Assessing the nonlinear decay of community similarity: permutation and site-block resampling significance tests

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-R2 statistic with either permutations or block-site resampling with replacement