Allometric scaling of mammalian metabolism
Authors: White Craig R. , Seymour Roger S. 
Published: April 2005

The importance of size as a determinant of metabolic rate (MR) was first suggested by Sarrus and Rameaux over 160 years ago. Max Rubner's finding of a proportionality between MR and body surface area in dogs (in 1883) was consistent with Sarrus and Rameaux's formulation and suggested a proportionality between MR and body mass (Mb) raised to the power of 2/3. However, interspecific analyses compiled during the first half of the 20th century concluded that mammalian basal MR (BMR, ml O2 h-1) was proportional to Mb3/4, a viewpoint that persisted for seven decades, even leading to its common application to non-mammalian groups. Beginning in 1997, the field was re-invigorated by three new theoretical explanations for 3/4-power BMR scaling. However, the debate over which theory accurately explains 3/4-power scaling may be premature, because some authors maintain that there is insufficient evidence to adopt an exponent of 3/4 over 2/3. If progress toward understanding the non-isometric scaling of BMR is ever to be made, it is first essential to know what the relationship actually is. We re-examine previous investigations of BMR scaling by standardising units and recalculating regression statistics. The proportion of large herbivores in a data set is positively correlated both with the scaling exponent(b, where BMR=aMbb) and the coefficient of variation (CV: the standard deviation of ln-ln residuals) of the relationship. Inclusion of large herbivores therefore both inflates b and increases variation around the calculated trendline. This is related to the long fast duration required to achieve the postabsorptive conditions required for determination of BMR, and because peak post-feeding resting MR (RMRpp) scales with an exponent of 0.75±0.03 (95%CI). Large herbivores are therefore less likely to be postabsorptive when MR is measured, and are likely to have a relatively high MR if not postabsorptive.

The 3/4 power scaling of RMRpp is part of a wider trend where,with the notable exception of cold-induced maximum MR(b=0.65±0.05), b is positively correlated with the elevation of the relationship (higher MR values scale more steeply). Thus exercise-induced maximum MR (b=0.87±0.05) scales more steeply than RMRpp, field MR (b=0.73±0.04), thermoneutral resting MR (RMRt, b=0.712±0.013) and BMR. The implication of this observation is that contamination of BMR data with non-basal measurements is likely to increase the BMR scaling exponent even if the contamination is randomly distributed with respect to Mb. Artificially elevated scaling exponents can therefore be accounted for by the inclusion of measurements that fail to satisfy the requirements for basal metabolism, which are strictly defined (adult,non-reproductive, postabsorptive animals resting in a thermoneutral environment during the inactive circadian phase). Similarly, a positive correlation between Mb and body temperature(Tb) and between Tb and mass-independent BMR contributes to elevation of b. While not strictly a defined condition for the measurement of BMR, the normalisation of BMR measurements to a common Tb (36.2°C) to achieve standard metabolic rate (SMR) further reduces the CV of the relationship. Clearly the value of the exponent depends on the conditions under which the data are selected. The exponent for true BMR is 0.686 (±0.014), Tb normalised SMR is 0.675 (±0.013) and RMRt is 0.712 (±0.013).