The evolution of squamosal shape in ceratopsid dinosaurs (Dinosauria, Ornithischia)

Ceratopsidae represents one of the last and best-known radiations of non-avian dinosaurs. Interspecific variation is well documented qualitatively with linear measurements, but little has been done to quantify shape differences in the frill that may indicate functional or evolutionary signals. In order to investigate shape change in the squamosal across Chasmosaurinae and Centrosaurinae, we applied geometric morphometrics to the outline of the squamosal for 155 specimens representing 27 ceratopsid species and Protoceratops spp. A Mantel test suggests that the shape of ceratopsid squamosals is highly constrained by phylogeny. MANOVA, ANOVA, and their phylogenetic versions suggest that an evolutionarily significant allometric signal exists between the two clades, but not within clades. Principal component analysis indicates that centrosaurines have a uniform squamosal shape, with the exceptions of Spinops and Diabloceratops. Even when accounting for phylogeny, the relationship between squamosal shape and size is significant. Mapping shape onto the phylogeny, we estimated ancestral shapes at nodes. The transition from the non-ceratopsid to ceratopsid condition is characterized by a squamosal with a wider angle between the infratemporal process and the caudoventral margin, and a more dorsoventrally elongated and caudally expanded blade. From root to tips, centrosaurine squamosals were found to be conservative, but exhibit a slight dorsoventral expansion and a narrow angle between the infratemporal process and the caudoventral margin in more derived taxa. Chasmosaurines, compared with centrosaurines, show a derived morphology, with a trend towards a blade that is strongly expanded dorsoventrally and with a narrower angle between the infratemporal process and the caudoventral margin.