun nAbun Get the vector of persistence values vecPers lt impMat pPers Get the maximum prob of persistence maxPers max vecPers na rm TRUE If there is more than one maximum ties if lengt
41. eDrive getwd batch_file bat sep wait TRUE system paste getwd afterMP sep Platform file sep wait TRUE Matrix to hold probability and abundance and other stats if desired statMat lt matrix NA nrow y ncol 2 colnames statMat lt c pExt nAbun Loop through replicate simulations and collect results for p in 1 y Get the file with interval extinction risk data intExtRisk lt paste IntExtRisk _ p txt sep Read the entire file extFile lt readLines intExtRisk Get the line with expected minimum metapopulation abundance firstLine lt grep Expected minimum abundance extFile If the line can t be found error 36 501 503 505 507 509 511 513 515 517 519 521 523 525 527 529 531 533 535 537 539 541 543 545 547 549 551 553 555 557 559 561 563 565 if length firstLine 0 stop Check file intExtRisk unable to reference the required line call FALSE Get the matrix of extinction data extList lt scan intExtRisk skip firstLine 2 quiet TRUE flush TRUE nlines 1 what list thresh 0 prob 0 First get cumulative probability of metapopulation extinction ifelse extList thresh gt 0 Note if threshold gt 0 prob 0 0 statMat p pExt 0 0 statMat p pExt extList prob Get expected minimum metapopulation abundance lin
42. eric framework for evaluating conservation limits and harvest strategies In H R Akcakaya M A Burgman O Kindvall C C Wood P Sj gren Gulve J Hatfield and M A McCarthy eds Species conservation and management Case studies Oxford University Press ISBN 0 19 516646 9 Garshelis D L Johnson A M and Garshelis J A 1984 Social organization of sea otters in Prince William Sound Alaska Canadian Journal of Zoology 62 12 2648 2658 doi 10 1139 z84 385 Gerber L R Buenau K E and VanBlaricom G 2004 Density dependence and risk of extinction in a small population of sea otters Biodiversity and Conservation 13 2741 2757 doi 10 1007 s10531 004 2146 1 25 Gregr E J Nichol L M Watson J C Ford J K B and Ellis G M 2008 Estimating carrying capacity for sea otters in British Columbia Journal of Wildlife Management 72 2 382 388 doi 10 2193 2006 518 Grinnell M H and Curtis J M R 2011 User manual for NetworkDistances 1 0 Calculating network wise distances between habitat patches for spatially restricted species Canadian Technical Report of Fisheries and Aquatic Sciences 2960 Fish eries and Oceans Canada URL www dfo mpo gc ca libraries bibliotheques tech eng htm Hatfield T 2009 Identification of critical habitat for sympatric stickleback species pairs and the Misty Lake parapatric stickleback species pair Research Document 2009 056 Canadian Science Advisory Secretariat Fisheries a
43. es do not appear to follow an obvious trend with respect to the calculated metapopulation statistics Table 2 British Columbia sea otter hatitat patches ordered by decreasing median relative importance and then by the 95 percentile range of relative importance not shown from top to bottom nIter 200 iterations Also indicated is whether the patch was initially occupied No gt 0 Metapopulation statistics female metapopulation abundance N area of occupancy AO as patch area number of patches NP and extent of occurrence EO as minimum convex polygon Units AO and EO are in square kilometres km Note that N assumes that every patch is at carrying capacity k 1 27 females km Gregr et al 2008 Cumulative Patch No gt 0 z N AO NP N AO EO Pop 69 Yes 1 000 1208 952 1 1208 952 952 Pop 47 Yes 0 987 1073 845 2 2282 1796 1796 Pop 76 Yes 0 975 722 569 3 3004 2365 7 569 Pop 70 Yes 0 899 227 179 4 3231 2544 7569 Pop 67 Yes 0 886 224 176 5 3455 2720 12094 Pop 63 Yes 0 848 167 131 6 3622 2852 12540 Pop 57 Yes 0 835 162 127 7 3783 2979 14936 Pop 62 Yes 0 797 113 89 8 3897 3068 14936 Pop 38 Yes 0 785 151 119 9 4048 3188 19118 Pop 56 Yes 0 658 68 54 10 4116 3241 21147 Pop 75 Yes 0 658 18 61 11 4194 3302 21351 Pop 46 Yes 0 633 73 57 12 4267 3300 21351 Pop 30 Yes 0 608 57 45 13 4324 3404 22989 Pop 32 Yes 0 557 36 28 14 4359 3432 22989 Pop 68 Yes 0 557 33 26 15 4393 3459 22989 Pop 34 Yes 0 557 28 22 16 4420 3480 23871 Pop 55 Yes
44. etimes multiple patches maximize Ppers we resolved these patch importance ties by selecting the patch that maximizes metapopulation EMA over nYr years Nuin Ak akaya 2005 from the subset of patches that also maximize Ph Note that RAMAS Metapop calculates Ny as the mean over the nRep population trajectories of the minimum metapopulation abundance We used EMA as a secondary statis tic because EMA is a strong predictor of persistence McCarthy and Thompson 2001 In cases where multiple patches were equally important in terms of both Ppers and Nyjn we selected a patch at random from the subset of patches that maximized both Ppers and Nmim Ultimately this step identifies the most influen tial patch i e rank 1 and includes this patch in successive RAMAS Metapop runs 3 For each remaining patch run RAMAS Metapop to simulate population dy namics in scenarios that include the new patch and all patches previously iden tified as influential 4 Identify the next most influential patch in the metapopulation using the procedure outlined in Step 2 and include this patch in successive RAMAS Metapop runs 5 Repeat Steps 3 amp 4 until the least influential patch is identified i e rank num Iterate this inner loop nIter times to account for the variability in patch ranks due to stochasticity e g environmental demographic catastrophic modeled by RAMAS Metapop nRep replications Ak akaya 2005 Results are written to the qi r
