Density-Dependent Patch Exploitation and Acquisition of Environmental Information

We study density-dependent resource harvest patterns due to Bayesian foraging for different distributions of resources. We first consider a forager with information about the stochastic properties of its environment. In this case we show that when the number of food items per patch follows a distribution from the exponential family, the density dependence is given by the ratio _2+ of the distribution of number of food items per patch. Bayesian foraging can therefore lead to positive (negative binomial distribution) or negative (binomial distribution) density dependent resource harvest and even to density independent (Poisson distribution) resource harvest, depending on the distribution of resources in the environment. In a second stage we incorporate learning about the distribution of resources in the whole environment. The mean of the distribution of number of food items per patch of a given environment is learnt faster than the variance of the distribution. Learning occurs faster in poorer than richer environments.] 1997 Academic Press Different foraging theory models focus on different aspects of the predator-prey interaction. A large body of the literature concentrates in looking for ‘‘optimal’’ foraging strategies, behaviors that will maximise expected net energy intake during the foraging period in a number of circumstances (see Stephens and Krebs, 1986; Lima and Dill, 1990; Ylo nen and Magnhagen, 1992 for different reviews). Other models study the changes in feeding efficiency in response to changes in resource den-sity across patches (Holling, 1965; Charnov, 1976; Green, 1988; Bernstein et al., 1991). This second aspect has obvious links with predatorprey theory and popula-tion dynamics and stability (see Murdoch and Oaten