Optimal foraging: Some simple stochastic models (original) (raw)
Summary
Some simple stochastic models of optimal foraging are considered. Firstly, mathematical renewal theory is used to make a general model of the combined processes of search, encounter, capture and handling. In the case where patches or prey items are encountered according to a Poisson process the limiting probability distribution of energy gain is found. This distribution is found to be normal and its mean and variance are specified. This result supports the use of Holling's disc equation to specify the rate of energy intake in foraging models. Secondly, a model based on minimization of the probability of death due to an energetic shortfall is presented. The model gives a graphical solution to the problem of optimal choices when mean and variance are related. Thirdly, a worked example using these results is presented. This example suggests that there may be natural relationships between mean and variance which make solutions to the problems of ‘energy maximization’ and ‘minimization of the probability of starvation’ similar. Finally, current trends in stochastic modeling of foraging behavior are critically discussed.
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Author notes
- D. W. Stephens
Present address: Smithsonian Institution, Chesapeake Bay Center for Environmental Studies, P.O. Box 28, 21037, Edgewater, Maryland, USA
Authors and Affiliations
- Department of Zoology, Edward Grey Institute, South Parks Road, OX1 3PS, Oxford, England
D. W. Stephens - Department of Biology, University of Utah, 84112, Salt Lake City, Utah, USA
Eric L. Charnov
Authors
- D. W. Stephens
- Eric L. Charnov
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Stephens, D.W., Charnov, E.L. Optimal foraging: Some simple stochastic models.Behav Ecol Sociobiol 10, 251–263 (1982). https://doi.org/10.1007/BF00302814
- Received: 09 November 1981
- Accepted: 24 April 1982
- Issue date: July 1982
- DOI: https://doi.org/10.1007/BF00302814