Ideal free distributions under predation risk

We examine the trade-off between gathering food and avoiding predation in the context of patch use by a group of animals. Often a forager will have to choose between feeding sites that differ in both energetic gain rate and predation risk. The ideal site will have a high gain rate and low risk of predation. However, intake rate will often decrease when the patch is shared with other foragers and it may be optimal for some individuals to feed elsewhere. Within the framework of ideal free theory, we investigate the distribution of foragers that will equalise individual fitness gains. We focus on a two-patch environment with continuous inputs of food. With reference to existing experimental studies, we examine the effects of risk dilution, food input rates and an animal's expectations of the future. We identify the effect of total animal numbers when one patch is subject to predation risk and the other is safe. Conditions under which the difference in intake rate in the two patches is constant are identified, as are conditions in which the ratio of animals in the two patches is constant, If current conditions do not alter future expectations an increase in input rates to the patches promotes increased use of the risky patch. Yet, if conditions are assumed to persist indefinitely the opposite effect is seen. When both patches are subject to predation risk, dilution of risk favours more extreme distributions, and may lead to more than one stable distribution. The results of these models are used to critically analyse previous work on the energetic equivalence of risk. This paper is intended to help guide the development of new experimental studies into the energy-risk trade-off.