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 ratioσ2/μof 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.