Quantifying the curvilinear metabolic scaling in mammals

A perplexing problem confronting students of metabolic allometry concerns the convex curvature that seemingly occurs in log-log plots of basal metabolic rate (BMR) vs. body mass in mammals. This putative curvilinearity has typically been interpreted in the context of a simple power function, Y=a*Xb, on the arithmetic scale, with the allometric exponent, b, supposedly increasing steadily as a dependent function of body size. The relationship can be quantified in arithmetic domain by exponentiating a quadratic equation fitted to logarithmic transformations of the original data, but the resulting model is not in the form of a power function and it is unlikely to describe accurately the pattern in the original distribution. I therefore re-examined a dataset for 636 species of mammal and discovered that the relationship between BMR and body mass is well-described by a power function with an explicit, non-zero intercept and lognormal, heteroscedastic error. The model has an invariant allometric exponent of 0.75, so the appearance in prior investigations of a steadily increasing exponent probably was an aberration resulting from undue reliance on logarithmic transformations to estimate statistical models in arithmetic domain. Theoretical constructs relating BMR to body mass in mammals may need to be modified to accommodate a positive intercept in the statistical model, but they do not need to be revised, or rejected, at present time on grounds that the allometric exponent varies with body size. New data from planned experiments will be needed to confirm any hypothesis based on data currently available.