45. figure sur la couverture et la page du titre Les rapports puis s seront fournis contre r tribution par les agents commerciaux Les num ros 1 456 de cette s rie ont t publi s titre de Rapports techniques de l Office des recherches sur les p cheries du Canada Les num ros 457 714 sont parus titre de Rapports techniques de la Direction g n rale de la recherche et du d veloppement Service des p ches et de la mer minist re de l Environnement Les num ros 715 924 ont t publi s titre de Rapports techniques du Service des p ches et de la mer minist re des P ches et de l Environnement Le nom actuel de la s rie a t tabli lors de la parution du num ro 925 Canadian Technical Report of Fisheries and Aquatic Sciences 2977 2012 USER MANUAL FOR PatchImportance 1 0 QUANTIFYING RELATIVE HABITAT PATCH IMPORTANCE BASED ON METAPOPULATION PERSISTENCE AND MINIMUM ABUNDANCE by M H Grinnell and J M R Curtis Fisheries and Oceans Canada Science Branch Pacific Region Pacific Biological Station 3190 Hammond Bay Road Nanaimo BC VOT 6N7 E mail matt grinnell dfo mpo gc ca tel 250 756 7326 TE mail janelle curtis dfo mpo gc ca tel 250 756 7157 Her Majesty the Queen in Right of Canada 2012 Cat No Fs 97 6 2977 E ISSN 0706 6457 Cat No Fs 97 6 2977 E PDF ISSN 1488 5379 Correct citation for this publication Grinnell M H and Curtis J M R 2012 User manual for PatchImporta
46. h which vecPers maxPers gt 1 Get the patches with the maximum pPers maxPersPops impMat impMat pPers maxPers Get the vector of abundances vecAbun lt maxPersPops nAbun Get the maximum of minimum abundance maxAbun max vecAbun na rm TRUE If there is more than one maximum more ties if length which vecAbun maxAbun gt 1 Get the patches with maximum persistence and abundance maxPersAbunPops lt impMat popID impMat pPers maxPers amp impMat nAbun maxAbun Break the tie by selecting a patch at random could use a third stat ranks m lt sample x maxPersAbunPops size 1 Update the number of random tie breaks nRandom lt nRandom 1 else End if there is more than one in maxAbun else Get the patch with the maximum abundance ranks m lt impMat popID impMat pPers maxPers amp impMat nAbun maxAbun Update the number of secondary tie breaks nSecond lt nSecond 1 End procedure if there is only one in maxThresh else End if more than one in maxPers else 37 567 569 571 573 575 577 579 581 583 585 587 589 591 593 595 597 599 601 603 605 607 609 611 613 615 617 619 621 623 625 627 629 Get the patch with the highest prob of persistence ranks m lt impMat popID impMat pPers maxPers End procedure for ranking patches Record persi
47. ich vec seqVec If there are less than 2 patches stop if nMatch lt 2 stop Require gt 2 patches named Pop 1 Pop 2 call FALSE Return the number of matches return nMatch End CountConsecutive function num lt CountPatches dat firstItemMP Print messages cat Input file mpFile with num patches nYr nYr nRep nRep and nIter nIter Nn The PatchImportance algorithm will call RAMAS Metapop nlter num num 1 2 times n sep if doSave cat Intermediate input and output files will not be saved to disk Nn Count the number of ties resolved using the second statistic and random nSecond O nRandom O Start loop over nIter for q in 1 nIter Vectors to fill in later could include other stats here if desired ranks lt vector Ranked patches 31 77 79 81 183 85 87 189 91 193 95 197 99 201 203 205 207 209 211 213 215 217 219 221 223 225 227 229 231 233 235 237 239 pProbs lt 0 Cumulative persistence probability nAbunds lt 0 Minimum metapopulation abundance Loop over the number of patches the determine next most influential patch for m in 1 num f Remove files from previous runs unlink x c batch file bat rep mp METABAT REC Metapop RES rep SCL Abund txt FinalStageN txt
48. ill issue errors and warnings if the required system dependent files are absent or if the user defined variables have values that are outside the aforementioned constraints Note that the PatchImportance code has extensive comments to enhance useability 4 2 Algorithm outline The goal of the PatchImportance code is to quantify the relative importance of each patch according to the probability of metapopulation persistence and metapopulation EMA Generally the PatchImportance algorithm is as follows 1 identify the most important patch 2 include the identified patch es in the metapopulation and identify the next most important patch 3 repeat Step 2 until the least important patch is identified and 4 repeat Steps 1 to 4 to quantify patch importance variability T More specifically the algorithm has an outer loop q over 1 nIter iterations and an inner loop m over 1 num patches within each iteration Figure 2 In the code and in this manual we use patch numbers 1 2 3 num to refer to patch names Pop 1 Pop 2 Pop 3 Pop num respectively The procedure for the inner loop is as follows 1 Run RAMAS Metapop once for each patch separately for nYr years and nRep replications 2 Identify the patch that maximizes the probability of metapopulation persistence P Pers LE Pg 2 where Pg is the cumulative probability of metapopulation extinction i e zero individuals over nYr years Ak akaya 2005 However som
49. movement and dispersal patterns among patches remain poorly quantified in BC We used data from a California sea otter radio tracking study Ralls et al 1996 in Krkosek et al 2007 to fit a dispersal distance function Mab 0 0524 1 2901e 67 1 where m is the yearly migration rate for juveniles and adults i e proportion of population a from patch a to patch b which are separated by centre to centre distance Da We modeled migration according to Equation 1 when 0 lt Das lt 100km we set m to zero for pups and when D gt 100km Garshelis et al 1984 Using this maximum dispersal distance allowed females to occupy offshore islands such as Haida Gwaii but prevented females from migrating along the entire coast in one year We modeled spatial environmental stochasticity by assuming that spatially proxi mate patches are subject to more similar environmental conditions i e weather events than distant patches For example two spatially proximate patches may have coinci dent variability in vital rates Ak akaya 2005 For our analysis we used Equation 1 to model the correlation of fecundity survival and carrying capacity among patches 3 3 Oil spill catastrophes We calculated probabilities for local e g between 0 16 and 16 million litres 1 and regional e g greater than 16 million 1 oil spills based on global tanker crude oil spill frequencies between 1985 and 1999 Anderson and LaBelle 2000 the volume of hy dro
