Abstract Aim To assess the relationship between species richness and distribution within regions arranged along a latitudinal gradient we use the North American mammalian fauna as a study case for testing theoretical models. Location North America. Methods We propose a conceptual framework based on a fully stochastic mid-domain model to explore geographical patterns of range size and species richness that emerge when the size and position of species ranges along a one-dimensional latitudinal gradient are randomly generated. We also analyse patterns for the mammal fauna of North America by comparing empirical results from a biogeographical data base with predictions based on randomization null models. Results We confirmed the validity of Rapoport's rule for the mammals of North America by documenting gradients in the size of the continental ranges of species. Additionally, we demonstrated gradients of mean regional range size that parallel those of continental range. Our data also demonstrated that mean range size, measured both as a continental or a regional variable, is significantly correlated with the geographical pattern in species richness. All these patterns deviated sharply from null models. Main conclusions Rapoport's statement of an areographic relationship between species distribution and richness is highly relevant in modern discussions about ecological patterns at the geographical scale.