The 3/4 mass exponent for energy metabolism is not a statistical artifact

The scaling law eta = alpha Mb is used to model basal energy metabolism (eta) in terms of body mass (M). The exponent b = 3/4 has commonly been applied to either inter-specific or intra-specific variation of body mass (the 'Brody-Kleiber law'). Heusner recently demonstrated that the exponent 2/3 provided a better description of intra-specific variation in a set of animal data from the literature and dismissed the value 3/4 as a 'statistical artifact.' Using the same data, we recast the statistical analysis in mathematically equivalent form and show that 3/4 nonetheless emerges as a precise numerical estimate of the mass exponent for inter-specific variation. We relate this finding to the theory of elastic similarity and demonstrate that there is both experimental and theoretical justification for the use of both exponents in describing the variation of basal energy metabolism among animals of different size and species.