OJE  Vol.5 No.1 , January 2015
Bayesian Estimation of Population Size via Capture-Recapture Model with Time Variation and Behavioral Response
Abstract: We consider the problem of population estimation using capture-recapture data, where capture probabilities can vary between sampling occasions and behavioural responses. The original model is not identifiable without further restrictions. The novelty of this article is to expand the current research practice by developing a hierarchical Bayesian approach with the assumption that the odds of recapture bears a constant relationship to the odds of initial capture. A real-data example of deer mice population is given to illustrate the proposed method. Three simulation studies are developed to inspect the performance of the proposed Bayesian estimates. Compared with the maximum likelihood estimates discussed in Chao et al. (2000), the hierarchical Bayesian estimate provides reasonably better population estimation with less mean square error; moreover, it is sturdy to underline relationship between the initial and re-capture probabilities. The sensitivity study shows that the proposed Bayesian approach is robust to the choice of hyper-parameters. The third simulation study reveals that both relative bias and relative RMSE approach zero as population size increases. A R-package is developed and used in both data example and simulation.
Cite this paper: Wang, X. , He, Z. and Sun, D. (2015) Bayesian Estimation of Population Size via Capture-Recapture Model with Time Variation and Behavioral Response. Open Journal of Ecology, 5, 1-13. doi: 10.4236/oje.2015.51001.

[1]   Agresti, A. (1994) Simple Capture-Recapture Models Permitting Unequal Catch Ability and Variable Sampling Effort. Biometrics, 50, 494-500.

[2]   Chao, A., Chu, W. and Hsu, C. (2000) Capture Recapture When Time and Behavioral Response Affect Capture Probabilities. Biometrics, 56, 427-433.

[3]   Norris III, J.L. and Pollock, K.H. (1995) A Capture-Recapture Model with Heterogeneity and Behavioural Response. Environmental and Ecological Statistics, 2, 305-313.

[4]   Norris, J.L. and Pollock, K.H. (1996) Nonparametric MLE under Two Closed Capture-Recapture Models with Heterogeneity. Biometrics, 52, 639-649.

[5]   Otis, D.L., Burghal, K.P., White, G. and Anderson, D. (1978) Statistical Inference from Capture Data on Closed Animal Populations. Wildlife Monographs, 62, 1-135.

[6]   Pledger, S. (2000) Uniffed Maximum Likelihood Estimates for Closed Capture-Recapture Models Using Mixtures. Biometrics, 56, 434-442.

[7]   Chao, A., Lee, S.M. and Jeng, S.L. (1992) Estimating Population Size for the Capture-Recapture Data When Capture Probabilities Very by Time and Individual Animal. Biometrics, 48, 201-216.

[8]   Lee, S.M. (1996) Estimating Population Size for Capture-Recapture Data When Capture Probabilities Vary by Time, Behavior and Individual Animal. Communications in Statistics-Simulation, 25, 431-457.

[9]   Lee, S.M. and Chao, A. (1994) Estimating Population Size via Sample Coverage for Closed Capture-Recapture Model. Biometrics, 50, 80-97.

[10]   Yip, P. (1989) An Inference Procedure for a Capture and Recapture Experiment with Time-Dependent Capture Probabilities. Biometrics, 45, 471-479.

[11]   Yip, P. (1991) A Martingale Estimating Equation for a Capture-Recapture Experiment in Discrete Time. Biometrics, 47, 1081-1088.

[12]   Yip, P.S.F. and Fong, D.Y.T. (1993) Estimating Population Size by Recapture Sampling via Estimating Function. Communications in Statistics-Stochastic Models, 9, 179-193.

[13]   Basu, S. and Ebrahimi, N. (2001) Bayesian Capture-Recapture Methods for Error Detection and Estimation of Population Size Heterogeneity and Dependence. Biometrika, 88, 269-279.

[14]   Bolfarine, H., Leite, J.G. and Rodrigues, J. (1992) On the Estimation of the Size of a Finite and Closed Population. Biometrical Journal, 34, 577-593.

