Stopping Rules for Optimal Foragers

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Abstract
If an animal forages for prey that are distributed in patches, it must use some rule to decide when to leave one patch and go on to another. Charnov''s marginal value theorem tells when an animal should leave a patch, but it does not tell how an animal should decide when to leave a patch. This is important if patches vary in quality and the forager must use its experience in a patch to decide when best to leave a patch. A mathematically tractable stochastic model is presented in which animals forage systematically for prey distributed in patches, and 3 possible strategies (stopping rules) are considered. The best rule is found and compared with the giving-up time (GUT) rule and a fixed-time rule in which the forager remains until it has exhausted each patch. The GUT rule is better than the fixed-time rule for variable patches. It is relatively insensitive to environmental changes, but it is not as good as the best rule, which is called the assessment rule. The assessment rule is not only efficient, but it is simple enough that animals might be expected to be able to use it. The assessment rule is robust in the sense that the rate of finding prey achieved by a rule of the assessment type changes very little as the rule changes. This also means that a rule that is best for one environment will be quite good for environments that are substantially different.