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Ceratopsidae represents a group of quadrupedal herbivorous dinosaurs that inhabited western North America and eastern Asia during the Late Cretaceous. Although horns and frills of the cranium are highly variable across species, the lower jaw historically has been considered to be relatively conservative in morphology. Here, the lower jaws from 58 specimens representing 21 ceratopsoid taxa were sampled, using geometric morphometrics and 2D finite element analysis (FEA) to explore differences in morphology and mechanical performance across Ceratopsoidea (the clade including Ceratopsidae, Turanoceratops and Zuniceratops). Principal component analyses and non-parametric permuted MANOVAs highlight Triceratopsini as a morphologically distinct clade within the sample. A relatively robust and elongate dentary, a larger and more elongated coronoid process, and a small and dorso-ventrally compressed angular characterize this clade, as well as the absolutely larger size. By contrast, non-triceratopsin chasmosaurines, Centrosaurini and Pachyrhinosaurini have similar morphologies to each other. Zuniceratops and Avaceratops are distinct from other taxa. No differences in size between Pachyrhinosaurini and Centrosaurini are recovered using non-parametric permuted ANOVAs. Structural performance, as evaluated using a 2D FEA, is similar across all groups as measured by overall stress, with the exception of Triceratopsini. Shape, size and stress are phylogenetically constrained. A longer dentary as well as a long coronoid process result in a lower jaw that is reconstructed as relatively much more stressed in triceratopsins.

Fil: Raia, Pasquale. Università degli Studi di Napoli Federico II; Italia Fil: Passaro, Federico. Università degli Studi di Napoli Federico II; Italia Fil: Carotenuto, Francesco. Università degli Studi di Napoli Federico II; Italia Fil: Maiorino, Leonardo. Università degli Studi Roma Tre; Italia Fil: Piras, Paolo. Università degli Studi Roma Tre; Italia Fil: Teresi, Luciano. Università degli Studi Roma Tre; Italia Fil: Meiri, Shai. Tel Aviv University; Israel Fil: Itescu, Yuval. Tel Aviv University; Israel Fil: Novosolov, Maria. Tel Aviv University; Israel Fil: Baiano, Mattia A. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Fil: Baiano, Mattia A. Instituto Catalán de Paleontología Miquel Crusafont; España Fil: Baiano, Mattia A. Universidad Nacional de Río Negro; Argentina Fil: Martínez, Ricard. Universitat Autònoma de Barcelona; España Fil: Fortelius, Mikael. University Of Helsinski; Finlandia Luxuriant, bushy antlers, bizarre crests, and huge, twisting horns and tusks are conventionally understood as products of sexual selection. This view stems from both direct observation and from the empirical finding that the size of these structures grows faster than body size (i.e., ornament size shows positive allometry).We contend that the familiar evolutionary increase in the complexity of ornaments over time in many animal clades is decoupled from ornament size evolution. Increased body size comes with extended growth. Since growth scales to the quarter power of body size, we predicted that ornament complexity should scale according to the quarter power law as well, irrespective of the role of sexual selection in the evolution and function of the ornament. To test this hypothesis, we selected three clades (ammonites, deer, and ceratopsian dinosaurs) whose species bore ornaments that differ in terms of the importance of sexual selection to their evolution.We found that the exponent of the regression of ornament complexity to body size is the same for the three groups and is statistically indistinguishable from0.25.We suggest that the evolution of ornament complexity is a by-product of Cope’s rule. We argue that although sexual selection may control size in most ornaments, it does not influence their shape.