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Ratio‐ and Predator‐Dependent Functional Forms for Predators Optimally Foraging in Patches

Functional forms of predator‐prey interactions are developed for predators optimally foraging on prey distributed in patches. The model uses mean free‐path‐length theory to develop functional forms for two idealized behaviors of prey in patches. For congregating prey that maintain a fixed density, for example, fish schools, the predation rate has a ratio‐dependent form, and predator interference depends only on predator density. For sessile prey, which maintain a fixed patch size, a new predator‐dependent form emerges in which predator interference depends on both prey and predator densities. The Beddington‐DeAngelis equation is a special case of the sessile form. The model provides behavioral and biological criteria with which to select the functional form and ranges of coefficients appropriate for a particular food web. Finally, the model illustrates that behavior is an essential factor in predator‐prey dynamics.