Mathematically and biologically consistent framework for presence–absence pairwise indices

Many indices based on presence‐absence data that compare two communities have been proposed, with the aim to characterize community similarity, species turnover or beta‐diversity, as well as other phenomena like community nestedness. These indices are often mathematically convertible to each other and are thus equivalent in terms of their information content. Based on this information equivalence, we classified all the indices to a few families, showing that only three families reflect ecologically relevant and directly interpretable phenomena, namely species turnover (family of Jaccard index that also includes Sørensen index of similarity), nestedness (the family of indices which compare species overlap with species richness of the species‐poor community), and the uniformity of species richness (comparing species richness of the two communities). Importantly, our analysis shows that any attempt to partition indices, including Baselga's approach to partition turnover and nestedness (i.e. to control an index for an effect of a different phenomenon), leads either to an index belonging to one of the three abovementioned families, or produces indices that do not measure any ecologically relevant phenomenon. We provide guidance on how to apply pairwise indices to make proper inference about ecological phenomena.