Multisite and multispecies measures of overlap, co‐occurrence, and co‐diversity

Abstract

Several indices measure the association or segregation between two species and the similarity or differentiation between two sets of species. These indices are based on the overlap in the distribution of species (measured with the number of co‐occurrences) or on the overlap in species composition of sites (measured with the number of species that are shared between two sites). This paper shows that when evaluating more than two species the number of overlaps and the number of pairwise co‐occurrences are not equal, as it is the case for two species. Equivalently, when comparing more than two species assemblages, the number of overlaps differ from the number of instances of species sharing by pairs of sites (the ‘co‐diversities’). Considering this distinction, two different types of multispecies and multisite indices can be derived: indices of general overlap and indices of co‐occurrence or co‐diversity. Here I present a complete series of the two types of indices that correspond to the popular Jaccard, Sørensen, and Simpson two‐species or two‐site indices. Indices of general overlap are defined by three parameters (the total number of species, the total number of sites, and the total number of occurrences), whereas indices of co‐occurrence or co‐diversity depend on those parameters plus an additional one that is defined by the values of species richness or range size. Consequently, the two types of indices respond differently to null models, depending on the parameters that are fixed or randomized. All indices correlate well with the mean of the traditional indices calculated pair by pair, and the correspondence is extremely close for the new indices of co‐occurrence and co‐diversity. These properties should be useful in clarifying some of the confusion that exists in the current discussion about the advantages and disadvantages of pairwise vs community‐wide approaches in the analysis of diversity.