Multiplicative by nature: Logarithmic transformation in allometry

Abstract

The traditional allometric method, which is at the heart of research paradigms used by comparative biologists around the world, entails fitting a straight line to logarithmic transformations of the original bivariate data and then back-transforming the resulting equation to form a two-parameter power function in the arithmetic scale. The method has the dual advantages of enabling investigators to fit statistical models that describe multiplicative growth while simultaneously addressing the multiplicative nature of residual variation in response variables (heteroscedasticity). However, important assumptions of the traditional method seldom are assessed in contemporary practice. When the assumptions are not met, mean functions may fail to capture the dominant pattern in the original data and incorrect form for error may be imposed upon the fitted model. A worked example from metabolic allometry in doves and pigeons illustrates both the power of newer statistical procedures and limitations of the traditional allometric method.