Permutation tests for phylogenetic comparative analyses of high-dimensional shape data: what you shuffle matters

Evaluating statistical trends in high-dimensional phenotypes poses challenges for comparative biologists, because the high-dimensionality of the trait data relative to the number of species can prohibit parametric tests from being computed. Recently, two comparative methods were proposed to circumvent this difficulty. One obtains phylogenetic independent contrasts for all variables, and statistically evaluates the linear model by permuting the PICs of the response data. The other uses a distance-based approach to obtain coefficients for generalized least squares models (D-PGLS), and subsequently permutes the original data to evaluate the model effects. Here we show that permuting PICs is not equivalent to permuting the data prior to the analyses as in D-PGLS. We further explain why PICs are not the correct exchangeable units under the null hypothesis, and demonstrate that this mis-specification of permutable units leads to inflated type I error rates of statistical tests. We then show t...