  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.
