Species range size shapes distance-decay in community similarity

Abstract

Aim: (i) To assess the dependence between the form of the decrease in biological similarity with distance (distance-decay) and species range size and (ii) to introduce the use of a sigmoidal model, the Gompertz function, as a flexible alternative able to fit distance-decay models under a wide variety of species range sizes. Location: Applicable worldwide. Methods: We computed distance-decay curves from simulated communities to assess how the species range sizes shape the functional form of distance-decay patterns (i.e. negative exponential, power-law or sigmoidal [Gompertz] relationships). Simulations were performed using different sample sizes and species detection probabilities. We also used distribution data of South American mammals to explore the relationship between species range size and the distance-decay form in an empirical dataset. Results: Our simulations showed that the power-law is the best supported model when range sizes tend to be small. An increase in range sizes leads to a negative exponential relationship, taking the shape of a sigmoidal (Gompertz) relationship with the largest range size values. Similar results have been found in the distance-decay pattern of South American mammals. Remarkably, the Gompertz function fits the data reasonably well in all scenarios. Main conclusions: The functional form of distance-decay patterns depends on a key biogeographical attribute: species range size. This dependence makes it an interesting tool to detect biodiversity threats associated with species range expansion, such as the biotic homogenization of faunas. The Gompertz function is the mathematical model that best accommodates different frequency distributions of species range size and, thus, allows cross-taxa comparison of this biogeographical and ecological pattern.