A Null Model for Competitive Hierarchies in Competition Matrices

A more demanding definition of competitive transitivity ("complete transitivity") is introduced that defines a strict hierarchy of competitive relationships and that has more desirable properties for inferring competitive exclusion.

Abstract

To evaluate the tendency of plant species to be arranged in hierarchies of competitive ability, Keddy and Shipley (1989) introduced a definition of competitive transitivity in multispecies competition matrices and developed an inferential statistic to test for such a pattern. Here, I introduce a more demanding definition of competitive transitivity ("complete transitivity") that defines a strict hierarchy of competitive relationships and that has more desirable properties for inferring competitive exclusion. A null model, and its accompanying Monte Carlo test, is developed that can be used in analyzing empirical competition matrices. Ten published competition matrices are analyzed; nine show clear evidence of complete transitivity.