Multiple site dissimilarity quantifies compositional heterogeneity among several sites, while average pairwise dissimilarity may be misleading

Several measures of multiple site dissimilarity have been proposed to quantify the overall heterogeneity in assemblage composition among any number of sites. It is also a common practice to quantify such overall heterogeneity by averaging pairwise dissimilarities between all pairs of sites in the pool. However, pairwise dissimilarities do not account for patterns of co-occurrence among more than two sites. In consequence, the average of pairwise dissimilarities may not accurately reflect the overall compositional heterogeneity within a pool of more than two sites. Here I use several idealized examples to illustrate why pairwise dissimilarity measures fail to properly quantify overall heterogeneity. Thereafter, the effect of this potential problem in empirical patterns is exemplified with data of world amphibians. In conclusion, when the attribute of interest is the overall heterogeneity in a pool of sites (i.e. beta diversity) or its turnover or nestedness components, only multiple site dissimilarity measures are recommended.