When to Sample a Changing Patch

The abundance of food in the environment is seldom stable: the availability or quality of particular feeding sites or prey types may change unpredictably over the course of time, perhaps caused by depletion or depression by other foragers or by changes in the weather. As a consequence, one of the problems faced by foraging animals is keeping track of the status of their food resources. Sometimes there may be environmental cues to prey availability, but in instances where there are no such cues, a forager will be forced to sample its environment periodically. Stephens (1987) modeled the problem of how a rate-maximizing forager should track a changing environment. He considered the situation where there are two patch types available to a forager, one that fluctuates between good and bad states and one that remains stable at a value between the two states of the fluctuating patch. The fluctuating patch has a constant probability of changing state, and Stephens assumed that the forager can determine the state of the fluctuating patch as the result of a single sample. Given these assumptions, Stephens asked how a rate-maximizing forager should sample the fluctuating environment. The theoretical results of his model show that an optimal forager should sample the fluctuating patch at regular intervals. The optimal sampling frequency depends on the ratio of two kinds of cost: the lost opportunity experienced in the stable patch when the forager samples the fluctuating patch, and missing the opportunity to forage in the fluctuating site when it is in its good state.

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