Comparative analysis of principal components can be misleading

Quantitative geneticists long ago recognized the value of studying evolution in a multivariate framework (Pearson, 1903). Due tolinkage, pleiotropy, coordinated selection and mutational covariance, the evolutionary response in any phenotypic trait can only be properly understood in the context ofother traits (Lande, 1979; Lynch and Walsh, 1998). This is of course also well-appreciated bycomparative biologists. However, unlike in quantitative genetics, most of the statistical and conceptual tools for analyzing phylogenetic comparative data (recently reviewed in Pennell and Harmon, 2013) are designed for analyzing a single trait (but see, for example Revell and Harmon, 2008; Revell and Harrison, 2008; Hohenlohe and Arnold, 2008; Revell and Collar, 2009; Schmitz and Motani, 2011; Adams, 2014b). Indeed, even classical approaches for testing for correlated evolution between two traits (e.g., Felsenstein, 1985; Grafen, 1989; Harvey and Pagel, 1991) are not actually multivariate as each trait is assumed to have evolved under a process that is independent of the state of the other (Hansen and Orzack, 2005; Hansen and Bartoszek, 2012). As a result of these limitations, researchers with multivariate datasets are often faced with a choice: analyze each trait as if they were independent or else decompose the dataset into statistically independent set of traits, such that each set can be analyzed with the univariate methods.