An empirical evaluation of several univariate methods that adjust for size variation in morphometric data

Abstract

A variety of univariate transformations that attempt to separate size and shape variation are available: logarithms, ratios, logarithms of ratios, allometric adjustment, and regression techniques (major axis, residuals). Using the same basic data set derived from morphometric measurements of a freshwater fish, these transformations were examined for their effects upon variable distributions, correlations, and covariances. Those that were at least partly effective in removing size variation affected the correlation and covariance structure of the data in different ways, and thus resulted in different biological interpretations for principal component and discriminant analyses. Adjustment of size using a regression technique (computation of residuals from a standard size axis) or allometric adjustment to a standard size was preferred because these allowed for the complete removal of size variation and adverse effects were minimal. Although the actual estimates of shape were different for these two transformations, the relationships that resulted between groups inherent in the data were very similar. If heterogeneity between samples exists in the regression slopes or the allometric coefficients, the common within-groups slope or coefficient must be used to adjust for size.