ON THE ALLOMETRIC MASS EXPONENT, WHEN IT EXISTS

Allometric power laws of the form q proportional to M(b) are commonly used to describe the dependence of a physiological variable q on body mass M in a class of animals that vary widely in size. The theoretical basis for such a law has been ignored or misstated in much of the bio logical literature. In this paper, an axiomatic basis for establishing the existence of a power law is proposed and a formula for calculatin g the theoretical mass exponent b is derived. It is shown that the val ue of b, when it exists, depends not only on the physical dimensions o f q but also on biological assumptions about the class of animals unde r consideration. Two examples are worked through, one concerning the f lying speed of birds and one concerning the controversial subject of m etabolic scaling in mammals. The wide range of mass exponents reported in the literature, it is argued, express no simple physical principle , but a variety of biological mechanisms including evolution, maturati on, and seasonal adaptation.