Phylogenetic eigenvectors and nonstationarity in the evolution of theropod dinosaur skulls

Despite the long-standing interest in nonstationarity of both phenotypic evolution and diversification rates, only recently have methods been developed to study this property. Here, we propose a methodological expansion of the phylogenetic signal-representation (PSR) curve based on phylogenetic eigenvectors to test for nonstationarity. The PSR curve is built by plotting the coefficients of determination R(2) from phylogenetic eigenvector regression (PVR) models increasing the number of phylogenetic eigenvectors against the accumulated eigenvalues. The PSR curve is linear under a stationary model of trait evolution (i.e. the Brownian motion model). Here we describe the distribution of shifts in the models R(2) and used a randomization procedure to compare observed and simulated shifts along the PSR curve, which allowed detecting nonstationarity in trait evolution. As an applied example, we show that the main evolutionary pattern of variation in the theropod dinosaur skull was nonstationary, with a significant shift in evolutionary rates in derived oviraptorosaurs, an aberrant group of mostly toothless, crested, birdlike theropods. This result is also supported by a recently proposed Bayesian-based method (AUTEUR). A significant deviation between Ceratosaurus and Limusaurus terminal branches was also detected. We purport that our new approach is a valuable tool for evolutionary biologists, owing to its simplicity, flexibility and comprehensiveness.