  The evolution and distribution of species body sizes for terrestrial mammals
is well-explained by a macroevolutionary tradeoff between short-term selective
advantages and long-term extinction risks from increased species body size,
unfolding above the 2g minimum size induced by thermoregulation in air. Here,
we consider whether this same tradeoff, formalized as a constrained
convection-reaction-diffusion system, can also explain the sizes of fully
aquatic mammals, which have not previously been considered. By replacing the
terrestrial minimum with a pelagic one, at roughly 7000g, the terrestrial
mammal tradeoff model accurately predicts, with no tunable parameters, the
observed body masses of all extant cetacean species, including the 175,000,000g
Blue Whale. This strong agreement between theory and data suggests that a
universal macroevolutionary tradeoff governs body size evolution for all
mammals, regardless of their habitat. The dramatic sizes of cetaceans can thus
be attributed mainly to the increased convective heat loss is water, which
shifts the species size distribution upward and pushes its right tail into
ranges inaccessible to terrestrial mammals. Under this macroevolutionary
tradeoff, the largest expected species occurs where the rate at which
smaller-bodied species move up into large-bodied niches approximately equals
the rate at which extinction removes them.