50. n the metapopulation which is small e g AO 8 km and has intermediate relative importance causes EO to increase from 23871 to 42849 km Two other small patches of relatively low importance cause EO to increase substantially the 36 most impor tant patch Pop 13 EO from 108344 to 130 582 km and the 5371 most important patch Pop 80 EO from 138302 to 153759 km Thus including these three small patches of relatively low importance in the metapopulation has a strong influence on EO due to their remote geographic location Additionally remote patches may help establish multiple locations which help minimize impacts due to threats Criteria B amp D IUCN 2010 In this context a location is a geographically distinct area in which every individual could be impacted by a single threatening event such as a catastrophic oil spill Consider a second application in which patch importance values help identify the number and location of patches required to achieve a target metapopulation EMA For example our analysis suggests that 18 patches are required to achieve a metapopulation EMA gt 750 female otters Table 3 A few patches were required every iteration e g Pop 69 but most patches were only required in a minority of the iterations e g 3 of iterations for Pop 67 At carrying capacity these 18 patches could support up to N 4819 female otters with cumulative AO 3794km and cumulative EO 46 479 km 6 Extensions
51. nce 1 0 Quan tifying relative habitat patch importance based on metapopulation persistence and minimum abundance Can Tech Rep Fish Aquat Sci 2977 vi 41 p i Contents List of Figures List of Tables List of Listings Abstract R sum 1 2 Motivation Background British Columbia sea otters 3 1 Habitat suitability and patches 2 4000 e wie oe SS 3 2 Metapopulation dynamics ud eur ae ee ow ee EIER a 3 3 Oil spill catastrophes uou uos oe 208 le Sg ne ee al 4 Implementing PatchImportance 4 1 Set up and user defined variables 4 2 Algorithm outline SE LR ee ee Fe A eae AS A gt OUD AS ite AT art a See ook ais m dra mente Wei watts ENSE 5 Sea otter habitat patch importance 5 1 Relative patch importance Liz secre dep MAY ho Rae oe es 5 2 Probability of metapopulation persistence 5 3 Metapopulation expected minimum abundance 5 4 Spatial autocorrelation of important patches 5 9 Setting conservation targets auam ax coy A ice LS ceed BS ca 6 Extensions 6 1 Alternative statistics and modifications 6 2 Incorporating additional conservation tools 1 1 1 124 1 7 Conclusions 8 Acknowledgements References Appendix Index ill iv iv iv TA VM ER COND OD 11 13 14 15 19 20 20 22 23 23 24 29 41 List of Figures 1 British Columbia sea otter dist
52. nd Oceans Canada URL www dfo mpo gc ca csas IUCN International Union for the Conservation of Nature 2010 Guidelines for us ing the IUCN Red List categories and criteria Version 8 1 IUCN Species Survival Commission URL www iucnredlist org Prepared by the Standards and Petitions Subcommittee in March 2010 Johst K Brandl R and Eber 5 2002 Metapopulation persistence in dynamic landscapes The role of dispersal distance Oikos 98 2 263 270 doi 10 1034 j 1600 0706 2002 980208 x Jordan F Baldi A Orci K M R cz I and Varga Z 2003 Characterizing the im portance of habitat patches and corridors in maintaining the landscape connectivity of a Pholidoptera transsylvanica Orthoptera metapopulation Landscape Ecology 18 1 83 92 doi 10 1023 A 1022958003528 Krkosek M Lauzon Guay J and Lewis M A 2007 Relating dispersal and range expansion of California sea otters Theoretical Population Biology 71 4 401 407 doi 10 1016 j tpb 2007 01 008 Langhammer P F Bakarr M I Bennun L A Brooks T M Clay R P Darwall W De Silva N Edgar G J Eken G Fishpool L D C da Fonseca G A B Foster M N Knox D H Matiku P Radford E A Rodrigues A S L Salaman P Sechrest W and Tordoff A W 2007 Identification and gap analysis of key biodiversity areas Targets for comprehensive protected area systems Best Practices Protected Area Guidelines Series 15 International Union fo
53. o estimate the required computation time 4 3 Output For each iteration we ranked patches according to Ppers and Nmin and output patch ranks to the file ranks txt as an nIter x num matrix 71 1 T1 T3 VA T 1 num T21 T2 2 T2 3 AP T2 num T3 1 T3 2 T3 3 Vio T3 num 4 Tniter l Vnlter 2 fTnIter 3 Vnlternum where r identifies the m most influential patch in the q iteration For example r3 2 indicates that patch Pop 2 was the most influential patch m 1 in the third iteration q 3 Similarly Ppers and Nyin are output to the files pProbs txt and nAbunds txt respectively We used patch ranks to calculate a more intuitive measure of patch influence which we call relative patch importance ign max r ram 1 5 where max r is the maximum rank e g num Unlike patch ranks high relative importance values 4448 correspond to influential patches We rescaled relative patch importance values to range between 0 0 and 1 0 to facilitate interpretation Li and Wu 2004 5200 dax min i fan max i min i 6 where min i is the minimum relative patch importance value e g 1 0 Henceforth we refer to these rescaled relative patch importance values z as relative importance Compared to the average patch with z 0 5 more influential patches have higher relative importance 0 5 lt z lt 1 0 while less influential patches have lower relative importance 0 0 z 0 5 We quantified patch imp
