Evolutionary Model of Species Body Mass Diversification

We present a quantitative model for the biological evolution of species body masses within large groups of related species, e.g., terrestrial mammals, in which body mass $M$ evolves according to branching (speciation), multiplicative diffusion, and an extinction probability that increases logarithmically with mass. We describe this evolution in terms of a convection-diffusion-reaction equation for $\ln M$. The steady-state behavior is in good agreement with empirical data on recent terrestrial mammals, and the time-dependent behavior also agrees with data on extinct mammal species between 95–50 Myr ago.