Phylogenetic Principal Components Analysis and Geometric Morphometrics

Phylogenetic Principal Components Analysis (pPCA) is a recently proposed method for ordinating multivariatedatainawaythattakesintoaccountthephylogeneticnon-independenceamongspecies means. We review this method in terms of geometric morphometric shape analysis and compare its properties to ordinary principal components analysis (PCA). We find that pPCA produces a shape space that preserves the Procrustes distances between objects, that allows shape models to be constructed, and that produces scores that can be used as shape variables for most purposes. Unlike ordinary PCA scores, however, the scores on pPC axes are correlated with one another and their variances do not correspond to the eigenvalues of the phylogenetically corrected axes. The pPC axes are oriented by the non-phylogenetic component of shape variation, but the positioning of the scores in the space retains phylogenetic covariance making the visual information presented in plots a hybrid of non-phylogenetic and phylogenetic. Presuming that all pPCA scores are used as shape variables, there is no dierence between them and PCA scores for the construction of distance-based trees (such as UPGMA), for morphological disparity, or for ordinary multivariate statistical analyses (so long as the algorithms are suitable for correlated variables). pPCA scores yielddierenttrait-basedtrees(suchasmaximumlikelihoodtreesforcontinuoustraits)becausethe scores are correlated and because the pPC axes dier from PC axes. pPCA eigenvalues represent the residual shape variance once the phylogenetic covariance has been removed (though there are scalingissues),andassuchtheyprovideinformationoncovariancethatisindependentofphylogeny. Tests for modularity on pPCA eigenvalues will therefore yield dierent results than ordinary PCA eigenvalues. pPCA can be considered another tool in the kit of geometric morphometrics, but one whose properties are more dicult to interpret than ordinary PCA.