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Biometrika 1971 58(1):61-75; doi:10.1093/biomet/58.1.61
© 1971 by Biometrika Trust
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On a theory of search

J. E. PALOHEIMO

University of Toronto

Stochastic models are developed to study the success of a search by what is termed a predator for randomly or contagiously located points, called prey. The model is specified by giving the distribution of the searching time to locate a prey, school or cluster of prey and the joint distribution of handling time and numbers caught from each cluster sighted. If a stationary distribution of prey is assumed and their removal is ignored, then the process is analogous to a cumulative renewal process. The mean numbers of prey or clusters of prey and their variances are readily obtained by use of limit theorems of renewal theory.

Key Words: Predator - prey interaction • Stochastic theory of search for contagiously distributed prey • Poisson search with a delay time • Catch by a predator


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