Optimal foraging in patches: A case for stochasticity

Like much mathematical modeling in biology, most optimal foraging theory is developed from deterministic analogs of basically stochastic processes. Unlike other models, however, it cannot depend on laws of large numbers to justify this simplification; ignoring stochasticity can lead to wrong answers. This is demonstrated for a predator searching spatially separated patches of prey; it is shown that the choice of an optimal procedure for deciding when to leave a patch must be based on a stochastic model—a predator whose procedure is based on a deterministic model can do arbitrarily badly by comparison with the stochastic optimizer. A general solution is given, and its complexity suggests some objections to standard optimality arguments, and some possible alternatives.