Within large taxonomic groups, extant species often exhibit a broad and right-skewed body mass distribution. This pattern can be explained as the result of "diffusion" over evolutionary time in the presence of both a minimum physiological size and extinction risks that increase with size. Although this explanation accurately predicts the extant distribution of mammals and their size diversification over the past 80 My, it remains unknown how well it applies to mammalian subclades. We test the idea that it holds at lower levels of taxonomic groupings by investigating the evolution of species body masses and diversity within the Equidae family using a novel database of fossil body sizes. We use the time-dependent solution of the constrained convection-diffusion-reaction model introduced by Clauset and Redner to investigate Equidae diversification over the past 56 My and to test how much of the dramatic increase in maximum size during the Miocene is due to diffusion of body sizes versus diversification of species.
Results/Conclusions
The Equidae family exhibits a minimum size of 20kg that remains relatively stable over the family's >55 My duration, and its expansion away from this boundary is well predicted by the constrained convection-diffusion-reaction model. This strong agreement between theory and data suggests that the constrained diffusion processes that hold for all of terrestrial mammals may also hold for smaller groups. Of the 10-fold increase in the largest horses during the early Miocene, we estimate that only 60% is attributable to the clade's dramatic 5-fold increase in diversity, i.e., disparity and diversity are only partly coupled during this period. This implies diversification at the upper end of the body size range into either niche space occupied by a poorer competitor or empty niche space. Unlike body size dynamics, variations in Equidae diversity track global temperatures, suggesting that ecological interactions are the main driver. Finally, the decline of Equidae's diversity in the late Miocene is largely concentrated among the smallest species, in contrast to the typical extinction pattern where large species disappear first. This pattern cannot be explained by the diffusion processes, and suggests large-scale competitive effects or ecological turnover.