Contributions to the Mathematics of Animal Trapping

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Abstract
The paper is concerned with probability distributions arising in live trapping studies on mammal populations, with emphasis on the effects of heterogeneity between animals. The distribution of observed length of residence of an animal in a defined study area is obtained for cases where: (i) the chance of capture on a given occasion varies between animals, having a beta distribution, while the probability of emigration during a given period is the same for all, and (ii) the probability of capture is constant but the emigration probability has a beta distribution. In the former case the distribution is a new one, whose probability generating function is essentially an Appell function of the fourth kind. Distributions of the number of times each animal would be captured in a fixed period are also discussed, and in a simple case the joint distribution of number of captures and length of residence is derived. Problems of estimation are considered, and the theory is illustrated by fitting data from recent work on voles and field mice.

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