A Null Model for Competitive Hierarchies in Competition Matrices

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.