On the role of patch density and patch variability in central-place foraging (Q1108965)

Existing models of the foraging behavior of single-prey loaders in patchy environments differs on whether the optimal forager is predicted to stay in a patch until a prey is found, or to leave a patch for a next one if a prey is not found by a certain ``deadline.'' This article examines conditions on the probability distribution of prey density across patches that are necessary or sufficient for the existence of a finite optimal deadline. It is shown that, for environments, in which prey density is variable but never falls below some strictly positive level, a finite, optimal deadline exists when and only when the spatial density of patches is ``high''. Also, a characterization is given of a large class of distributions (including the gamma distribution) for which a finite, optimal deadline exists for all levels of spatial density of patches.