Optimal foraging in nonpatchy habitats. I. Bounded one-dimensional resource

Abstract

We present a model of optimal foraging in habitats where the food has an arbitrary density distribution (continuous or not). The classical models of foraging strategies assume that the food is distributed in patches and that the animal divides its time between the two distinct behaviors of patch exploitation and interpatch travel. This assumption is hard to accept in instances where the food distribution is continuous in space, and where travel and feeding cannot be sharply distinguished. In this paper, the habitat is assumed to be one-dimensional and bounded, and the animal is assumed to have a limited foraging time available. The problem is treated mathematically in the context of the calculus of variations. The optimal solution is to divide the habitat in two subsets according to the food density. In the richer subset, the animal equalizes the density distribution; in the poorer subset, it travels as fast as possible.