Energy metabolism and body size. II. Dimensional analysis and energetic non-similarity

The allometric equation P = aMb (P: standard metabolism, M: body mass, a: mass coefficient, and b: mass exponent) can be theoretically derived from the following relations: l/L = t/T = lambda, m/M = lambda 3 where 1 and L are homologous lengths, t and T homologous times and lambda is the coefficient of similitude of two animals. Animals are homomorphic when b = 2/3, a = constant, and when their density is the same. These conditions appear to be realized in mature mammals of the same species, but mammals of different species are not homomorphic. Homomorphism means that the physiological time-scale is not the same in small and large animals, but that the energy spent per unit mass and unit of physiological time remain the same in homomorphic animals [mass-specific physiological power, phi]. The mass coefficient 'a' is equal to phi, therefore 'a' is physiologically the most significant parameter in the allometric equation. The physiological implications of phi are discussed.