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In landmarks-based Shape Analysis size is measured, in most cases, with Centroid Size. Changes in shape are decomposed in affine and non affine components. Furthermore the non affine component can be in turn decomposed in a series of local deformations (partial warps). If the extent of deformation between two shapes is small, the difference between Centroid Size and m-Volume increment is barely appreciable. In medical imaging applied to soft tissues bodies can undergo very large deformations, involving large changes in size. The cardiac example, analyzed in the present paper, shows changes in m-Volume that can reach the 60%. We show here that standard Geometric Morphometrics tools (landmarks, Thin Plate Spline, and related decomposition of the deformation) can be generalized to better describe the very large deformations of biological tissues, without losing a synthetic description. In particular, the classical decomposition of the space tangent to the shape space in affine and non affine components is enriched to include also the change in size, in order to give a complete description of the tangent space to the size-and-shape space. The proposed generalization is formulated by means of a new Riemannian metric describing the change in size as change in m-Volume rather than change in Centroid Size. This leads to a redefinition of some aspects of the Kendall's size-and-shape space without losing Kendall's original formulation. This new formulation is discussed by means of simulated examples using 2D and 3D platonic shapes as well as a real example from clinical 3D echocardiographic data. We demonstrate that our decomposition based approaches discriminate very effectively healthy subjects from patients affected by Hypertrophic Cardiomyopathy., (Copyright © 2018 Elsevier B.V. All rights reserved.)

Objectives: To study coronary heart disease (CHD) death versus 11 other causes of death using the cumulative incidence function (CIF) and the competing risks procedures to disentangle the differential role of risk factors for different end-points., Material and Methods: Standard Cox and Fine-Gray models among 1712 middle-aged men were compared during 50years of follow-up. CHD death was the primary event, while deaths from 11 selected causes, mutually exclusive from the primary end-point, were considered as secondary events. Reverse solutions were also performed. We considered 10 selected risk factors., Results: CHD death risk was the second highest among 12 mostly specific causes of death. Some risk factors were specific: serum cholesterol for CHD death whereas, systolic blood pressure, cigarette smoking and age may have a differential role in other causes of death. Application of the Fine-Gray model based on CIF enabled to dissect, at least in part, the respective role that baseline covariates may have to segregate the probabilities of two types of death in contrast from each other. They also point to the absence of contributing significance for some of the selected risk factors and this calls for a parsimonious approach in predictions., Conclusions: The relative rarity of competing risk challenges when defining the risk factors role at long-term needs now be corrected since we have clearly shown, with Fine-Gray model, at direct or reverse use, that comparing different end-points heavily influences the risk factor predictive capacity., (Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.)

Conventional wisdom holds that the complex shapes of deer antlers are produced under the sole influence of sexual selection. We questioned this view by demonstrating that trends for increased body size evolution passively yield more-complex ornaments, even in organisms where no effect of sexual selection is possible, with similar allometric slopes. Recent investigations suggest that sexual selection on antlers of larger deer species is stronger than that in smaller species; hence, the use of conspicuous antlers for display in large male deer is a secondary function driven by especially intense sexual selection on these large-bodied species. Since ancestral deer were small and had very simple antlers, such an intense selection on antlers shape was probably absent in early deer. Therefore, the evolution of complex ornaments is coupled with body size evolution, even in deer.

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., (© 2015 Anatomical Society.)

The enigmatic Early Miocene fossorial mammal Mesoscalops montanensis shows one of the most modified humeri among terrestrial mammals. It has been suggested, on qualitative considerations, that this species has no extant homologues for humerus kinematics and that, functionally, the closest extant group is represented by Chrysochloridae. We combine here three dimensional geometric morphometrics, finite element analysis and phylogenetic comparative methods to explore the shape and mechanical stress states of Mesoscalops montanensis as well as of extant and extinct Talpidae and Chrysochloridae under realistic digging simulations. Evolutionary convergence analyses reveal that the shape of Mesoscalops montanensis represents a unique morphology in the context of fossorial mammals and that its functional performance, albeit superficially similar to that of extant Chrysochloridae, still represents a nonconvergent optimum for adaptation to digging., (© 2015 Wiley Periodicals, Inc.)

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.

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.

Mandibles and teeth of ungulates have been extensively studied to discern the functional significance of their design. Grazing ungulates have deeper mandibles, longer coronoid processes, flatter incisor arcades, and more hypsodont molars in comparison to browsers. If the functional significance of both mandible and teeth shapes is well-established, it remains uncertain to what extent mandible shapes are really adapted to grazing, meaning that they evolved either to serve their current biological function or just as a structural requirement to accommodate higher crowned molars. Here, we address this question by studying the contribution of phylogeny, hypsodonty, and body size to mandibular shape variation. The mandible shape appeared to be significantly influenced by hypsodonty but not by body size. Interestingly, hypsodonty-related changes influenced the tooth row in artiodactyls and perissodactyls significantly but in the opposite directions, which is ultimately related to their different digestive strategies. Yet, we obtained a strong phylogenetic effect in perissodactyls, suggesting that their mandible shape should be strongly inherited. The strength of this effect was not significant within artiodactyls (where hypsodonty explained much more variance in mandible shape). Digestive strategy is deemed to interplay with hypsodonty to produce different paths of adaptation to particular diets in ungulates.