Species associations: The Kendall coefficient of concordance revisited

The search for species associations is one of the classical problems of community ecology. This article proposes to use Kendall's coefficient of concordance (W) to identify groups of significantly associated species in field survey data. An overall test of independence of all species is first carried out. If the null hypothesis is rejected, one looks for groups of correlated species and, within each group, tests the contribution of each species to the overall statistic, using a permutation test. A field survey of oribatid mites in the peat blanket surrounding a bog lake is presented as an example. In the permutation framework, an a posteriori test of the contribution of each "judge" (species) to the overall W concordance statistic is possible; this is not the case in the classical testing framework. A simulation study showed that when the number of judges is small, which is the case in most real-life applications of Kendall's test of concordance, the classical chi(2) test is overly conservative, whereas the permutation test has correct Type I error; power of the permutation test is thus also higher. The interpretation and usefulness of the a posteriori tests are discussed in the framework of environmental studies. They can help identify groups of concordant species that can be used as indices of the quality of the environment, in particular in cases of pollution or contamination of the environment.