Metapopulations, community assembly, and scale invariance in aspect space

The hierarchical competition model has been a useful tool in investigating the mechanisms of coexistence between competing species, and thus for understanding the foundations of biodiversity. Here we show that the geometric picture of community assemblage found by Nowak and May for the constant-fecundity version of this model can be extended to a whole family of tradeoffs between fecundity and mortality. In this picture, the proportion of the remaining space used by a species can be related to the amount of free space (in aspect space) behind the "competitive shadow" of the adjacent superior competitor, and in turn to the size of the competitive shadow cast by the species itself. We show that this geometric model is scale invariant in the rescaled aspect space and use this fact to investigate the limits to diversity and explore how communities assemble under this model.