How does the size distribution of male territories depend on the spatial distribution of females?

Abstract

We consider the relation between the spatial distribution of resource related to the mating activity, for instance, spatially distributed females themselves and the size distribution of territories established by males for purpose of mating. Assuming the ranking related to the position of territory, we construct and analyze a mathematical model to consider how the spatial size distributions of the territories and the mating groups are affected by the spatial distribution of mating resource. Our modelling analyses clearly demonstrate that the size distribution of territories is significantly affected by the spatial distribution of mating resource. Although the general tendency of the spatial size distribution of territories is monotonically increasing as the territorial site becomes far from the most favorable place, a specific spatial distribution of mating resource can realize a monotonically decreasing size distribution of territories.