The relationship between species replacement, dissimilarity derived from nestedness, and nestedness

Aim Beta diversity can be partitioned into two components: dissimilarity due to species replacement and dissimilarity due to nestedness (Baselga, 2010, Global Ecology and Biogeography, 19, 134143). Several contributions have challenged this approach or proposed alternative frameworks. Here, I review the concepts and methods used in these recent contributions, with the aim of clarifying: (1) the rationale behind the partitioning of beta diversity into species replacement and nestedness-resultant dissimilarity, (2) how, based on this rationale, numerators and denominators of indices have to match, and (3) how nestedness and nestedness-resultant dissimilarity are related but different concepts. Innovation The rationale behind measures of species replacement (turnover) dictates that the number of species that are replaced between sites (numerator of the index) has to be relativized with respect to the total number of species that could potentially be replaced (denominator). However, a recently proposed partition of Jaccard dissimilarity fails to do this. In consequence, this partition underestimates the contribution of species replacement and overestimates the contribution of richness differences to total dissimilarity. I show how Jaccard dissimilarity can be partitioned into meaningful turnover and nestedness components, and extend these new indices to multiple-site situations. Finally the concepts of nestedness and nestedness-resultant dissimilarity are discussed. Main conclusions Nestedness should be assessed using consistent measures that depend both on paired overlap and matrix filling, e.g. NODF, whereas beta-diversity patterns should be examined using measures that allow the total dissimilarity to be separated into the components of dissimilarity due to species replacement and dissimilarity due to nestedness. In the case of multiple-site dissimilarity patterns, averaged pairwise indices should never be used because the mean of the pairwise values is unable to accurately reflect the multiple-site attributes of dissimilarity.