54. olygon Units AO and EO are in square kilometres km Note that N assumes that every patch is at carrying capacity k 1 27 females km Gregr et al 2008 Cumulative Patch No gt O Ix N AO NP N AO EO Pop 69 Yes 100 1208 952 1 1208 952 952 Pop 47 Yes 100 1073 845 2 2282 1796 1796 Pop 76 Yes 100 722 569 3 3004 2365 7569 Pop 67 Yes 3 224 176 4 3228 2542 12094 Pop 70 Yes 3 227 179 5 3455 2720 12094 Pop 62 Yes 2 113 89 6 3568 2810 12094 Pop 57 Yes 1 162 127 r 3730 2937 14936 Pop 38 Yes 1 151 119 8 3881 3056 19118 Pop 75 Yes 1 78 6l 9 3959 3118 19322 Pop 74 Yes 1 8 6 10 3967 3124 20184 Pop8 No 1 9 7 11 39 6 3131 38603 Pop 46 Yes 1 73 57 12 4049 3188 38603 Pop 68 Yes 1 33 26 13 4082 3214 38603 Pop 29 No 1 43 34 14 4126 3249 44407 Pop 49 No 1 193 152 15 4319 3401 46479 Pop 39 No 1 1385 106 16 4454 3507 46479 Pop 25 No 1 350 2 6 17 4804 3783 46479 Pop59 No 1 14 11 18 4819 3794 46479 values may vary according to the statistics used to measure importance the metapopu lation dynamics parameter values as well as the spatial scale and extent of the habitat suitability map A number of other potential modifications are possible and we mention three of them here First users could quantify predictors e g patch size patch isolation associated with important patches to develop predictions based on patch attributes V geli et al 2010 Quantifying predictor importance could also help identify thresholds Fahrig 2001 Fagan et al 2003
55. onservation tools such as NetworkDistances Grinnell and Curtis 2011 and Conefor Sensin ode Saura and Torn 2009 to address some of the simplifying assumptions in RA MAS As one example RAMAS Metapop models that employ dispersal distance functions typically ignore the influence of barriers and other landscape attributes that influence dispersal rates However the effective distance between patches may not fall on a straight line for some species Because migration rates and connectivity may influ ence patch importance values it is critical to measure accurate distances among patches Spatially restricted species such as lotic fish may be required to travel further than the Euclidean i e straight line distance between patches In these cases Euclidean dis tances may under estimate effective inter patch distances which may affect simulated patch dynamics Johst et al 2002 Previously we developed the NetworkDistances code to measure non Euclidean inter patch distances Grinnell and Curtis 2011 which could modify the Pairwise_distance matrix Because patch centroids remain con stant among iterations only one instance of NetworkDistances would be required to parameterize the RAMAS Metapop input file Users could merge these two tools to quantify patch importance for spatially restricted species Second users could quantify patch importance based on connectivity statistics using the Conefor Sensinode software Saura and Torn 2009
56. op over rows for i in 1 nrow relImp i Add line for 95 range segments xO relImp impO25 i yO i xi relImp imp975 i yi i lwd 1 Add a grey rectangle for 50 4 range rect xleft relImp imp25 i ybottom i 0 25 xright relImp imp75 il ytop i 0 25 col grey 0 75 border NA Re plot dots points x relImp impMed i y i pch 19 cex 1 Add vertical lines for end of 95 range segments xO relImp impO25 i y0 i 0 15 xi relImp impO25 il yi i 0 15 lwd 1 5 segments xO relImp imp975 i y0 i 0 15 xi relImp imp975 i yi i 0 15 lwd 1 5 End i loop over rows Close the pdf dev off Plot probability of metapopulation persistence pdf height 6 width 6 file Persistence pdf Set up the plot area par mar c 3 6 3 5 1 5 0 1 Plot the median plot x 1 num y apply X dat2 MARGIN 2 FUN median ylim c 0 1 lwd 3 type l ann FALSE mtext side 1 line 2 5 Number of patches cex 1 25 mtext side 2 line 2 5 Probability of metapopulation persistence cex 1 25 mtext side 3 line 0 5 paste RAMAS Metapop file mpFile sep cex 1 25 Add 50 polygon polygon x c i num num 1 border NA col rgb 0 0 0 0 35 y c apply X dat2 MARGIN 2 FUN quantile probs 0 25 rev apply X dat2 MARGIN 2 FUN quantile probs 0 75 Add 95 lines 39 lines x 1 num y apply X dat2 MARGIN 2 FUN quantile probs 0 025 697 col black lwd 1 lines x 1 num y apply
57. operating systems provided they install the WineHQ pro gramme WPD 2010 which is required by RAMAS Metapop 4 1 Set up and user defined variables A minimum of three files are required in the working directory batch txt Listing 1 the RAMAS Metapop input file e g seaotter mp and the PatchImpor tance code PatchImportance R Two additional files must be present to run RA MAS Metapop on non Windows operating systems beforeMP and afterMP Listing 2 Because PatchImportance removes various temporary files and directories from the working directory additional files or directories in the working directory may be removed inadvertently Specify appropriate values for the required user defined variables before sourcing the PatchImportance code PatchImportance R Listing 3 Appendix mpFile RAMAS Metapop input file name with appropriate values and settings for the metapopulation Ak akaya 2005 Note that patch names must follow the GRIP naming convention e g Pop 1 Pop 2 Pop 3 Pop num where num is the number of patches satisfying the constraint num gt 2 to locate specific lines in the input file Value character e g seaotter mp Listing 1 The batch txt file is used by PatchImportance to create RAMAS Metapop Ak akaya 2005 batch files Note that the third line references the RAMAS Metapop executable START WAIT R SAM C Program Files RAMASGIS Metapop exe RUN YES TEX Listing
58. org R foundation for Statistical Computing Vienna Austria R version 2 14 0 2 Akcakaya H R 2005 RAMAS GIS Linking spatial data with population viability analysis Applied Biomathematics URL www ramas com User manual for version 5 3 WPD Wine Project Developers 2010 WineHQ Wine is not an emulator URL www winehq org Version 1 2 2 39 41 43 Tk Gk HH HR Gk Gb CHR RH HHH RH HK RH HHH RH HH RH HHH RH GE CHE RH HH CHR RH 45 29 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 01 03 105 07 4 4 Grinnell M H and Curtis J M R 2012 User manual for PatchImportance 1 0 Quantifying relative habitat patch importance based on metapopulation persistence and minimum abundance Can Tech Rep Fish Aquat Sci 2977 vi 41 p EEEE EE EEEE EE EEEE EEEE EEEE EEE EEEE EEEE EEEE EEE EEEE EEE EEEE EEEE EEEE EEE EEEE EEE EEE EEE Ed EEEE E EEEE EEEE EEEE EEEE EEEE EEEE EEEE EEEE EEEE Start file PatchImportance R EEEE EEE EEE EEEE EEEE EEEE EEEE EEEE EEEE EEE EEEE Housekeeping rm list ls graphics off ge sTime lt Sys time Clear the workspace Turn graphics off Empty the trash Start the timer VEEE EEEE EEEE EEEE EEEE EEEE EEEE E EEEE EEEE E E E Start user defined variables HHHHHETSHHUHTHHHHHHSSHUHHSSHTHTETHHHTETHHE
