Conventional methods may cause allometric analyses to be unreliable

Contemporary analyses of allometric variation typically entail the fitting of a straight line to logarithmic transformations of the original data, with the slope for the line then being interpreted in the context of untransformed observations. In the process, investigators unwittingly commit statistical errors that may compromise the analyses and ensuing interpretations. Here, I re-examine published data for oxygen consumption vs. body mass in an ontogenetic series of crucian carp (Carassius auratus) to illustrate both the problem and how to avoid it altogether by using nonlinear regression to examine untransformed observations. Whereas a straight line fitted to logarithmic transformations pointed to a two-parameter power equation with an allometric exponent of 0.78 for describing data on the linear scale, the best description for pattern in the original data is shown here to be a straight line with a non-zero intercept. The overall pattern of variation is allometric because of the intercept. However, the pattern of variation over the range in the data is isometric because the implied exponent for the predictor variable is 1. Findings reported here have important implications for the study of bivariate allometry, where the objective of primary importance is to accurately describe the pattern of variation in untransformed observations. The methods applied here provide a useful roadmap for attaining that objective.