Phylogenetic Eigenvector Regression in Paleobiology

Phylogenetic Eigenvector Regression (PVR) is a fl exible comparative method that allows testing several hypotheses on phylogenetic signal and correlated evolution among traits. Selected phylogenetic eigenvectors extracted from a phylogenetic distance matrix among taxa allow representing their phylogenetic relatedness in a raw-data form (i.e. instead of a distance matrix) and can then be used as explanatory variables in statistical models aiming to estimate phylogenetic signal or phylogenetically corrected correlations. Because of the growing use of PVR by paleobiologists in recent times, here the main theoretical/statistical basis of the method and the developments made in the 15 years after its original proposition are reviewed, highlighting further potential applications in paleobiology. For the fi rst time, a multivariate extension of the phylogenetic signal-representation curve for estimating phylogenetic signal is presented. Another innovation is to show how PVR can be used to assess morphological disparity in a phylogenetic context. A dataset of cranial morphology and function of 35 theropod dinosaur genera is used to illustrate the applications of PVR and how it can be used to answer four questions: (i) what are the phylogenetic patterns in theropod skull shape? (ii) is possible to tease apart the evolutionary models underlying variation in traits? (iii) how are evolutionary history, function, and diet related to variation in theropod skulls? (iv) what are the evolutionary components of morphological disparity in theropod skulls? Answering these questions provide a roadmap for using PVR to address a range of issues relevant to contemporary paleobiology research programs.