Chapter 4 - Closed Population Models

Abstract

In this chapter we introduce traditional (non-spatial) closed-population capture-recapture models for estimating abundance, emphasizing analysis in a Bayesian framework. If population size (N) is known, these models resemble simple logistic regressions, where the observations (0 = not captured or 1 = captured on each occasion) are Bernoulli trials with detection probability p. Usually, though, we are interested in estimating N, and we can do so using data augmentation, which involves adding a large number of all-zero encounter histories to the n observed encounter histories, and estimating how many of these hypothetical individuals are part of the population but were never observed. This reformulation of the capture-recapture model facilitates Bayesian analysis and the inclusion of individual covariates, and thus we use data augmentation frequently throughout the rest of the book. To demonstrate data augmentation, we present examples and BUGS code for non-spatial capture-recapture models incorporating different sources of variation in p. The drawback of non-spatial estimates of abundance is that they are not linked to a specific area and so ad hoc approaches are necessary to define an area in order to estimate density. We present some common approaches to do so and discuss their shortcomings. We show that individual covariate models, where the covariate is some description of an animal’s location in space, such as average capture location, are a step towards fully spatial capture-recapture models. The last section of this chapter highlights the parallels of distance sampling and spatial capture-recapture. Providing background on capture-recapture in general, the chapter facilitates understanding of spatial capture-recapture models, which are fully introduced in the following chapter.