Species richness and range size of the terrestrial mammals of the world: biological signal within mathematical constraints.

We explore global spatial diversity patterns for terrestrial mammals using as a tool range-diversity plots. These plots display simultaneously information about the number of species in localities and their spatial covariance in composition. These are highly informative, as we show by linking range-diversity plots with maps and by highlighting the correspondences between well defined regions of the plots with geographical regions or with taxonomic groups. Range-diversity plots are mathematically constrained by the lines of maximum and minimum mean covariance in species composition. We show how regions in the range-diversity plot corresponding to the line of maximum covariance correspond to large continental masses, and regions near the lower limit of the range-diversity plot correspond to archipelagos and mountain ranges. We show how curves of constant covariance correspond to nested faunas. Finally, we show that the observed distribution of the covariance range has significantly longer tails than random, with clear geographic correspondences. At the scale of our data we found that range-diversity plots reveal biodiversity patterns that cannot be replicated by null models, and correspond to conspicuous terrain features and taxonomic groupings.