A new twist on a very old binary similarity coefficient

Pairwise similarity coefficients are downward biased when samples only record presences and sampling is partial. A simple but forgotten index proposed by Stephen Forbes in 1907 can help solve this problem. His original equation requires knowing the number of species absent in both samples that could have been present. It is proposed that this count should simply be ignored and that the coefficient should be adjusted using a simple heuristic correction. Four analyses show that the corrected equation outperforms the Dice and Simpson indices, which are highly correlated with many others. In two-sample simulations, similarity is almost always closer to the assumed value when the species pool size and sampling intensity are varied, regardless of whether the underlying abundance distribution is uniform, log-normal, or geometric. The index is also much more robust when sampling is unequal. An analysis of bat samples from peninsular Malaysia buttresses these conclusions. The corrected coefficient also indicates that local assemblages of North American mammals are random subsamples of larger species pools by returning similarity of values of around 1, and it suggests a more consistent relationship between biome-scale comparisons and local-scale comparisons. Finally, it yields a better-dispersed pattern when the biome-scale inventories are ordinated. If these results are generalizable, then the new and old equation should see wide application, potentially taking the place of the two most commonly used alternatives (the interrelated Dice and Jaccard indices) whenever sampling is incomplete.