Interspecific variation in critical patch size and gap-crossing ability as determinants of geographic range size distributions.

How biological processes such as reproduction and dispersal relate to the size of species' geographic ranges constitutes a major challenge in spatial ecology and biogeography. Here we develop a spatially explicit theoretical framework that links fundamental population-level ecological traits (e.g., rates of dispersal and population growth or decay) with landscape heterogeneity to derive estimates of species' geographic range sizes and, further, distributions of geographic range sizes across species. Although local (patch-scale) population dynamics in this model are completely deterministic, we consider a fragmented landscape of patches and gaps in which the spatial heterogeneity is itself stochastic. This stochastic spatial structure, which juxtaposes landscape-level patch and gap characteristics against population-level critical patch sizes and maximum gap-crossing abilities, determines how far a novel species can spread from its evolutionary origin. Given reasonable assumptions about landscape structure and about the distribution of critical patch sizes and critical gap lengths among species, we obtain distributions of geographic range sizes that are qualitatively similar to those routinely found in nature (e.g., many species with small geographic ranges). Collectively, our results suggest that both interspecific differences in population-level traits and the landscapes through which species spread help determine patterns of occupancy and geographic extent.