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 (a) 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 a } (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 } a?1, but not for a }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.
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