Why allometric variation in mammalian metabolism is curvilinear on the logarithmic scale

Studies performed over the last 20 years have repeatedly documented a slight convex curvature (relative to the x-axis) in double-logarithmic plots of basal metabolic rate (BMR) versus body mass in mammals. This curvilinear pattern has usually been interpreted in the context of a simple, two-parameter power function on the arithmetic scale, y  =  a  ×  x^b , with the exponent in the equation supposedly increasing systematically with body size. An equation of this form has caused concern among ecologists because a variable exponent is inconsistent with an assumption underlying the metabolic theory of ecology (MTE). However, the appearance of an exponent that varies with body size is an artifact resulting from the widespread use of logarithmic transformations in allometric analyses. Curvature in the distribution on the logarithmic scale actually is caused by a requirement for an explicit, non-zero intercept-and not a variable exponent-in the model describing the distribution on the arithmetic scale. Thus, the MTE need not be revised to accommodate an exponent that varies with body size in the scaling of mammalian BMR, but the theory may need to be tweaked to accommodate an intercept in the allometric equation. In general, any bivariate dataset that is well described by a three-parameter power equation on the arithmetic scale will follow a curvilinear path when displayed on the logarithmic scale. Consequently, reports of curvilinearity in log domain (i.e., "complex allometry") need to be revisited because conclusions from those investigations are likely to be flawed.