Testing the metabolic theory of ecology: Allometric scaling exponents in mammals

Many fundamental traits of species measured at different levels of biological organization appear to scale as a power law to body mass (M) with exponents that are multiples of 1/4. Recent work has united these relationships in a "metabolic theory of ecology'' (MTE) that explains the pervasiveness of quarter-power scaling by its dependence on basal metabolic rate ( B), which scales as M-0.75. Central to the MTE is theory linking the observed -0.25 scaling of maximum population growth rate (r(m)) and body mass to the 0.75 scaling of metabolic rate and body mass via relationships with age at first reproduction (alpha) derived from a general growth model and demographic theory. We used this theory to derive two further predictions: that age at first reproduction should scale inversely to mass-corrected basal metabolic rate alpha proportional to ( B/M)(-1) such that r(m) proportional to (B/M)(1). We then used phylogenetic generalized least squares and model selection methods to test the predicted scaling relationships using data from 1197 mammalian species. There was a strong phylogenetic signal in these data, highlighting the need to account for phylogeny in allometric studies. The 95% confidence intervals included, or almost included, the scaling exponent predicted by MTE for B proportional to M-0.75, r(m) proportional to M-0.25, and r(m) proportional to alpha(-1), but not for alpha proportional to M-0.25 or the two predictions that we generated. Our results highlight a mismatch between theory and observation and imply that the observed -0.25 scaling of maximum population growth rate and body mass does not arise via the mechanism proposed in the MTE.