Beta Diversity Calculator

Beta diversity is the compositional difference between communities, the bridge between local richness at one site (alpha) and total richness across a region (gamma). The three indices here approach that difference in two different ways. Jaccard and Sorensen are pairwise similarity coefficients built only from presence and absence: a species is either recorded at a site or it is not, and abundance is ignored. Jaccard divides shared species by the union of both lists, while Sorensen counts shared species twice and divides by the sum of the two lists. Sorensen is therefore always greater than or equal to Jaccard for the same data, and the two are related exactly by S = 2J / (1 + J). Whittaker beta works at a different scale, dividing regional gamma richness by mean alpha richness and subtracting one, so a value of 0 means every site holds the same species and a value of 3 means the region contains roughly four distinct community types. In practice, forest plots a few hundred metres apart often return Jaccard values of 0.5 to 0.8, while sites on opposite sides of a mountain range or across a salinity gradient can fall below 0.1. Two limitations dominate interpretation. First, incomplete sampling inflates beta diversity, because a species present but undetected reads as genuine turnover; rarefaction is needed before comparing sites sampled with different effort. Second, a single dissimilarity value cannot distinguish true species replacement from nestedness, where a poor site is simply a subset of a rich one, and those two patterns imply opposite reserve designs.

Paul Jaccard, a Swiss botanist working on alpine plant assemblages, published his coefficient de communaute in 1901 and refined it in a 1912 paper in the New Phytologist, seeking a way to state numerically how far the flora of one alpine district resembled another. The Danish botanist Thorvald Sorensen proposed his own coefficient in 1948 in a monograph on the analysis of Danish plant sociology, doubling the weight on shared species; the identical formula had been derived independently by Lee Raymond Dice in 1945 for ecological association, which is why it appears in the literature under both names. The scale-based framing came from Robert H. Whittaker. In his 1960 study of the vegetation of the Siskiyou Mountains of Oregon and California he introduced the terms alpha, beta and gamma diversity and defined beta as the ratio of gamma to alpha, giving ecologists a way to talk about turnover along environmental gradients rather than merely between pairs of plots. The field expanded sharply in the 2000s. Hakan Koleff and colleagues catalogued and compared 24 presence-absence beta measures in 2003, and Andres Baselga showed in 2010 that Sorensen dissimilarity can be partitioned additively into a turnover component and a nestedness component. Lou Jost argued in 2006 and 2007 that diversity partitions should be expressed in effective numbers of species, a correction that reshaped how multiplicative beta values are now reported.