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MC ( MC ) MC : exploring M onte C arlo integration within MCMC for mark–recapture models with individual covariates
Author(s) -
Bonner Simon,
Schofield Matthew
Publication year - 2014
Publication title -
methods in ecology and evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.425
H-Index - 105
ISSN - 2041-210X
DOI - 10.1111/2041-210x.12095
Subject(s) - markov chain monte carlo , covariate , reversible jump markov chain monte carlo , inference , sampling (signal processing) , population , abundance estimation , statistics , mark and recapture , gibbs sampling , computer science , abundance (ecology) , mathematics , algorithm , biological system , bayesian probability , biology , ecology , artificial intelligence , demography , filter (signal processing) , sociology , computer vision
Summary Estimating abundance from mark–recapture data is challenging when capture probabilities vary among individuals. Initial solutions to this problem were based on fitting conditional likelihoods and estimating abundance as a derived parameter. More recently, B ayesian methods using full likelihoods have been implemented via reversible jump M arkov chain M onte C arlo sampling ( RJMCMC ) or data augmentation ( DA ). The latter approach is easily implemented in available software and has been applied to fit models that allow for heterogeneity in both open and closed populations. However, both RJMCMC and DA may be inefficient when modelling large populations. We describe an alternative approach using M onte C arlo ( MC ) integration to approximate the posterior density within a M arkov chain M onte C arlo ( MCMC ) sampling scheme. We show how this M onte C arlo within MCMC ( MCWM ) approach may be used to fit a simple, closed population model including a single individual covariate and present results from a simulation study comparing RJMCMC , DA and MCWM . We found that MCWM can provide accurate inference about population size and can be more efficient than both RJMCMC and DA . The efficiency of MCWM can also be improved by using advanced MC methods like antithetic sampling. Finally, we apply MCWM to estimate the abundance of meadow voles ( Microtus pennsylvanicus ) at the P atuxent W ildlife R esearch C enter in 1982 allowing for capture probabilities to vary as a function body mass.