Macroevolutionary pattern in Ceratopsian Dinosaurus (Dinosauria: Ornithischia) and biomechanics : an integrated approach by means of geometric morphometrics and finite element analysis

Ceratopsians (Dinosauria: Ornithischia) were herbivorous dinosaurs widespread in Laurasia from the Late Jurassic through the Late Cretaceous. During the last 60 million years of their evolution, their size increased along with the development of elaborate facial horns and frills and a wide range of mandibular morphologies, probably reflecting a variety of dietary adaptations. In order to investigate shape changes across ceratopsians, I applied two-dimensional geometric morphometrics using a 42 landmark configuration for 120 skulls and a 33 landmark configuration for 116 lower jaws. 3D Principal Component Analyses performed on the two samples confirm different cranial and mandibular morphologies among clades; within ceratopsids both centrosaurines and chasmosaurines have similar mandibular shapes. An evolutionarily significant allometric signal exists between major clades, but not within clades. Even after accounting for phylogeny (Phylogenetic Generalized Least Squares), the relationship between shape and size is still significant. Partial Least Square Analysis indicates high co-variance between cranial and lower jaw shape. I also explored morphological integration between the skull and lower jaw (RV coefficient). Results show a decreasing morphological integration: skulls and jaws were more integrated in basal taxa than the later ones. Linear regressions between shape and time demonstrate a greater morphological disparity for ceratopsians in the Late Cretaceous (particularly in the Campanian stage) than the Early Cretaceous. When exploring evolutionary models for shape and size in the several datasets, the Early Burst represents the best-fitting evolutionary model for both phenotypes, and secondarily by the Delta model. These results highlight an increasing evolutionary rates for shape and size through time. Phenotypic evolutionary rate analyses on shape and size revealed a significant phenotypic shift in skull shape at the nodes for psittacosaurids and Ceratopsoidea, and for psittacosaurids in lower jaw shape. Skull size shows a significantly decreasing rate for psittacosaurids and leptoceratopsids, and an increasing rate for coronosaurians and ceratopsids. Only psittacosaurids show a significant decrease in the rate of change of lower jaw size, whereas Leptoceratopsidae + Coronosauria shows an increasing rate for size. In order to examine the mechanical performance of the mandibular shape, I applied the Finite Element Analysis and calculated the von Mises stress on the whole mandible to explore the mechanical behavior of ceratopsian lower jaws. Mandibular shape is not significantly related to von Mises stress. By contrast, after accounting for phylogeny (Phylogenetic Generalized Least Squares), the relationship between shape and stress is significant. Moreover, results are non-significant when regressing shape on stress size-corrected, thus by taking into account the evolutionary allometric effect. Shape variation is highly constrained by phylogeny, as shown by a Mantel test between the phylogenetic covariance and Procrustes distance matrices. Phylogenetic ANOVAs reveal that size is phylogenetically constrained within Ceratopsia, whereas von Mises stress is not. Additionally, von Mises stress is not significantly different among the ceratopsian clades. When exploring evolutionary models for stress, von Mises stress does not show any significant phylogenetic signal (White Noise model). These previously unquantified patterns in cranial evolution suggest that ceratopsids was characterized by greatly disparate frill morphologies but with a less disparate feeding apparatus than in basal clades, possibly related to climatic and floral changes in Latest Cretaceous. The results of this study highlighted a non phylogenetically structured von Mises stress of lower jaws when loaded to simulate biting, strongly correlated with mandibular shape. The evolution of this phenotype seems mainly due to adaptation rather than a shared ancestry. Shape evolves through time to arrange a lower jaw able to produce low stresses in the morphology. Size variation does not significantly influence structural performance within Ceratopsia