Two major classes of distance-overlap (or similarity) measures and their special cases based on the functional beta diversity .

The corresponding differentiation measures are the one-complements of the similarity measures. (The indices i and j are used to identify species, i, j = 1, 2, …, S, and the indices k and m are used to identify assemblages, k, m = 1, 2, …, N.)Notation.zik = the abundance of the ith species in the kth assemblage, , , and ; see text for details. = sum of the pairwise distances between species in the pooled assemblage; = sum of FAD over all possible pairs of assemblages (there are N2 pairs of assemblages). S = species richness in the pooled assemblage. = average species richness per assemblage.