Tests for character displacement

Character displacement is an important concept in ecology which has been surrounded by controversy due largely to a lack of clearly stated hypotheses and statistical tests. Existing tests implicity assume random species sizes estimated without error--a random-effects model. We introduce the log-uniform distribution for species sizes and show that it has properties of direct relevance to character displacement. We present tests which assume uniform and log-normal species sizes and have the log-uniform distribution as an alternative. The tests have low power for sample sizes typically encountered in ecology. The effect of estimating species sizes is small. The results exemplify the shortcomings of the traditional random-effects model for species sizes.