Species distribution models (SDMs) are a useful mean to understand how environmental variation influences species geographical distribution. SDMs are implemented by several different algorithms. Unfortunately, these algorithms consistently lose accuracy exactly when they are needed the most, that is with rare species, originating the so-called rare-species modelling paradox. Although approaches exist to tackle this problem, most notably by performing and then averaging a number of bivariate models, they are usually computationally intensive and were never shown to apply successfully to the rarest species (i.e. with less than 20 geographical occurrences). Here, we present a new algorithm, ENphylo, embedded in the readily-available R package RRdtn, which couples Environmental Niche Factor Analysis (ENFA) and phylogenetic imputation to model the distribution of rare species. Using the fossil record of 31 species of large mammals that lived during the late Pleistocene as the source data to sample from, we demonstrate ENphylo provides good SDM evaluation scores, with area under the curve and Sorensen Index both consistently above 0.75, True Skills Statistics above 0.4 and Boyce Index above 0.5 in most cases, when just 10 fossil occurrences are randomly drawn from their respective fossil records. ENphylo proved significantly more accurate than ENFA and the ensemble of bivariate models using Maxent, Generalized Linear Model and Random Forest algorithms. Intriguingly, we found that randomly drawing as little as 10 occurrence data points per species allows ENphylo to perform equally well as Maxent run using the entire fossil record of these same species and data. ENphylo provides a fast and accurate solution to perform species distribution modelling with rare species, which will help predicting their distribution in the light of climate change, and to delineate how rare extinct species reacted to past climatic variation.
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