Is logarithmic transformation necessary in allometry?

Abstract

The Metabolic Theory of Ecology (MTE) transformed the field of biological allometry from a discipline that is focused on description to a discipline that is focused more on formulating and testing theory. However, much of the empirical research providing essential background for the MTE – as well as research to test predictions of the theory – is based on the ‘allometric method’, which is a simple procedure for estimating the parameters in a two-parameter power functiony=a xbby exponentiating the equation for a straight line fitted to logarithmic transformations of the original bivariate data. The allometric method has been in widespread use for so long that many investigators now apply the procedure mechanically and without due consideration for limitations of the approach. What has been missing from much of the contemporary research on allometric variation is exploratory analysis of untransformed data and graphical validation of the fitted model. I use two examples from the current literature: (1) to demonstrate the utility of exploratory analysis; (2) to illustrate how transformation may lead investigators to conclusions that are not supported by their data; and (3) to show how nonlinear regression may obviate the putative need to transform. The MTE (and other theories pertaining to patterns of allometric variation) will benefit from greater awareness that the traditional allometric method is not well suited for fitting statistical models to data expressed in the arithmetic scale.