Assessing the nonlinear decay of community similarity: Permutation and site‐block resampling significance tests

Aim Modelling how community similarity decays with spatial distance is a key tool for the study of the processes behind community variation (beta diversity). Distance‐decay models are computed from pairwise metrics (i.e. community similarity and spatial distance between localities) and hence suffer from pairwise dependence in the data, precluding the use of standard significance tests. Besides, distance‐decay patterns are inherently nonlinear because similarity is bounded between 1 and 0. However, the only standard method to assess model significance under pairwise dependency is the Mantel test, which considers a linear model. To allow the use of nonlinear models in the assessment of distance‐decay patterns, we introduce here a nonlinear significance test combining a pseudo‐ R 2 statistic with either permutations or block‐site resampling with replacement. Location Global. Taxon Applicable to any taxon. Methods To assess the performance of the pseudo‐ R 2 significance test (i.e. type I error and statistical power), we have applied this method to exponential and power‐law generalized linear models of simulated distance‐decay data. We compared its performance with the one of a linear model (i.e. Mantel test) and illustrated its use with real data. Results The pseudo‐ R 2 significance test has generally good type I error and statistical power, even for highly nonlinear relationships. The Mantel test shows an adequate empirical approximation of type I error, but presents lower statistical power when the distance‐decay relationship highly departs from linearity. Main conclusions The proposed pseudo‐ R 2 significance test for nonlinear models is adequate for exponential and power‐law models of distance‐decay of similarity and should be preferred over the linear Mantel test. Furthermore, this significance test could also be used in other nonlinear distance‐based regressions. The novel site‐block resampling method could also be applied to other statistical questions related to distance‐decay models that cannot be tackled using permutations, such as estimating the variance of model parameters.