Scaling of species diversity and body mass in mammals: Cope's rule and the evolutionary cost of large size

Equations are constructed describing the inverse correlation of species diversity and body mass in extant and Cenozoic mammals. Cope's rule, the tendency for many mammal clades to increase in body size through time, through phyletic change in single lineages or turnover within species groups, is interpreted as a probability function reducing diversity potential as a tradeoff for ecological/evolutionary gains. The inverse rule predicts that large species in clades will be less diverse than smaller species and, unless origination rates remain high among smaller clade members, clades conforming to Cope's rule will decline in diversity, moving towards extinction. This proposition is evaluated in the Cenozoic histories of five North American mammal clades; cotton rats, felids, canids, hyaenodontids, and equids. Diversity potential of different size classes within the 3.75 million year phyletic history of the muskrat, Ondatra zibethicus, is also examined. A corollary prediction of the inverse rule, that large species should have longer durations (species lifespans) than small species, is unresolved. Successful clades maintain small size or a significant number of smaller species relative to clade average size. The potential loss of unique extant large mammal species justifies the conservation effort to protect them. The similarity of scaling exponents of species diversity to mass around a slope of -1.0 suggests that species diversity is correlated with home range size, the latter related to the probability of population fragmentation.