Hierarchical Modeling of Abundance in Closed Population Capture-Recapture Models Under Heterogeneity

摘要

Hierarchical modeling of abundance in space or time using closed-populationmark-recapture under heterogeneity (model M$_{h}$) presents two challenges: (i)finding a flexible likelihood in which abundance appears as an explicitparameter and (ii) fitting the hierarchical model for abundance. The firstchallenge arises because abundance not only indexes the population size, italso determines the dimension of the capture probabilities in heterogeneitymodels. A common approach is to use data augmentation to include these captureprobabilities directly into the likelihood and fit the model using Bayesianinference via Markov chain Monte Carlo (MCMC). Two such examples of thisapproach are (i) explicit trans-dimensional MCMC, and (ii) superpopulation dataaugmentation. The superpopulation approach has the advantage of simplespecification that is easily implemented in BUGS and related software. However,it reparameterizes the model so that abundance is no longer included, except asa derived quantity. This is a drawback when hierarchical models for abundance,or related parameters, are desired. Here, we analytically compare the twoapproaches and show that they are more closely related than might appearsuperficially. We exploit this relationship to specify the model in a way thatallows us to include abundance as a parameter and that facilitates hierarchicalmodeling using readily available software such as BUGS. We use this approach tomodel trends in grizzly bear abundance in Yellowstone National Park from1986-1998.