Bayesian estimation of survival from mark-recapture data
Tóm tắt
An understanding of survival patterns is a fundamental component of animal population biology. Mark-recapture models are often used in the estimation of animal survival rates. Maximum likelihood estimation, via either analytic solution or numerical approximation, has typically been used for inference in these models throughout the literature. In this article, a Bayesian approach is outlined and an easily applicable implementation via Markov chain Monte Carlo is described. The method is illustrated using 13 years of mark-recapture data for fulmar petrels on an island in Orkney. Point estimates of survival are similar to the maximum likelihood estimates (MLEs), but the posterior variances are smaller than the corresponding asymptotic variances of the MLEs. The Bayesian approach yields point estimates of 0.9328 for the average annual survival probability and 14.37 years for the expected lifetime of the fulmar petrels. A simple modification that accounts for missing data is also described. The approach is easier to apply than augmentation methods in this case, and simulations indicate that the performance of the estimators is not significantly diminished by the missing data.
Tài liệu tham khảo
Ananda, M. M. A. (1997), “Bayesian Methods for Mark-Resighting Surveys,” Communications in Statistics—Theory and Methods, 26, 685–697.
Brooks, S. P., Catchpole, E. A., Morgan, B. J. T., and Barry, S. C. (2000), “On the Bayesian Analysis of Ring-Recovery Data,” Biometrics, 56, 951–956.
Buckland, S. T. (1980), “A Modified Analysis of the Jolly-Seber Capture-Recapture Model,” Biometrics, 36, 419–435.
— (1982), “A Mark-Recapture Survival Analysis,” Journal of Animal Ecology, 51, 833–847.
Carrick, R., and Dunnet, G. M. (1954), “Breeding of the Fulmar Fulmarus glacialis,” Ibis, 96, 356–370.
Castledine, B. J. (1981), “A Bayesian Analysis of Multiple-Recapture Sampling for a Closed Population,” Biometrika, 68, 197–210.
Clobert, J. (1981), “Etude de la Dynamique d’une Population d’Etourneauex Sansonnets (Sturris vulgaris, L.),” doctoral dissertation, Universite Catholique de Louvain, Louvain-la-Neuve, Belgique.
Cormack, R. M. (1964), “Estimates of Survival From the Sighting of Marked Animals,” Biometrika, 51, 429–438.
Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood From Incomplete Data via the EM Algorithm” (with discussion). Journal of the Royal Statistical Society, Series B, 39, 1–38.
Dunnet, G. M., Anderson, A., and Cormack, R. M. (1963), “A Study of the Survival of Adult Fulmars With Observations on the Pre-Laying Exodus,” British Birds, 56, 2–18.
Dupuis, J. A. (1995), “Bayesian Estimation of Movement and Survival Probabilities From Capture-Recapture Data,” Biometrika, 82, 761–772.
Fienberg, S. E., Johnson, M. S., and Junker, B. W. (1999), “Classical Multilevel and Bayesian Approaches to Population Size Estimation Using Multiple Lists,” Journal of the Royal Statistical Society, Series A, 162, 383–405.
Gaskell, T. J., and George, B. J. (1972), “A Bayesian Modification of the Lincoln Index,” Journal of Applied Ecology, 41, 377–384.
Gelman, A. (1996), “Inference and Monitoring Convergence,” in Markov Chain Monte Carlo in Practice, eds. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, London: Chapman and Hall, pp. 131–143.
George, E. I., and Robert, C. P. (1992), “Capture-Recapture Estimation via Gibbs Sampling,” Biometrika, 79, 677–683.
Gilks, W. R., Richardson, S., and Spiegelhalter, D. J., (eds.) (1996), Markov Chain Monte Carlo in Practice, London: Chapman and Hall.
Hastings, W. K. (1970), “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” Biometrika, 57, 97–109.
Jolly, G. M. (1965), “Explicit Estimates From Capture-Recapture Data With Both Death and Immigration—Stochastic Model,” Biometrika, 52, 225–247.
— (1982), “Mark-Recapture Models With Parameters Constant in Time,” Biometrics, 38, 301–321.
Kinas, P. G., and Bethlem, C. B. P. (1998), “Empirical Bayes Abundance Estimation of a Closed Population Using Mark-Recapture Data, With Application to Humpback Whales, Megaptera novaeangliae, in Abrolhos, Brazil,” Report of the International Whaling Commission, 48, 447–450.
Madigan, D., and York, J. C. (1997), “Bayesian Methods for Estimation of the Size of a Closed Population,” Biometrika, 84, 19–31.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A., and Teller, E. (1953), “Equations of State Calculations by Fast Computing Machines,” Journal of Chemistry and Physics, 21, 1087–1091.
Pollock, K. H. (1981), “Capture-Recapture Models Allowing for Age-Dependent Survival and Capture Rates,” Biometrics, 37, 521–529.
— (1991), “Modeling Capture, Recapture, and Removal Statistics for Estimation, of Demographic Parameters for Fish and Wildlife Populations: Past, Present, and Future,” Journal of the American Statistical Association, 86, 225–238.
Raftery, A. E., and Lewis, S. M. (1996), “Implementing MCMC,” in Markov Chain Monte Carlo in Practice, eds. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, London: Chapman and Hall, pp. 115–130.
Rodrigues, J., Bolfarine, H., and Galvao Leite, J. (1988), “A Bayesian Analysis in Closed Animal Populations From Capture Recapture Experiments With Trap Response,” Communications in Statistics, Part B—Simulation and Computation, 17, 407–430.
Sandland, R. L., and Kirkwood, G. P. (1981), “Estimation of Survival in Marked Populations With Possibly Dependent Sighting Probabilities,” Biometrika, 68, 531–541.
Seber, G. A. F. (1965), “A Note on the Multiple-Recapture Census,” Biometrika, 52, 249–259.
Smith, P. J. (1988), “Bayesian Methods for Multiple Capture-Recapture Surveys” Biometrics, 44, 1177–1189.
— (1991), “Bayesian Analyses for a Multiple Capture-Recapture Model,” Biometrika, 78, 399–408
Spiegelhalter, D. J., Thomas, A., Best, N. G., and Gilks, W. R. (1994), BUGS: Bayesian Inference Using Gibbs Sampling (Ver. 0.30). Cambridge: Medical Research Council Biostatistics Unit.
Vounatsou, P., and Smith, A. F. M. (1995), “Bayesian Analysis of Ring-Recovery Data via Markov Chain Monte Carlo Simulation,” Biometrics, 51, 687–708.
Zeh, J. E., Poole, D., Miller, G. W., Koski, W. R., Baraff, L., and Rugh, D. J. (2000), “Survival of Bowhead Whales, Balaena mysticetus, Estimated From 1981–98 Photo-Identification Data.” Paper SC/52/AS19 presented to the IWC Scientific Committee, June 2000.