  The distribution of species body size within taxonomic groups exhibits a
heavy right-tail extending over many orders of magnitude, where most species
are significantly larger than the smallest species. We provide a simple model
of cladogenetic diffusion over evolutionary time that omits explicit mechanisms
for inter-specific competition and other microevolutionary processes yet fully
explains the shape of this distribution. We estimate the model's parameters
from fossil data and find that it robustly reproduces the distribution of 4002
mammal species from the late Quaternary. The observed fit suggests that the
asymmetric distribution arises from a fundamental tradeoff between the
short-term selective advantages (Cope's rule) and long-term selective risks of
increased species body size, in the presence of a taxon-specific lower limit on
body size.