59. ortance z among iterations by the median and variability by the 50 and 95 percentile ranges These summary statistics could be used to 10 identify patches that differ significantly in importance such as patches for which the 95 percentile range does not overlap 0 5 Because we define patch importance by the 95 percentile range we expect that approximately 5 of patches will be significantly different from 0 5 due to chance alone The function CalcPatchImp dati dat2 dat3 calculates the aforementioned summary statistics for z Ppes and Nmin and writes these statistics to the file Relativelmportance csv The function also displays patch importance statistics in a figure PatchImportance pdf Figure 3 Two additional figures are created the relationship between the number of patches and Ppers Persistence pdf and the re lationship between the number of patches and Nu Abundance pdf Figure 4a amp b respectively Finally the function returns a list patchImp with four objects the aforementioned summary statistics in the data frame patchImp stats z in the ma trix patchImp imps Ppers in the matrix patchImp probs and Nyj in the matrix patchImp abunds If desired users could modify this function to calculate additional statistics and plot additional figures Although we have tested the PatchImportance code with several RAMAS Metapop input files users must ensure that PatchImportance results are mean ingful For example inves
60. ow of three text files at the end of each iteration patch ranks in ranks txt Pp in lPatch importance ties usually occur when Ppers 0 00 or Ppers 1 00 and their prevalence may be reduced by using a different nYr quasi extinction threshold or both The analysis counts the number of ties broken using the secondary statistic and by selecting a patch at random and prints a message to the R console if the number is gt 1 Note that the analysis evaluates num 1 x nIter ranks Create batch_file bat file and run RAMAS Metapop for nYr years and nRep replications TT Write output to text files TE he yes Quantify relative patch importance and variability End Patchimportance Figure 2 Simplified flow diagram of the PatchImportance algorithm which quanti fies the relative importance of habitat patches based on their influence on the probability of metapopulation persistence and the metapopulation expected minimum abundance using RAMAS Metapop Akcakaya 2005 pProbs txt and Nmin in nAbunds txt Because of the two nested loops the number of times that RAMAS Metapop is run Nmp is a function of nIter and num MERCI zem 3 which can result in a large number of RAMAS Metapop runs To reduce computation time users can divide the nIter iterations among several processors and then append the aforementioned text files by row q The analysis prints a progress message to the R console after each iteration to allow users t
61. pansion of the southern sea otter Ecological Applications 18 7 1781 1794 URL www jstor org stable 40062251 Tinker M T Doak D F Estes J A Hatfield B B Staedler M M and Bodkin J L 2006 Incorporating diverse data and realistic complexity into demographic estimation procedures for sea otters Ecological Applications 16 6 2293 2312 URL www jstor org stable 40061959 Urban D and Keitt T 2001 Landscape connectivity A graph theoretic perspective Ecology 82 5 1205 1218 doi 10 1890 0012 9658 2001 082 1205 LCAGTP 2 0 C0 2 Vogeli M Serrano D Pacios F and Tella J L 2010 The relative importance of patch habitat quality and landscape attributes on a declining steppe bird metapopu lation Biological Conservation 143 5 1057 1067 doi 10 1016 j biocon 2009 12 040 Watson J C Ellis G M Smith T G and Ford J K B 1997 Updated status of the sea otter Enhydra lutris in Canada The Canadian Field Naturalist 111 2 277 286 URL www biodiversitylibrary org Williams J C ReVelle C S and Levin S A 2005 Spatial attributes and reserve design models A review Environmental Modeling and Assessment 10 3 163 181 doi 10 1007 s10666 005 9007 5 WPD Wine Project Developers 2010 Wine Wine is not an emulator URL www winehq org Version 1 2 2 28 Appendix Electronic copies of the PatchImportance code PatchImportance R Listing 3 and the RAMAS Metapop input file for British Columbia
62. r influence on the probability of metapopulation persistence breaking ties based on the expected minimum metapopulation abundance That is to say compared to less important patches the inclusion of more important patches in the metapopulation increases the probability of metapopulation persistence or the expected minimum metapopulation abundance by a larger amount 17 19 21 Requirements In addition to this code at least two files are required in the working directory batch txt and the metapopulation input file e g seaotter mp Two programmes must be installed R 1 and RAMAS Metapop 2 Note that non Windows operating systems require two additional files beforeMP and afterMP to convert end of line characters between dos and unix as well as an additional programme WineHQ 3 to run RAMAS Metapop Read the PatchImportance user manual 4 for more implementation details analysis and an example using the British Columbia sea otter metapopulation 23 25 27 29 31 Notes Please contact the authors if you have questions comments suggestions or concerns regarding the code We are attempting to keep track of this code s use please cite the user manual 4 and contact the authors if you use PatchImportance for research Note that PatchImportance comes with absolutely no warranty 33 35 37 References 1 RDCT R Development Core Team 2011 R A language and environment for statistical computing URL www R project
