Julian Huxley and the quantification of relative growth

Abstract

In 1932, Julian Huxley introduced biologists around the world to a simple method for fitting two-parameter power equations, $$ Y\, = \,b \times \, X^{k} $$, to bivariate observations that follow a curvilinear path on the arithmetic (= linear) scale. The method entails fitting a straight line to logarithmic transformations of the data and then (at least implicitly) back-transforming the resulting equation to the arithmetic domain. This general approach continues to be in wide use by students of biological allometry despite its several limitations and shortcomings. For example, Huxley’s allometric method requires that the bivariate data of interest follow the path of a straight line in log domain (i.e., that the data be loglinear). However, many datasets that are otherwise suitable for allometric analysis do not meet the requirement for loglinearity and consequently are beyond the scope of Huxley’s method. Such data can usually be examined in the untransformed state by nonlinear regression, and the regression approach enables investigators to fit models with different functional form and random error. Moreover, by combining nonlinear regression with a categorical variable, investigators can compare sets of observations that follow curvilinear paths on the arithmetic scale. The regression protocol is illustrated by re-examining data for relative growth by the internal hinge ligament in a bivalve mollusk and by the elongated snout in garfish (Actinopterygii). The methodology promoted by Huxley has played a major role in development of the field of biological allometry, but the procedure has been superseded by nonlinear regression.