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, with a significant shift in evolutionary rates in derived oviraptorosaurs, an aberrant group of mostly toothless, crested, bird-like 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.

Diniz-Filho_etal_Theropoda35There are two txt in the rar file. One is the phylogeny of 35 Theropoda genera in newick format (Theropoda_35_phy.txt"). The other file (Theropoda35_geomPC.txt") contains the two "traits" analyzed in the paper (geom1 and geom2), which are principal warps of morphometric data representing variation in skull shape. For details of morphometric analyses, see Brusatte et al. (Journal of Evolutionary BIology 35: 365-377, 2012). With these two files, all analyses in the paper can be reproduced using the R script found in the online supporting information.