Plausible combinations: An improved method to evaluate the covariate structure of Cormack-Jolly-Seber mark-recapture models

Jeffrey F. Bromaghin, Trent L. McDonald, Steven C. Amstrup

Polar Bears International, Bozeman, USA.
US Geological Survey, Alaska Science Center, Anchorage, USA.
Western Ecosystems Technology, Inc., Cheyenne, USA.

DOI: 10.4236/oje.2013.31002                

Abstract

Mark-recapture models are extensively used in quantitative population ecology, providing estimates of population vital rates, such as survival, that are difficult to obtain using other methods. Vital rates are commonly modeled as functions of explanatory covariates, adding considerable flexibility to mark-recapture models, but also increasing the subjectivity and complexity of the modeling process. Consequently, model selection and the evaluation of covariate structure remain critical aspects of mark-recapture modeling. The difficulties involved in model selection are compounded in Cormack-Jolly-Seber models because they are composed of separate sub-models for survival and recapture probabilities, which are conceptualized independently even though their parameters are not statistically independent. The construction of models as combinations of sub-models, together with multiple potential covariates, can lead to a large model set. Although desirable, estimation of the parameters of all models may not be feasible. Strategies to search a model space and base inference on a subset of all models exist and enjoy widespread use. However, even though the methods used to search a model space can be expected to influence parameter estimation, the assessment of covariate importance, and therefore the ecological interpretation of the modeling results, the performance of these strategies has received limited investigation. We present a new strategy for searching the space of a candidate set of Cormack-Jolly-Seber models and explore its performance relative to existing strategies using computer simulation. The new strategy provides an improved assessment of the importance of covariates and covariate combinations used to model survival and recapture probabilities, while requiring only a modest increase in the number of models on which inference is based in comparison to existing techniques.

Keywords

Capture-Recapture; Survival; Model Building; Model Selection; Model Averaging; Multi-Model Inference; Covariates; Covariate Weights; CJS; Akaike’s Information Criterion; AIC; AIC_C

