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Aims To propose and analyze a general, dynamic, process-oriented theory of the area of distribution. 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 by mathematical analysis. We show that the mid-domain effect is a direct consequence of dispersal; that to include movements to Ecological Niche Modeling significantly affects 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 modeling 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 analyzing the matrices representing the dynamics.