A dynamic theory of the area of distribution

Abstract Aims The aim of this study is to propose and analyse a general, dynamic, process‐oriented theory of the area of distribution. Location Mexico, Southern United States and the Caribbean. Taxon Pierid butterflies. Methods The area of distribution is modelled by combining (by multiplication) three matrices: one matrix represents movements, another niche tolerances and a third, biotic interactions. Results are derived from general properties of this product and from simulation of a cellular automaton defined in terms of the matrix operations. Everything is implemented practically in an R package. Results Results are obtained by simulation and mathematical analysis. We show that the mid‐domain effect is a direct consequence of dispersal; that to include movements to Ecological Niche Modelling significantly affect results, but cannot be done without choosing an ancestral area of distribution. We discuss ways of estimating such ancestral areas. We show that, in our approach, movements and niche effects are mixed in ways almost impossible to disentangle, and show this is a consequence of the singularity of a matrix. We introduce a tool (the Connectivity‐Suitability‐Dispersal plot) to extend the results of simple niche modelling to understand the effects of dispersal. Main conclusions The conceptually straightforward scheme we present for the area of distribution integrates, in a mathematically sound and computationally feasible way, several key ideas in biogeography: the geographic and environmental matrix, the Grinnellian niche, dispersal capacity and the ancestral area of origin of groups of species. We show that although full simulations are indispensable to obtain the dynamics of an area of distribution, interesting results can be derived simply by analysing the matrices representing the dynamics.