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Kuparinen, A., Alho, J.S., Olin, M. and Lehtonen, H. (2012) Estimation of northern pike population sizes via mark-recapture monitoring. Fisheries Management and Ecology, 19, 323-332. doi:10.1111/j.1365-2400.2012.00846.x
[2]	Harris, R.B., Winnie, J., Amish, S.J., Beja-Pereira, A., Godinho, R., Costa, V. and Luikart, G. (2010) Argali abundance in the Afghan Pamir using capture-recapture modeling from fecal DNA. Journal of Wildlife Management, 74, 668-677. doi:10.2193/2009-292
[3]	Sandercock, B.K. and Jaramillo, A. (2002) Annual survival rates of wintering sparrows: Assessing demographic consequences of migration. The Auk, 119, 149-165.
[4]	Duriez, O., S?ther, S.A., Ens, B.J., Choquet, R., Pradel, R., Lambeck, R.H.D. and Klaassen, M. (2009) Estimating survival and movements using both live and dead recoveries: A case study of oystercatchers confronted with habitat change. Journal of Applied Ecology, 46, 144-153. doi:10.1111/j.1365-2664.2008.01592.x
[5]	Doherty, P.F., Nichols, J.D., Tautin, J.,Voelzer, J.F., Smith, G.W., Benning, D.S., Bentley, V.R., Bidwell, J.K., Bollinger, K.S., Brazda, A.R., Buelna, E.K., Goldsberry, J.R., King, R.J., Roetker, F.H., Solberg, J.W., Thorpe, P.P. and Wortham, J.S. (2002) Sources of variation in breeding-ground fidelity of mallards (Anasplatyrhynchos). Behavioral Ecology, 13, 543-550. doi:10.1093/beheco/13.4.543
[6]	Punt, A.E., Buckworth, R.C., Dichmont, C.M. and Ye, Y. (2009) Performance of methods for estimating size-transition matrices using tag-recapture data. Marine and Freshwater Research, 60, 168-182. doi:10.1071/MF08217
[7]	Conn, P.B. and Cooch, E.G. (2009) Multistate capture-recapture analysis under imperfect state observation: An application to disease models. Journal of Applied Ecology, 46, 486-492. doi:10.1111/j.1365-2664.2008.01597.x
[8]	Schwarz, C.J., Bailey, R.E., Irvine, J.R. and Dalziel, F.C. (1993) Estimating salmon spawning escapement using capture-recapture methods. Canadian Journal of Fisheries and Aquatic Sciences, 50, 1181-1197. doi:10.1139/f93-135
[9]	O'Hara, R.B., Lampila, S. and Orell, M. (2009) Estimation of rates of births, deaths, and immigration from mark–recapture data. Biometrics, 65, 275-281. doi:10.1111/j.1541-0420.2008.01048.x
[10]	Conn, P.B., Gorgone, A.M., Jugovich, A.R., Byrd, B.L. and Hansen, L.J. (2011) Accounting for transients when estimating abundance of bottlenose dolphins in Choctawhatchee Bay, Florida. The Journal of Wildlife Management, 75, 569-579. doi:10.1002/jwmg.94
[11]	Fearnbach, H., Durban, J., Parsons, K. and Claridge, D. (2012) Photographic mark-recapture analysis of local dynamics within an open population of dolphins. Ecological Applications, 22, 1689-1700.
[12]	White, G.C., and Burnham, K.P. (1999) Program MARK: Survival estimation from populations of marked animals. Bird Study, 46, S120-S139. doi:10.1080/00063659909477239
[13]	Steidl, R.J. (2007) Limits of data analysis in scientific inference: Reply to Sleep et al. Journal of Wildlife Management, 71, 2122-2124. doi:10.2193/2007-187
[14]	Shaffer, T. L., and D. H. Johnson. (2008) Ways of learning: Observational studies versus experiments. Journal of Wildlife Management, 72, 4-13. doi:10.2193/2007-293
[15]	Burnham, K.P. and Anderson, D.R. (2001) Kullback-Leibler information as a basis for strong inference in ecological studies. Wildlife Research, 28, 111-119. doi:10.1071/WR99107
[16]	Lukacs, P.M., Burnham, K.P. and Anderson, D. (2010) Model selection bias and Freedman’s paradox. Annals of the Institute of Statistical Mathematics, 62, 117-125. doi:10.1007/s10463-009-0234-4
[17]	Sleep, D.J.H., Drever, M.C. and Nudds, T.D. (2007) Statistical versus biological hypothesis testing: Response to Steidl. Journal of Wildlife Management, 71, 2120-2121. doi:10.2193/2007-140
[18]	Sisson, S.A. and Fan, Y. (2009) Towards automating model selection for a mark-recapture-recovery analysis. Journal of the Royal Statistical Society: Series C, 58, 247-266. doi:10.1111/j.1467-9876.2008.00656.x
[19]	Stephens, P.A., Buskirk, S.W., Hayward, G.D. and Martinez Del Rio, C. (2005) Information theory and hypothesis testing: A call for pluralism. Journal of Applied Ecology, 42, 4-12. doi:10.1111/j.1365-2664.2005.01002.x
