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 ¼. 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 M0.75. Central to the MTE is theory linking the observed −0.25 scaling of maximum population growth rate (rm) and body mass to the 0.75 scaling of metabolic rate and body mass via relationships with age at first reproduction (α) 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 α ∝ (B/M)−1 such that rm ∝ (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 ∝ M0.75, rm ∝ M−0.25, and rm ∝ α−1, but not for α ∝ M0.25 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