Phylogenetic eigenvector regression in paleobiology

<p>ABSTRACT – Phylogenetic Eigenvector Regression (PVR) is a fl exible comparative method that allows testing severalhypotheses on phylogenetic signal and correlated evolution among traits. Selected phylogenetic eigenvectors extracted from aphylogenetic distance matrix among taxa allow representing their phylogenetic relatedness in a raw-data form (i.e. instead ofa distance matrix) and can then be used as explanatory variables in statistical models aiming to estimate phylogenetic signal orphylogenetically corrected correlations. Because of the growing use of PVR by paleobiologists in recent times, here the maintheoretical/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 phylogeneticsignal-representation curve for estimating phylogenetic signal is presented. Another innovation is to show how PVR can beused to assess morphological disparity in a phylogenetic context. A dataset of cranial morphology and function of 35 theropoddinosaur genera is used to illustrate the applications of PVR and how it can be used to answer four questions: (i) what are thephylogenetic patterns in theropod skull shape? (ii) is possible to tease apart the evolutionary models underlying variation intraits? (iii) how are evolutionary history, function, and diet related to variation in theropod skulls? (iv) what are the evolutionarycomponents of morphological disparity in theropod skulls? Answering these questions provide a roadmap for using PVR toaddress a range of issues relevant to contemporary paleobiology research programs.</p>