Optimal Foraging on Arbitrary Food Distributions and the Definition of Habitat Patches

Abstract

Most models for the optimal allocation of foraging effort in space and time assume that food is distributed in distinct patches. This assumption is often not justified. The problem, therefore, is in finding the optimal strategy for an animal exploiting a resource with an arbitrary spatial distribution, whether or not it is patchy. In this paper, we deal with the situation of a one-dimensional habitat. The model describes the optimal allocation of time to each point of the habitat. It is a generalization to arbitrary habitats of the classical "marginal-value theorem," which is obtained as the special case of an infinite environment with equally spaced patches. The model can also be extended to describe the optimal distribution of a population, thereby generalizing the "ideal free distribution." The model predicts that foraging should be restricted to places where food availability is higher than some threshold. In these places only, the foraging activity should follow the spatial variations in richness. A field study on insectivorous bats illustrates the model''s predictions. Finally, the model points to the difficulty of delimiting food patches when they need to be defined operationally, because a "patchy" distribution of consumers can overlie a continuous food distribution.