Mark–Recapture: Basic Models

Abstract

In this chapter, we consider the situation where we have a sequence of s samples with the ith sample taking place at time t i and, at each sample, individuals are captured, the unmarked are individually marked, and then they are all released, with the possibility that some do not survive the capture process. The first two models we consider are the time-specific Cormack-Jolly-Seber (CJS) and the Jolly-Seber (JS) models. They can be regarded as essentially the same model as it depends on which variables are treated as unknown constants. In the CJS model, we make a release of marked individuals of size R i , which is regarded as fixed, and the model only considers the histories of marked individuals. This type of approach can be referred to as the conditional likelihood, as it is conditional on the first captures. A helpful review of the literature using this idea for closed populations, with a particular focus on covariate information, was given by Huggins and Hwang (2011). Other reviews of capture-recapture models (as well as other methods of estimating population parameters) for both closed and open populations are given in Sect. 1.3. Since the same model can be used for either recaptures or just resighting of individuals (providing there are no losses on capture), it is not surprising that both processes can be combined in the same model, which we consider in a later chapter. Age-dependent models are considered in Sect. 7.4.6. We discussed the CJS model developed by Cormack (1964) in the previous chapter where resighting avoids some of the problems associated with the multiple handling of individuals. We assumed that the release is made at the beginning of each year (or interval) and a resighting is made at the beginning of the next year, just before the next new release of marked individuals. To fit in with the literature, we now label the first release as sample 1 and assume it is a representative (random) sample from the population, which is marked and then released. In the JS model, the ith sample is regarded as random with the u i unmarked forming the newly marked ith release. We can therefore condition on the R i or the u i , and we essentially have the same model