Phylogenetic eigenvectors and non-stationarity in the evolution of theropod dinosaur skulls

Despite the longstanding interest in non-stationarity 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 non-stationarity. The PSR is built by plotting the coefficients of determination R2 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 R2 and used a randomization procedure to compare observed and simulated shifts along the PSR curve, which allowed detecting non-stationarity in trait evolution. As an applied example, we show that the main evolutionary pattern of variation in the theropod dinosaur skull was non-stationary, wi...