Allometric analysis beyond heterogeneous regression slopes: use of the Johnson-Neyman technique in comparative biology.

Abstract

Allometry (or scaling) is a common technique used to evaluate and compare physiological, morphological, and other variables in organisms of different size. The relationship between many variables (Y) and body mass (X) is well described by a power function of the form . Typically, the procedure involves b Y p aX log-transforming both the variable and body mass and calculating a linear regression of the form log (Y ) p log (a) . An advantage of log-linear analysis is that it allows b log (X) calculation of associated 95% confidence intervals for the regression mean and 95% prediction intervals. Furthermore, allometric regressions for two or more groups can be compared. This is often accomplished by ANCOVA (Fisher 1932), a statistical procedure that combines ANOVA and analysis of variance of regressions (ANOVAR) to compare treatment means (groups) after accounting for and removing their relationship with the covariate (often body mass). Generally, ANCOVA is more appropriate for most data than is ANOVA, carried out on ratios of the variable and covariate, because many variables do not have an isometric relationship with body mass (Huxley 1932; Gould 1966; Packard and Boardman 1987, 1988, 1999). A requirement of ANCOVA is that the relationship with the covariate is uniform across groups; that is, the regression slopes (b) must be identical. In practice, before commencing ANCOVA it must therefore be demonstrated that the slopes are not significantly different between groups. When the slopes differ, regression elevations (a) cannot be statistically compared using ANCOVA (Zar 1999). The standard texts on allometry (Peters 1983; Calder 1984; Schmidt-Nielsen 1984; Brown and West 2000) provide little advice on how to continue analysis