The need to scale for differences in body size and mass: an explanation of Kleiber's 0.75 mass exponent.

Abstract

When modeling intraspecific relationships between selected measurements (Y) for differences in body mass (m) using the allometric equation Y = amb (where a is a constant and b is the exponent parameter), various studies have reported exponents greater than the anticipated 2/3, often closer to the exponent 0.75 identified by Kleiber. A possible explanation for these exponents is proposed based on the findings of Alexander et al. (J. Zool. Lond. 194: 539-552, 1981), who observed that, within a variety of species, larger mammals have a greater proportion of proximal leg muscle mass in relation to their body mass, m1.1. If subjects that are used to record Y exhibit a similar disproportionate increase in muscle mass with body size, then the allometric equation is likely to identify both a contribution proportional to the subject's body mass and a contribution from the disproportionate increase in muscle mass within the group. These confounding influences in Y can be identified separately by incorporating a body size parameter as well as a mass component in the allometric equation. The factor "body size" can be introduced either by partitioning the sample into discrete subgroups according to body size or, in studies involving human subjects, by introducing height as a continuous covariate. In both studies reported involving human maximal exercise, these methods were able to identify a systematic increase in Y with body size, leaving the subject's body mass component, found to be proportional to m2/3, independent of body size.