Density dependence, territoriality, and divisibility of resources: from optimality models to population processes.

Species differ enormously in their territorial systems. Some species defend only small areas surrounded by undefended space, while others defend large contiguous territories. Using an optimization approach, we show that this variation can be explained from the density of two types of resources: divisible and nondivisible. We assume that benefits of territories are monotonously related to the defended amount of divisible resources (hereafter called food). In contrast, no benefits are obtained without a nondivisible resource (hereafter called nest site) in the territory, while more than one nest site does not further increase the benefits. The optimal territory size depends on the relative abundance of these resources. With a low density of nest sites, the optimal territory size is small and includes only the nest site. If the density of nest sites is relatively large, the optimal territory size is high, and territories are contiguous. Competition for these different resources yields contrasting patterns of how populations are regulated. If there is mainly competition for nest sites, we expect density-dependent exclusion through territoriality and no density-dependent reproduction. When competition is mainly for food, we expect density-dependent reproduction because optimal territory size will be compressed at higher densities, resulting in lower reproductive success. These predicted patterns indeed are observed in some well-studied passerine species for which both the territorial system and the occurrence of density dependence is known.