Inferring the similarity of species distributions using Species' Distribution Models

A common problem in ecology is our need to reliably compare information on the distributions of distinct species. Since it is not always possible to directly compare the distributions of two species, numerous papers now seek to compare the predictions of Species' Distribution Models (SDMs, estimates of the probability that two species are present, given environmental data). At present, it is not clear when these analyses of SDMs actually reproduce comparisons of species' distributions. I use analytic results and simulations to show that even if the SDMs for two species are identical; their distributions may still differ dramatically. I use this problem to motivate a new index to compare SDMs - an estimate of the SOrensen's similarity of the distributions of two species. I then provide a script to compute this estimator in R. Using simulations I show that this estimator provides a much stronger inference of the similarity of species distributions than previously proposed methods. This work clarifies the interpretation of comparisons of SDMs.