Data from necropsy studies and in vitro tissue studies lead to a model for allometric scaling of basal metabolic rate

The basal metabolic rate (BMR) of a mammal of mass M is commonly described by the power function alphaM(beta) where alpha and beta are constants determined by linear regression of the logarithm of BMR on the logarithm of M (i. e., beta is the slope and alpha is the intercept in regression analysis). Since Kleiber's demonstration that, for 13 measurements of BMR, the logarithm of BMR is closely approximated by a straight line with slope 0.75, it has often been assumed that the value of beta is exactly 3/4 (Kleiber's law).

For two large collections of BMR data (n = 391 and n = 619 species), the logarithm of BMR is not a linear function of the logarithm of M but is a function with increasing slope as M increases. The increasing slope is explained by a multi-compartment model incorporating three factors: 1) scaling of brain tissue and the tissues that form the surface epithelium of the skin and gastrointestinal tract, 2) scaling of tissues such as muscle that scale approximately proportionally to body mass, and 3) allometric scaling of the metabolic rate per unit cell mass. The model predicts that the scaling exponent for small mammals (body weight < 0.2 kg) should be less than the exponent for large mammals (> 10 kg). For the simplest multi-compartment model, the two-compartment model, predictions are shown to be consistent with results of analysis using regression models that are first-order and second-order polynomials of log(M). The two-compartment model fits BMR data significantly better than Kleiber's law does.

The F test for reduction of variance shows that the simplest multi-compartment allometric model, the two-compartment model, fits BMR data significantly better than Kleiber's law does and explains the upward curvature observed in the BMR.