On the hidden physical dimensions of the allometric equation.

Abstract

The aim of the present study was to submit Huxley's allometric equation (Y = aMb) to a dimensional analysis; in this equation Y is any biological variable, a is the mass-coefficient, M represents body mass, and b the mass-exponent. The dimensions of each of its components is thoroughly analyzed by means of the MLT-system of physics, as is the dimensionality of the whole equation. The relationship between the dimensional analysis and the postulates of some theories of biological similarity is discussed. In conclusion, parameter a of the allometric equation is always dimensionless, while the physical dimensions of the dependent variable Y can be defined by means of the power function Mb.