The Limiting Similarity, Convergence, and Divergence of Coexisting Species

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Abstract
1. There is a limit to the similarity (and hence to the number) of competing species which can coexist. The total number of species is proportional to the total range of the environment divided by the niche breadth of the species. The number is reduced by unequal abundance of resources but increased by adding to the dimensionality of the niche. Niche breadth is increased with increased environmental uncertainty and with decreased productivity. 2. There is a different evolutionary limit, L, to the similarity of two coexisting species such that a) If two species are more similar than L, a third intermediate species will converge toward the nearer of the pair. b) If two species are more different than L, a third intermediate species will diverge from either toward a phenotype intermediate between the two.

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