Combining prey choice and patch use–what does rate-maximizing Predict?

Theoretical work on optimal foraging has usually concentrated on either diet choice (which type of items should be accepted and which rejected) or patch use (when should a forager leave the patch and travel to a new one). We look at the combination of these paradigms and develop a general approach for the case of a forager that forages without time-constraints. The method we develop makes it easy to calculate which prey items to take and how long to stay in a patch given the habitat gain rate γ^* is known. We then give an algorithm to find both the optimal behaviour and γ^*. In contrast to previous results we show that the optimal diet for a rate-maximizing forager changes neither within a patch nor between patches. We further analyse the dependence of γ^* and therefore the optimal behaviour on encounter rates with prey items, the energetic value of the prey types, and travel time between patches.