[15]   Castledine, B.J. (1981) A Bayesian Analysis of Multiple-Recapture Sampling for a Closed Population. Biometrika, 68, 197-210.

[16]   Chavez-Demoulin, V. (1999) Bayesian Inference for Small Sample Capture-Recapture Data. Biometrics, 55, 727-731.

[17]   Dupuis, J.A. (1995) Bayesian Estimation of Movement and Survival Probabilities from Capture-Recapture Data. Biometrics, 82, 761-772.

[18]   Gazey, W.J. and Staley, M.J. (1986) Population Estimation from Mark-Recapture Experiments Using a Sequential Bayes Algorithm. Ecology, 67, 941-951.

[19]   King, R. and Brooks, S. (2008) On the Bayesian Estimation of a Closed Population Size in the Presence of Heterogeneity and Model Uncertainty. Biometrics, 64, 816-824.

[20]   Lee, S.M. and Chen, C.W.S. (1998) Bayesian Inference of Population Size for Behavioral Response Models. Statistical Sinica, 8, 1233-1247.

[21]   Lee, S.M., Hwang, W.H. and Huang, L.H. (2003) Bayes Estimation of Population Size from Capture-Recapture Models with Time Variation and Behavior Response. Statistical Sinica, 13, 477-494.

[22]   Wang, X. (2002) Bayesian Analysis of Capture-Recapture Sampling for a Closed Population. Ph.D. Dissertation, University of Missouri-Columbia, Columbia.

[23]   Wang, X., He, Z. and Sun, D. (2007) Bayesian Population Estimation for Small Sample Capture-Recapture Data Using Non-Informative Prior. Journal of Statistical Planning and Inference, 137, 1099-1118.

[24]   Amstrup, S.C., McDonald, T.L. and Manly, B.F.J. (2005) Handbook of Capture Recapture Analysis. Princeton University Press, Princeton.

[25]   Chao, A. (2001) An Overview of Closed Capture-Recapture Models. Journal of Agricultural, Biological, and Environmental Statistics, 6, 158-175.

[26]   Pollock, K.H., Nichols, J.D., Brownie, C. and Hines, J.E. (1990) Statistical Inference for Capture-Recapture Experiments. Wildlife Monographs, 107, 1-97.

[27]   Schwarz, C.J. and Seber, G.A.F. (1999) Estimating Animal Abundance: Review III. Statistical Science, 14, 427-456.

[28]   Seber, G.A.F. (1992) A Review of Estimating Animal Abundance II. International Statistical Review, 60, 129-166.

[29]   Williams, B.K., Nichols, J.D. and Conroy, M.J. (2002) Analysis and Management of Animal Populations. Academic Press, San Diego.

[30]   Tanaka, R. (1951) Estimation of Vole and Mouse Population on Mount Ishizuchi and on the Uplands of Southern Shikoku. Journal of Mammalogy, 32, 450-458.

[31]   Tanaka, R. (1952) Theoretical Justification of the Mark and Release Index for Small Mammals. Bulletin of the Kochi Women’s College, 1, 38-47.

[32]   Seber, G. (1973) The Estimation of Animal Abundance and Related Parameters. Griffin, London.

[33]   George, E.I. (1992) Capture-Recapture Estimation via Gibbs Sampling. Biometrika, 79, 677-683.

[34]   Raftery, A.E. (1987) Inference and Prediction for General Order Statistic Model. Journal of the American Statistical Association, 82, 1163-1168.

[35]   Raftery, A.E. (1988) Analysis of Simple Debugging Model. Applied Statistics, 37, 12-32.

[36]   Raftery, A.E. (1988) Inference for the Binomial N Parameter: A Hierarchical Bayes Approach. Biometrika, 75, 223-228.

[37]   Smith, P.J. (1991) Bayesian Analysis for a Multiple Capture-Recapture Model. Biometrika, 78, 399-407.

[38]   Gilk, W. (1992) Derivative-Free Adaptive Rejection Sampling for Gibbs Sampling. In: Bernardo, J.M., Beger, J.O., Dawi, A.P. and Smith, A.F.M., Eds., Bayesian Statistics 4, Oxford University Press, Oxford, 641-649.