[20]	Jakeman, A.J., Letcher, R.A. and Norton, J.P. (2006) Ten iterative steps in development and evaluation of environmental models. Environmental Modelling & Software, 21, 602-614. doi:10.1016/j.envsoft.2006.01.004
[21]	Mac Nally, R. (2000) Regression and model-building in conservation biology, biogeography and ecology: The distinction between—and reconciliation of—“predictive” and “explanatory” models. Biodiversity and Conservation, 9, 655-671. doi:10.1023/A:1008985925162
[22]	Hunter, C.M., Caswell, H.,Runge, M.C., Regehr, E.V., Amstrup, S.C. and Stirling, I. (2010) Climate change threatens polar bear populations: A stochastic demographic analysis. Ecology, 91, 2883-2897. doi:10.1890/09-1641.1
[23]	McCrea, R.S. and Morgan, B.J.T. (2011) Multistate markrecapture model selection using score tests. Biometrics, 67, 234-241. doi:10.1111/j.1541-0420.2010.01421.x
[24]	King, R. and Brooks, S.P. (2008) On the Bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty. Biometrics, 64, 816-824. doi:10.1111/j.1541-0420.2007.00938.x
[25]	Lebreton, J.D., Burnham, K.P., Clobert, J. and Anderson, D.R. (1992) Modeling survival and testing biological hypotheses using marked animals—A unified approach with case-studies. Ecological Monographs, 62, 67-118. doi:10.2307/2937171
[26]	Amstrup, S.C., McDonald, T.L. and Manly, B.F.J. (2005). Handbook of capture-recapture analysis. Princeton University Press, Princeton.
[27]	Regehr, E.V., Hunter, C.M., Caswell, H., Amstrup, S.C. and Stirling, I. (2010) Survival and breeding of polar bears in the southern Beaufort Sea in relation to sea ice. Journal of Animal Ecology, 79, 117-127. doi:10.1111/j.1365-2656.2009.01603.x
[28]	Stirling, I., McDonald, T.L., Richardson, E.S., Regehr, E.V. and Amstrup, S.C. (2011) Polar bear population status in the northern Beaufort Sea, Canada, 1971-2006. Ecological Applications, 21, 859-876. doi:10.1890/10-0849.1
[29]	Chaloupka, M., and Limpus, C. (2005) Estimates of sex- and age-class-specific survival probabilities for a southern Great Barrier Reef green sea turtle population. Marine Biology, 146, 1251-1261. doi:10.1007/s00227-004-1512-6
[30]	Vogeli, M., Laiolo, P., Serrano, D. and Tella, J.L. (2008) Who are we sampling? Apparent survival differs between methods in a secretive species. Oikos, 117, 1816-1823. doi:10.1111/j.1600-0706.2008.17225.x
[31]	Marucco, F., Pletscher, D.H., Boitani, L., Schwartz, M.K., Pilgrim, K.L. and Lebreton, J. (2009) Wolf survival and population trend using non-invasive capture-recapture techniques in the western Alps. Journal of Applied Ecology, 46, 1003-1010. doi:10.1111/j.1365-2664.2009.01696.x
[32]	Catchpole, E.A., Fan, Y., Morgan, B.J.T., Clutton-Brock, T. and Coulson, T. (2004) Sexual dimorphism, survival and dispersal in red deer. Journal of Agricultural, Biological, and Environmental Statistics, 9, 1-26. doi:10.1198/1085711043172
[33]	Bromaghin, J.F., Gates, K.S. and Palmer, D.E. (2010) A likelihood framework for joint estimation of salmon abundance and migratory timing using telemetric mark- recapture. North American Journal of Fisheries Management, 30, 1385-1394. doi:10.1577/M10-065.1
[34]	Doherty, P., White, G. and Burnham, K. (2012) Comparison of model building and selection strategies. Journal of Ornithology, 152, 317-323. doi:10.1007/s10336-010-0598-5
[35]	RDCT (R Development Core Team) (2012) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://cran.r-project.org/
[36]	McDonald, T. (2012) mra: Analysis of mark-recapture data. R package version 2.10. http://cran.r-project.org/web/packages/mra/index.html
[37]	Thinh, V.T., Doherty, P.F., Bui, T.H. and Huyvaert, K.P. (2012) Road crossing by birds in a tropical forest in northern Vietnam. The Condor, 114, 639-644. doi:10.1525/cond.2012.100199
[38]	Pyne, M.I., Byrne, K.M., Holfelder, K.A., McManus, L., Buhnerkempe, M., Burch, N., Childers, E., Hamilton, S., Schroeder, G. and Doherty Jr., P.F. (2010) Survival and breeding transitions for a reintroduced bison population: A multistate approach. Journal of Wildlife Management, 74, 1463-1471.