Patch choice and population size

The distribution of animals between feeding patches has been the subject of considerable theoretical and empirical investigation. When all animals are equal and fitness is well represented by intake rate, the ideal free distribution requires the animals to be distributed in such a way as to equalize intake rate in each feeding patch. We refer to this as the equal rates policy. This approach ignores the effect of stochasticity in the food supply on starvation. It also ignores predation. An alternative approach is based on the assumption that each animal tries to minimize its death rate. An optimal policy now involves making decisions about which patch to use on the basis of the current level of energy reserves. We investigate a simple model of population dynamics in which over-winter mortality is either derived from animals adopting the equal rates policy or the optimal state-dependent policy to decide between two feeding patches. We show that the state-dependent policy results in a larger equilibrium population size than the equal rates policy. This difference can be considerable when the foraging environment is very stochastic. Furthermore, the state-dependent policy may result in a viable equilibrium population when the equal rates policy does not. The equilibrium under the state-dependent policy may be less stable than that under the equal rates policy. We identify conditions under which the state-dependent policy results in approximately equal intake rates on the two feeding patches. Levels of mortality as a result of predation are investigated. We show that, under some circumstances, the proportion of mortality that is due to predation may decrease as the predation pressure increases.