Size of environmental grain and resource matching

For most animals their foraging environment consists of a patch network. In random environments there are no spatial autocorrelation at all, while in fine‐grained systems positive autocorrelations flip to negative ones and back again against distance. With increasing grain size the turnover rate of spatial autocorrelation slows down. Using a cellular automaton with foragers having limited information about their feeding environment we examined how well consumer numbers matched resource availability, also known as the ideal free distribution. The match is the better the smaller the size of the environmental grain. This is somewhat contrary to the observation that in large‐grained environments the spatial autocorrelation is high and positive over long distances. In such an environment foragers, by knowing a limited surrounding, should in fact know a much larger area because of the spatially autocorrelated resource pattern. Yet, when foragers have limited knowledge, we observed that the degree of undermatching (i.e., more individuals in less productive patches than expected) increases with increasing grain size.