A new twist on a very old binary similarity coefficient

Abstract

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.

Olson's Extinction and the latitudinal biodiversity gradient of tetrapods in the Permian

“…A recent modification of the Forbes similarity index [27], hereafter referred to as Forbes* index, was used to compare the faunas in the four latitudinal bins: palaeotemperate and equatorial in both the Kungurian and Roadian. The Inta fauna (Kungurian palaeotemperate) is found to show greater similarity to the Kungurian equatorial formation than to the Roadian palaeotemperate fauna from Golyurshma (table 1).…”

The Brazilian freshwater wetscape: Changes in tree community diversity and composition on climatic and geographic gradients

“…Because most pair-wise dissimilarity coefficients are upward biased when sampling is partial [49], we were concerned about potential biases introduced by collating many surveys undertaken by a large number of researchers using a variety of methodologies. To account for potential differences in sampling effort we opted to use a modification of the Forbes F´ index on presence-absence data only [49]. F´ assumes that sampling is partial and is consequently a robust measure of compositional dissimilarity for incidence data obtained under a broad array of sampling conditions.…”

The identification of Oligo-Miocene mammalian palaeocommunities from the Riversleigh World Heritage Area, Australia and an appraisal of palaeoecological techniques

“…Presence/absence data were examined using the Dice, Simpson and Raup–Crick indices. A ‘corrected’ Forbes index was also used due to its purported superior accuracy and resistance to sample-size effects (Alroy, 2015a). The Jaccard, Ochiai and Kulczynski coefficients were not used due to their high correlation with the Dice index (Alroy, 2015a).…”

“…A ‘corrected’ Forbes index was also used due to its purported superior accuracy and resistance to sample-size effects (Alroy, 2015a). The Jaccard, Ochiai and Kulczynski coefficients were not used due to their high correlation with the Dice index (Alroy, 2015a). The ‘unweighted pair group method using arithmetic averages’ (UPGMA) and neighbour-joining clustering algorithms were used with each of the indices (Saitou & Nei, 1987; Popov, Gerasimov & Marinska, 1994; Brenchley & Harper, 1998; Etter, 1999; Hammer, Harper & Ryan, 2001).…”