Pairwise beta diversity resolves an underappreciated source of confusion in calculating species turnover

Beta diversity is an important metric in ecology quantifying differentiation or disparity in composition among communities, ecosystems, or phenotypes. To compare systems with different sizes (N, number of units within a system), beta diversity is often converted to related indices such as turnover or local/regional differentiation. Here we use simulations to demonstrate that these naive measures of dissimilarity depend on sample size and design. We show that when N is the number of sampled units (e.g., quadrats) rather than the true number of communities in the system (if such exists), these differentiation measures are biased estimators. We propose using average pairwise dissimilarity as an intuitive solution. That is, instead of attempting to estimate an N-community measure, we advocate estimating the expected dissimilarity between any random pair of communities (or sampling units)- - especially when the true N is unknown or undefined. Fortunately, measures of pairwise dissimilarity or overlap have been used in ecology for decades, and their properties are well known. Using the same simulations, we show that average pairwise metrics give consistent and unbiased estimates regardless of the number of survey units sampled. We advocate pairwise dissimilarity as a general standardization to ensure commensurability of different study systems.