Spatial distribution and deviations from the IFD when animals forage over large resource patches

Animal distribution among resource patches in a habitat has for the most part been treated as a deterministic process. When patch size is large compared with the animal's foraging range, individuals assess the quality of the patch by sampling small fractions of it, the sampled area (SA). In doing so, each individual may experience different patch qualities because of stochastic distribution of animal numbers in different SAs. We constructed an analytical model to explore the effect of stochasticity in the number of individuals within an SA on animal distribution between 2 patch types. We show that under certain assumptions, a global stable equilibrium in animal distribution is achieved, but this distribution is usually not ideal because different individuals experience different patch quality even within the same patch. We calculated the animal distribution at equilibrium for 2 different well-known gain functions and recorded their deviation from their respective ideal free distributions. The dependence of those deviations on population size may exhibit complex behaviors, which include minimal and maximal points, and the occurrence of undermatching and overmatching of the superior patch. The deviations depend strongly on the used gain function and its parameters. Our study illustrates the dramatic effects of stochastic assessment of patch value on animal spatial distribution.