Recently published in Oikos online is the paper by Carvalho et al. “Measuring fractions of beta diversity and their relationships to nestedness: a theoretical and empirical comparison of novel approaches”. Here, José Carvalho gives us the background and a summary of the paper:
Paul Jaccard proposed the well known Jaccard index of similarity in 1901. Since then the index has been used, in its (dis)similarity forms, widely by ecologists, notably in beta diversity studies. Beta diversity is one of the most broadest concepts in ecology, leading to multiple interpretations, meanings and discussions. This is probably the reason why ecologists took over more than 100 years to discover that the Jaccard index can be decomposed into two sound components of dissimilarity, replacement (turnover) and richness differences. Interestingly, after such a long time, two teams arrived independently to the same conclusions. This work represents the unification of the efforts made by the authors of both teams to elucidate others about the advantages of this approach in understanding the processes that originate beta diversity. However, the proposed decomposition is, indeed, much more general than a simple partitioning of a beta diversity measure, and applications in other fields may be expected. The generality of this approach comes from the fact that it may be viewed as the natural decomposition of a contingency table into two asymmetric components, representing the substitution of units (replacement) and differences in the number of units (richness differences).
Therefore, there is an intrinsic beauty in this approach, which comes from its generality, deep significance and remarkable simplicity.