Congestion Models of Competition

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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 fol- lowing 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 containsnocycles. This propertyhasmanyimplications. Thefraction 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 habi- tat. Ideal free distribution of predators may promote stability of two- trophic level 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. Much of the evidence supporting the view that interspecific competi- tion is important in shaping animal communities is concerned with the patterns of distribution of actual or potential competitors among habitats or microhabitats or with the ways the habitat distribution and the abun- dance of species are changed in the presence of competitors (e.g., Lack 1971; Schoener 1974; Diamond 1978, 1986; Cody 1985, p. 36; Diamond and Case 1986).

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