Congestion Models of Competition

Igal Milchtaich

The American Naturalist 147 (), 760–783

Abstract

A model of habitat use, or more generally of resource use in a coarse-grained environment, is presented. Competitors are assumed to respond to the combined competitive pressure of conspecifics and heterospecifics by an ideal free distribution among (micro-)habitats—“ideal” in the sense that individuals are choosing only habitats where the negative effects of congestion are minimal and “free” in the sense that no direct interference and no travel costs are involved. It is shown that an ideal free habitat distribution generically has the following graph-theoretic property: when competitors and habitats are represented by vertices and each competitor is connected with each of the habitats in which it occurs, the resulting (undirected) graph contains no cycles. This property has many implications. The fraction of (micro-) habitats occupied by an average competitor should vary inversely with the number of competing species. Pairwise overlap between competitors should be limited to a maximum of one habitat. Ideal free distribution of predators may promote stability of two-trophic-Ievel communities. The chances that incipient species will be able to complete their speciation process during secondary contact are enhanced if their habitat distribution is ideal free.