63. r Endangered due to identified threats such as oil spills COSEWIC 2007 Despite the lack of quantitative recovery targets range expansion is crucial to reduce threats from oil spill catastrophes Nichol 2007 Quantifying patch importance is a critical step in identifying areas of high conserva tion value for sea otters In addition to supporting species specific conservation actions such areas could be used to inform science based processes to identify high priority ar eas for protection in Canadian marine spatial planning initiatives Clarke and Jamieson 2006a b To identify important sea otter patches using PatchImportance we mod eled the BC sea otter metapopulation using a realistic habitat map and population dynamics data as well as a possible future oil spill catastrophe scenario Table 1 3 1 Habitat suitability and patches Gregr et al 2008 quantified BC sea otter habitat suitability on a 0 5 x 0 5 kilometre 2 i Alaska United States 6000 British Columbia Canada North East Pacific Ocean 5800 Area Ve enlarged Le Aristazabal United Island States O Goose 500 0 9 N Islands 59051 UTM northing km 5600 Vancouver e Island Checleset EN Campbell eo River Bay EN current distribution 7907073 Vietoria 5400 e habitat patch centroid occupied o habitat patch centroid unoccupied 400 600 800 UTM easting km Figure 1 Current British Columbia sea otter distrib
64. r the Conservation of Nature URL www iucn org publications Gland Switzerland Li H and Wu J 2004 Use and misuse of landscape indices Landscape Ecology 19 4 389 399 doi 10 1023 B LAND 0000030441 15628 d6 Loughlin T R 1980 Home range and territoriality of sea otters near Monterey California The Journal of Wildlife Management 44 3 576 582 URL www jstor org stable 3808005 26 Mazet J A K Gardner I A Jessup D A and Lowenstine L J 2001 Effects of petroleum on mink applied as a model for reproductive success in sea otters Journal of Wildlife Diseases 37 4 686 692 URL www jwildlifedis org content 37 4 686 abstract McCarthy M A and Thompson C 2001 Expected minimum population size as a mea sure of threat Animal Conservation 4 4 351 355 doi 10 1017 5136794300100141X McLeod E Salm R Green A and Almany J 2009 Designing marine protected area networks to address the impacts of climate change Frontiers in Ecology and the Environment 7 7 362 370 doi 10 1890 070211 Nichol L 2007 Recovery potential assesment for sea otters Enhydra lutris in Canada Research Document 2007 034 Canadian Science Advisory Secretariat Fisheries and Oceans Canada URL www dfo mpo gc ca csas Nichol L M Boogaards M D and Abernethy R 2009 Recent trends in the abun dance and distribution of sea otters Enhydra lutris in British Columbia Research Document 2009 016 Canadian Science Advisory Secretari
65. relative importance In these cases quantifying the relative importance of each patch may be useful to the decision making process Urban and Keitt 2001 For example identifying the most important patches can help prioritize areas for protection and inform the development of conservation strategies to maxi mize the probability of species persistence given limited conservation resources Jord n et al 2003 In this paper we describe our simulation approach using PatchImpor tance which quantifies relative patch importance according to each patch s influence on the probability of metapopulation persistence and metapopulation expected minimum abundance EMA 2 Background This user manual follows the same outline as the NetworkDistances user manual Grinnell and Curtis 2011 because both tools may be useful to similar audiences and because both tools require similar data and programmes Users familiar with the GRIP Curtis and Naujokaitis Lewis 2008a b version 2 0 script or the NetworkDistances version 1 0 code may find it easier to implement the PatchImportance code but prior knowledge of either tool is not necessary The PatchImportance code can be implemented on a personal computer using easily accessible software Like GRIP PatchImportance is written in the programming language R RDCT 2011 and interacts with RAMAS Metapop Ak akaya 2005 Unlike GRIP PatchImpor tance quantifies the relative importance of each patch measured by i
66. ribution and habitat patches 3 2 Flow diagram of the PatchImportance algorithm 9 3 Relative importance of British Columbia sea otter habitat patches 12 4 Number of British Columbia sea otter habitat patches versus probability of persistence and minimum abundance 13 5 Number of British Columbia herring habitat patches versus probability of persistence and minimum abundance 15 6 Map of British Columbia sea otter habitat patch relative importance 16 List of Tables 1 British Columbia sea otter metapopulation model parameters 4 2 Relative habitat patch importance and metapopulation statistics for British Columbia sea otters a X4 uy su dant ane En ae EA 17 3 Patches required for metapopulation expected minimum abundance gt 750 female British Columbia sea otters 21 List of Listings 1 RAMAS Metapop batch file 6 2 Conversion files for non Windows machines T 3 The PatchImportance code 29 Abstract Grinnell M H and Curtis J M R 2012 User manual for PatchImportance 1 0 Quan tifying relative habitat patch importance based on metapopulation persistence and minimum abundance Can Tech Rep Fish Aquat Sci 2977 vi 41 p Those developing conservation strategies that include protected areas to ensure species persistence are often faced with the difficult choice of selecting a sub
