Cope's Rule and the Universal Scaling Law of Ornament Complexity.

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 from 0.25. 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.

Variation in the shape and mechanical performance of the lower jaws in ceratopsid dinosaurs (Ornithischia, Ceratopsia).

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.

Males Resemble Females: Re-Evaluating Sexual Dimorphism in Protoceratops andrewsi (Neoceratopsia, Protoceratopsidae).

BACKGROUND: Protoceratops andrewsi (Neoceratopsia, Protoceratopsidae) is a well-known dinosaur from the Upper Cretaceous of Mongolia. Some previous workers hypothesized sexual dimorphism in the cranial shape of this taxon, using qualitative and quantitative observations. In particular, width and height of the frill as well as the development of a nasal horn have been hypothesized as potentially sexually dimorphic. METHODOLOGY/PRINCIPAL FINDINGS: Here, we reassess potential sexual dimorphism in skulls of Protoceratops andrewsi by applying two-dimensional geometric morphometrics to 29 skulls in lateral and dorsal views. Principal Component Analyses and nonparametric MANOVAs recover no clear separation between hypothetical "males" and "females" within the overall morphospace. Males and females thus possess similar overall cranial morphologies. No differences in size between "males" and "females" are recovered using nonparametric ANOVAs. CONCLUSIONS/SIGNIFICANCE: Sexual dimorphism within Protoceratops andrewsi is not strongly supported by our results, as previously proposed by several authors. Anatomical traits such as height and width of the frill, and skull size thus may not be sexually dimorphic. Based on PCA for a data set focusing on the rostrum and associated ANOVA results, nasal horn height is the only feature with potential dimorphism. As a whole, most purported dimorphic variation is probably primarily the result of ontogenetic cranial shape changes as well as intraspecific cranial variation independent of sex.

Is torosaurus triceratops? Geometric morphometric evidence of late maastrichtian ceratopsid dinosaurs.

BACKGROUND: Recent assessments of morphological changes in the frill during ontogeny hypothesized that the late Maastrichtian horned dinosaur Torosaurus represents the "old adult" of Triceratops, although acceptance of this finding has been disputed on several lines of evidence. METHODOLOGY/PRINCIPAL FINDINGS: Examining the cranial morphology of 28 skulls in lateral view and 36 squamosals of Nedoceratops hatcheri, Triceratops spp. and Torosaurus spp. by means of landmark-based geometric morphometrics, we compared ontogenetic trajectories among these taxa. Principal Component Analysis and cluster analysis confirmed different cranial morphologies. Torosaurus shape space is well separated from Triceratops, whereas Triceratops horridus and Triceratops prorsus partially overlap within Triceratops shape space. Linear regressions between shape and size suggest different ontogenetic trajectories among these taxa. Results support the "traditional" taxonomic status of Torosaurus. We hypothesize that ontogeny drives cranial morphology with different patterns between Torosaurus and Triceratops. CONCLUSIONS/SIGNIFICANCE: Torosaurus is a distinct and valid taxon. Whether looking at entire skulls, skulls without the frill, frills alone, or squamosals, Torosaurus has different morphologies and distinct allometric trajectories compared to Triceratops. This new approach confirms the taxonomic status of Torosaurus as well as the comparatively low diversity of ceratopsids at the end of the Maastrichtian in North America.

Bite of the cats: relationships between functional integration and mechanical performance as revealed by mandible geometry.

Cat-like carnivorous mammals represent a relatively homogeneous group of species whose morphology appears constrained by exclusive adaptations for meat eating. We present the most comprehensive data set of extant and extinct cat-like species to test for evolutionary transformations in size, shape and mechanical performance, that is, von Mises stress and surface traction, of the mandible. Size and shape were both quantified by means of geometric morphometrics, whereas mechanical performance was assessed applying finite element models to 2D geometry of the mandible. Additionally, we present the first almost complete composite phylogeny of cat-like carnivorans for which well-preserved mandibles are known, including representatives of 35 extant and 59 extinct species of Felidae, Nimravidae, and Barbourofelidae. This phylogeny was used to test morphological differentiation, allometry, and covariation of mandible parts within and among clades. After taking phylogeny into account, we found that both allometry and mechanical variables exhibit a significant impact on mandible shape. We also tested whether mechanical performance was linked to morphological integration. Mechanical stress at the coronoid process is higher in sabertoothed cats than in any other clade. This is strongly related to the high degree of covariation within modules of sabertooths mandibles. We found significant correlation between integration at the clade level and per-clade averaged stress values, on both original data and by partialling out interclade allometry from shapes when calculating integration. This suggests a strong interaction between natural selection and the evolution of developmental and functional modules at the clade level.