Optimal Patch Time Under Exploitative Competition

Abstract

An important theoretical problem in behavioral ecology is the issue of how animals should use patchily distributed resources in order to maximize their rate of resource intake. Charnov (1976) provided an optimal-time solution (the marginal-value theorem) whereby a predator leaves a patch as the rate of prey capture decreases. Parker (1978) similarly analyzed the optimal copulation time for a male, with females considered as resource patches. In these works and most of the subsequent theoretical and experimental studies on optimal foraging, a single animal has been considered the optimizer of time investment (Pyke et al. 1977; Iwasa et al. 1981; Kamil and Sargent 1981; Krebs and McCleery 1984). In natural habitats, however, many animals appear to use their resources competitively, and therefore, the optimal strategy of each animal may depend on the strategies of other animals (Maynard Smith 1974). Here we present a simple game-theoretical model in which animals attempt to maximize their own rate of resource intake. Resource patches considered here are small enough that only one consumer can occupy a given patch. The patch may be a small area where prey is found, as in several experimental studies on small birds (Krebs et al. 1974; Cowie 1977); or it may be a single prey item (Cook and Cockrell 1978), a flower for bumblebees (Whitham 1977), or a female as a mate (Parker 1978). Competition for patches among consumers is assumed to exist as a natural consequence of the exploitation of limited resources, not because of direct interference (Miller 1967). Incorporation of interference competition in the model will be discussed later. The primary purposes of this paper are twofold: to demonstrate a method for finding the optimal strategy in competitive foraging; and to show how the optimal strategy depends on such parameters as the resource supply rate, the number of competitors, and searching efficiency. We also analyze a cooperative case, in which a number of animals attempt to maximize their total rate of resource intake, and we compare the results of the cooperative case and the competitive case. Finally, we discuss the implications of the model for application to actual experimental and observational studies.