Measuring fractions of beta diversity and their relationships to nestedness: a theoretical and empirical comparison of novel approaches

Beta diversity and nestedness are central concepts of ecology and biogeography and evaluation of their relationships is in the focus of contemporary ecological and conservation research. Beta diversity patterns are originated from two distinct processes: the replacement (or turnover) of species and the loss (or gain) of species leading to richness differences. Nested distributional patterns are generally thought to have a component deriving from beta diversity which is independent of replacement processes. Quantification of these phenomena is often made by calculating a measure of beta diversity, and the resulting value being subsequently partitioned into a contribution by species replacement plus a fraction shared by beta diversity and nestedness. Three methods have been recently proposed for such partitioning, all of them based on pairwise comparisons of sites. In this paper, the performance of these methods was evaluated on theoretical grounds and tested by a simulation study in which different gradients of dissimilarity, with known degrees of species replacement and species loss, were created. Performance was also tested using empirical data addressing land‐use induced changes in endemic arthropod communities of the Terceira Island in the Azores. We found that the partitioning of βcc (dissimilarity in terms of the Jaccard index) into two additive fractions, β‐₃ (dissimilarity due to species replacement) plus βᵣᵢcₕ (dissimilarity due to richness differences) reflects the species replacement and species loss processes across the simulated gradients in an ecologically and mathematically meaningful way, whilst the other two methods lack mathematical consistency and prove conceptually self‐contradictory. Moreover, the first method identified a selective local extinction process for endemic arthropods, triggered by land‐use changes, while the latter two methods overweighted the replacement component and led to false conclusions. Their basic flaw derives from the fact that the proposed replacement and nestedness components (deemed to account for species loss) are not scaled in the same way as the measure that accounts for the total dissimilarity (Sørensen and Jaccard indices). We therefore recommend the use of βcc=β‐₃+βᵣᵢcₕ, since its components are scaled in the same units and their responses are proportional to the replacement and the gain/loss of species.