Shape in morphometrics: Comparative analyses

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Abstract
Comparative morphology has long been vexed by conflicting considerations of size and shape (relative size); a subsidiary consideration has been the effect of allometry (shape change with size) on results and interpretations.A review of history and opinion indicates the lack of universal acceptance of the following points: the inherent relatedness and/or separability of size and shape; the greater importance (anatomically, functionally, and/or taxonomically) of shape than size; the existence of residual size effects (allometry) after canceling the gross linear size factor from morphometric data; the failure of covariance matrix inversion to negate size always; the dimensionless quality of shape variables; the effect of logarithmic transformation; and the inadvisability of simple ratios.Two morphometric data sets (primate postcranial proportions, hominoid maxillary premolar odontometrics) encompassing significant size and taxonomic diversity in primates enable illustration and examination of these points.Although determination of optimum procedures is problematic, accuracy of classification and partition of variance among known morphogroups are criteria that can be applied. Intergroup distances generated after inversion of the covariance matrix show little improvement over raw size distances, unlike the shape distances expressed by shape vector (ratio), double‐centered, Penrose, common part removed, and Q‐mode correlation methods; very slight further improvement is accomplished using pooled within‐group adjustment to remove residual size (allometric) effects. No improvement emanates solely from log transformation of measurements. Significant problems are indicated by the results obtained with interspecific regression residuals: particularly, large and small forms in the analysis become unrealistically similar. Also, regression‐corrected distances still correlate with size even though the univariate residual values, by definition, do not.