67. s N stage matrices lt scan mpFile skip Line N stage matrices 1 nlines 1 what list quiet TRUE 33 307 309 311 313 315 317 319 321 323 325 327 329 331 333 335 337 339 341 343 345 347 349 351 353 355 357 359 361 363 365 367 369 The number of stage and standard deviation matrices N matrices lt as numeric N_stage_matrices 1 Read in the 4 line descriptions of the Stage_matrices and save as list Description_Stage_matrix lt vector list N_matrices Stage_matrices lt list for i in 1 N_matrices Description_Stage_matrix i lt scan mpFile quiet TRUE nlines 4 skip Line_N_stage_matrices i 1 4 i 1 N_stages sep what list Stage_matrices i lt matrix scan mpFile quiet TRUE skip Line_N_stage_matrices 4 i 1 4 i 1 N_stages nlines N_stages N_stages N_stages byrow TRUE Reference the location of the standard deviation matrix Line_N_stdev_matrices lt grep st dev matrix inputFile perl TRUE Get the information on this line N_stdev_matrices lt scan mpFile skip Line_N_stdev_matrices 1 nlines 1 what list quiet TRUE Read in the 1 line descriptions of the Stdev_matrices as a list Description_stdev_matrix lt vector list N_matrices Stdev matrices lt list for i in 1 N_matrices Description stdev matrix il lt scan
68. s txt sep 735 dat3 read table file nAbunds txt sep 737 Remove old output files from the directory unlink x c batch_file bat rep_ mp METABAT REC Metapop RES 739 rep_ SCL Abund txt FinalStageN txt Harvest txt Int txt Loc txt MetapopOcc txt Quasi txt Ter txt 741 Print end of file message and elapsed time 743 cat End of file PatchImportance R sep print Sys time sTime 745 Messages if ties broken using secondary statistic or random 747 if nSecond gt 0 message Note nSecond tie s resolved using the secondary statistic 749 format nSecond 100 num 1 nIter digits 3 if nRandom gt 0 message Note nRandom 751 tie s resolved by selecting a patch at random format nRandom 100 num 1 nIter digits 3 753 HHHHEHTHTETHTEHTHTHTHTETHTHETHTHHHTHTHTHTESTEHT 755 End of file PatchImportance R VERE EEEE EEE EE EEEE EE EEE EEE EE EEEE EE EEE EE E EE EE 40 Index Abundance pdf 11 afterMP 6 29 batch txt 6 29 beforeMP 6 29 CalcPatchImp dati dat2 dat3 11 Conefor Sensinode 22 critical habitat 1 DataOutput 11 doSave 7 11 ecological trap 15 GRIP 2 location 20 metapopulation 5 mpFile 6 nAbunds txt 10 NetworkDistances 1 22 nlter 7 non Windows operating systems 6 7 nRep 7 num 6 nYr 7 PacificHerring mp 14 29 P
69. set of the total area of suitable habitat for protection In these instances protecting the most impor tant habitat patches will facilitate efficient resource use and maximize the probability of metapopulation persistence However identifying important patches presents chal lenges and important patches may be currently unoccupied which makes their iden tification even more difficult To help identify candidate patches for protection we developed PatchImportance a tool that quantifies the relative importance of each patch based on its influence on the probability of metapopulation persistence and metapopulation expected minimum abundance We demonstrate our analysis using the British Columbia sea otter Enhydra lutris metapopulation as a case study R sum Grinnell M H and Curtis J M R 2012 User manual for PatchImportance 1 0 Quan tifying relative habitat patch importance based on metapopulation persistence and minimum abundance Can Tech Rep Fish Aquat Sci 2977 vi 41 p Dans le cadre des strat gies de conservation en plein d veloppement comprenant des zones prot g es pour garantir la survie des esp ces il faut souvent faire le choix diffi cile de s lectionner une sous partie de la zone totale constituant un habitat appropri pour la protection Dans ces cas la protection des parcelles d habitat les plus impor tantes permettra une utilisation plus efficace des ressources et maximisera les chances de survie de
70. stence and abundance could include other stats pProbs m lt maxPers nAbunds m lt impMat nAbun impMat popID ranks m Save output if specified if doSave Get list of required files could include other stats if desired mpFiles lt list files pattern rep mp extFiles lt list files pattern IntExtRisk txt Create a subdirectory to hold output data newDir lt paste OutputData output q m sep dir create path newDir Copy desired files file copy from c mpFiles extFiles to newDir End if doSave End m loop over num Write output data to text files write additional stats if included write ranks file ranks txt append TRUE sep ncolumns num write pProbs file pProbs txt append TRUE sep ncolumns num write nAbunds file nAbunds txt append TRUE sep ncolumns num Print progress message cat Finished iteration q of nIter sep print Sys time sTime End q loop over nIter Calculate and plot relative patch importance CalcPatchImp lt function dati dat2 dat3 Set up a matrix to hold importance values mati matrix NA nrow ncol dati ncol nrow dati Add row names rownames mati lt paste Pop 1 num sep Set up identical matrices to hold probability and incremental probability mat2 lt mati mat3 lt mati Loop over patches and assemble patch statistics
71. table patches may be sufficient to meet conservation goals Rosenfeld and Hatfield 2006 In such cases recovery teams are faced with the difficult problem of selecting which patches to protect i e deciding the number size shape and spatial configuration Di amond 1975 Pascual Hortal and Saura 2006 McLeod et al 2009 For example a given patch could be crucial to metapopulation persistence due to its location despite sup porting a low abundance of individuals Jordan et al 2003 Also currently unoccupied patches could be important in the future to facilitate an expanding distribution The issue of selecting patches for protection is further complicated by the complex nature of metapopulations which are influenced by factors that include patch specific population dynamics parameters that may be correlated among patches dispersal environmental stochasticity and catastrophes Selecting patches for protection can involve tradeoffs such as many small patches versus few large patches or closely spaced patches ver sus widely spaced patches Williams et al 2005 Metapopulation models are valuable conservation tools which can incorporate the aforementioned and other complexities to reveal underlying patterns compare alternative management actions and ultimately guide the management of species at risk Ak akaya et al 2007 Although most patches have the potential to support species survival and recovery patches may differ in their
