Complex curvilinear allometry of brain size scaling in mammals

Abstract

The scaling relationship between log(brain size [E]) and log(body size [P]) is usually described by linear regression using the simple allometry equation log(E) = log(k) + a · log(P). The k ≈ 0.67 of early studies was thought to reflect the geometric scaling of brain volume to body surface area. The k ≈ 0.75 of later work was thought to reflect metabolic rate which also scales to the ¾ power of body size. We use data from the literature on 856 mammalian species to show that such coefficients are artifacts of forcing a linear model on curvilinear data. Brain size scaling is best described by the second‐order polynomial log(E) = log(k) + a1 · log(P) + a2 · [log(P)]2 fit by least‐squares polynomial regression. “Instantaneous allometry coefficients” (ki; i.e., the slope of the tangent to the curved polynomial regression line analogous to the k's of simple allometry) decrease as body size increases (e.g., ki = 0.89 for 10 g species to ki = 0.49 for 10,000 kg species). The same pattern of complex allometry holds for the individual mammalian orders with the notable exception of marsupials whose ki's increase as body size increases. Besides requiring revisions to biological explanations of brain size scaling, our finding of complex curvilinear allometry affects predictions of brain size from body size as well as calculation of encephalization quotients (EQ) used as a comparative measure of intelligence.