How to Derive Biological Information from the Value of the Normalization Constant in Allometric Equations

Allometric equations are widely used in many branches of biological science. The potential information content of the normalization constant b in allometric equations of the form Y = bXa has, however, remained largely neglected. To demonstrate the potential for utilizing this information, I generated a large number of artificial datasets that resembled those that are frequently encountered in biological studies, i.e., relatively small samples including measurement error or uncontrolled variation. The value of X was allowed to vary randomly within the limits describing different data ranges, and a was set to a fixed theoretical value. The constant b was set to a range of values describing the effect of a continuous environmental variable. In addition, a normally distributed random error was added to the values of both X and Y. Two different approaches were then used to model the data. The traditional approach estimated both a and b using a regression model, whereas an alternative approach set the exponent a at its theoretical value and only estimated the value of b. Both approaches produced virtually the same model fit with less than 0.3% difference in the coefficient of determination. Only the alternative approach was able to precisely reproduce the effect of the environmental variable, which was largely lost among noise variation when using the traditional approach. The results show how the value of b can be used as a source of valuable biological information if an appropriate regression model is selected.