72. tigate the RAMAS Metapop input and output files e g rep y mp and IntExtRisk y txt respectively where y indexes the RAMAS Metapop run If specified e g if doSave these files are saved in the directory DataOutput output q m where q indexes the outer loop and m indexes the inner loop 5 Sea otter habitat patch importance For our BC sea otter metapopulation case study with 80 patches we calculated Pp and Ny at nYr 100 years which corresponds to approximately 13 generations COSEWIC 2007 Using a 100 year timeline was sufficient for metapopulation abun dance to stabilize results not shown This timeline is also suggested for evaluating the probability of extinction for Canadian species at risk Criterion E COSEWIC 2010 which is adapted from the International Union for Conservation of Nature s Red List categories and criteria IUCN 2010 We also specified nRep 50 replications and nlter 200 iterations which was sufficient to stabilize patch ranks and variability 5 1 Relative patch importance The 95 percentile range of patch importance for the majority of patches overlaps 0 5 indicating that these patches are not significantly different than the average patch Figure 3 However the 95 percentile range for 5 patches lies completely above 0 5 suggesting that these patches may be more important than the average patch For example the 95 percentile range for the fourth most important patch Pop 70 on the West Co
73. ts influence on the probability of metapopulation persistence and metapopulation EMA We demonstrate PatchImportance by analysing the British Columbia BC sea ot ter Enhydra lutris metapopulation a marine mammal of Special Concern in Canada COSEWIC 2007 We provide some background information on BC sea otter habitat metapopulation dynamics and oil spill catastrophes in order to illustrate concepts lim itations and opportunities where appropriate The PatchImportance code is generic and could be applied to other species given sufficient metapopulation dynamics data We attempt to highlight sections of the code that may be customized to investigate other species or provide advice on related science based questions Please contact the authors if you have questions comments suggestions or concerns regarding this manual or the code We are attempting to keep track of this code s use please cite this manual and contact the authors if you use PatchImportance for research Note that PatchImportance comes with absolutely no warranty 3 British Columbia sea otters BC sea otters were hunted for their dense fur and extirpated in the early 20 century Since their reintroduction to Checleset Bay between 1969 and 1972 sea otters have increased in abundance and distribution Figure 1 Nichol et al 2009 BC sea otters are currently listed as Special Concern because the small population and limited range is susceptible to becoming Threatened o
74. uld be used to identify the number and location of patches required to achieve a target metapopulation statistic For example common metapop ulation statistics mentioned in species at risk recovery documents include metapop ulation abundance N of either all individuals or mature individuals AO number of patches and EO IUCN 2010 COSEWIC 2010 Patch importance values could help set recovery targets for species at risk for example consider the hypothetical recovery target of protecting the habitat required to support a theoretical maximum of N 5000 female otters According to our analysis protecting the 21 most important patches i e Pop 69 Pop 47 Pop 76 Pop 5 meets this target with cumulative N 5022 females when populations are at carrying capacity k 1 27 females km 2For consistency we continue to quantify metapopulation abundance in terms of female otters Also note that adult i e mature otters generally account for approximately 50 of total abundance COSEWIC 2007 19 Gregr et al 2008 and is associated with cumulative AO 3954 km and cumulative EO 73779 km Regarding the possibly under represented important patches on Haida Gwaii sug gested by our analysis Pop 10 is the most important of the 19 patches on Haida Gwaii but Pop 10 is the 18 most important patch in BC Also Pop 10 is the most important patch of the subset of patches that was not initially occupied The inclusion of Pop 10 i
75. ution Nichol et al 2009 habitat patches and place names mentioned in the text Geographic coordinates are projected in Universal Transverse Mercator UTM zone 9 in kilometres km km grid as a function of coastline and bathymetric complexity We used this habitat suitability map to identify discrete patches based on neighbourhood distance and a habitat suitability threshold As in Gregr et al 2008 we excluded the area East of Vancouver Island between Victoria and Campbell River and areas gt 5km from land We ran the RAMAS Patch programme Ak akaya 2005 on this habitat suitability map and identified 80 discrete patches of suitable sea otter habitat in BC Although the current distribution only covers a portion of the BC coast Nichol et al 2009 we 3 Table 1 Parameters used to model the British Columbia BC sea otter metapopula tion Units distance is in kilometres km Parameter description Value Type or units Reference Neighbourhood distance 2 500 km Loughlin 1980 Habitat suitability threshold 0 200 proportion Gregr et al 2008 Initial abundance 0 510 females km Greer et al 2008 Carrying capacity 1 270 females km Gregr et al 2008 Maximum growth rate 1 186 proportion Watson et al 1997 Survival of pups to juveniles 0 600 proportion Krkosek et al 2007 Juvenile survival 0 631 proportion Krkosek et al 2007 Survival of juveniles to adults 0 269 proportion Krkosek et al 2007 Adult surviv

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