Supplemental data from: Exploring phylogenetic signal in multivariate phenotypes by maximizing Blomberg’s K

Due to the hierarchical structure of the tree of life, closely related species often resemble each other more than distantly related species; a pattern termed phylogenetic signal. Numerous univariate statistics have been proposed as measures of phylogenetic signal for single phenotypic traits, but the study of phylogenetic signal for multivariate data, as is common in modern biology, remains challenging. Here we introduce a new method to explore phylogenetic signal in multivariate phenotypes. Our approach decomposes the data into linear combinations with maximal (or minimal) phylogenetic signal, as measured by Blomberg's K. The loading vectors of these phylogenetic components or K-components can be biologically interpreted, and scatterplots of the scores can be used as a low-dimensional ordination of the data that maximally (or minimally) preserves phylogenetic signal. We present algebraic and statistical properties, along with two new summary statistics, KA and KG, of phylogenetic sign..., , , Supplementary materials to the paper, providing mathematical details, R code, and additional results for the simulations and empirical examples. These examples use previously published data available at github.com/rnfelice/Croc_Skulls and https://doi.org/10.5061/dryad.zkh189373 (see also the main paper for more details).