Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

Abstract Background Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry. Results We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis. Conclusions The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.</p

Comparative analysis of squamate brains unveils multi-level variation in cerebellar architecture associated with locomotor specialization

Ecomorphological studies evaluating the impact of environmental and biological factors on the brain have so far focused on morphology or size measurements, and the ecological relevance of potential multi-level variations in brain architecture remains unclear in vertebrates. Here, we exploit the extraordinary ecomorphological diversity of squamates to assess brain phenotypic diversification with respect to locomotor specialization, by integrating single-cell distribution and transcriptomic data along with geometric morphometric, phylogenetic, and volumetric analysis of high-definition 3D models. We reveal significant changes in cerebellar shape and size as well as alternative spatial layouts of cortical neurons and dynamic gene expression that all correlate with locomotor behaviours. These findings show that locomotor mode is a strong predictor of cerebellar structure and pattern, suggesting that major behavioural transitions in squamates are evolutionarily correlated with mosaic brain changes. Furthermore, our study amplifies the concept of 'cerebrotype', initially proposed for vertebrate brain proportions, towards additional shape characters.Peer reviewe

The ecological origins of snakes as revealed by skull evolution

The ecological origin of snakes remains amongst the most controversial topics in evolution, with three competing hypotheses: fossorial; marine; or terrestrial. Here we use a geometric morphometric approach integrating ecological, phylogenetic, paleontological, and developmental data for building models of skull shape and size evolution and developmental rate changes in squamates. Our large-scale data reveal that whereas the most recent common ancestor of crown snakes had a small skull with a shape undeniably adapted for fossoriality, all snakes plus their sister group derive from a surface-terrestrial form with non-fossorial behavior, thus redirecting the debate toward an underexplored evolutionary scenario. Our comprehensive heterochrony analyses further indicate that snakes later evolved novel craniofacial specializations through global acceleration of skull development. These results highlight the importance of the interplay between natural selection and developmental processes in snake origin and diversification, leading first to invasion of a new habitat and then to subsequent ecological radiations.Peer reviewe

Geometric morphometrics reveals shifts in flower shape symmetry and size following gene knockdown of CYCLOIDEA and ANTHOCYANIDIN SYNTHASE

Peer reviewe

A Step-by-Step Guide for Geometric Morphometrics of Floral Symmetry

This paper provides a step-by-step guide for the morphological analysis of corolla and the decomposition of corolla shape variation into its symmetric and asymmetric components. The shape and symmetric organisation of corolla are key traits in the developmental and evolutionary biology of flowering plants. The various spatial layout of petals can exhibit bilateral symmetry, rotational symmetry or more complex combination of symmetry types. Here, I describe a general landmark-based geometric morphometric framework for the full statistical shape analysis of corolla and exemplify its use with four fully worked out case studies including tissue treatment, imaging, landmark data collection, file formatting, and statistical analyses: (i) bilateral symmetry (Fedia graciliflora), (ii) two perpendicular axes of bilateral symmetry (Erysimum mediohispanicum), (iii) rotational symmetry (Vinca minor), and (iv) combined bilateral and rotational symmetry (Trillium undulatum). The necessary tools for such analyses are not implemented in standard morphometric software and they are therefore provided here as functions running in the R environment. Principal Component Analysis is used to separate symmetric and asymmetric components of variation, respectively, quantifying variation among and within individuals. For bilaterally symmetric flowers, only one component of left-right asymmetric variation is extracted, while flowers with more complex symmetric layout have components of asymmetric variation associated with each symmetry operator implied (e.g., left-right asymmetry and adaxial-abaxial asymmetry). Fundamental information on the genetic, developmental, and environmental determinants of shape variation can be inferred from this decomposition (e.g., directional asymmetry, fluctuating asymmetry) and further exploited to document patterns of canalization, developmental stability, developmental modularity and morphological integration. Even if symmetry and asymmetry are not the primary interest of a study on corolla shape variation, statistical and anatomical arguments support the use of the framework advocated. This didactic protocol will help both morphometricians and non-morphometricians to further understand the role of symmetry in the development, variation and adaptive evolution of flowers.Peer reviewe

Geometric morphometric methods for analysis of complex symmetric structures

Bilateral symmetry is the simplest and most common type of symmetry in organisms and for this reason it has been extensively studied in many biological contexts. Geometric morphometrics is concerned with the quantification of morphological variation in organisms and has been specifically developed for studies of symmetry and asymmetry. Most studies of symmetry have focused on bilaterally symmetric structures (e.g., human faces). However, bilateral symmetry is not the only type of symmetry in biological shapes and other types of symmetry exist as well (e.g., radial symmetry in flowers). So far, there are no general methods for morphological analysis of these types of symmetry. Here, I propose a new and general approach for norphological analysis of structures with any type of symmetry. This framework combines the tools of geometric morphometries with a mathematical definition of symmetry. Depending on the type of symmetry under study, this method can separate a component of symmetric variation among individuals from one or more asymmetry components.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Data from: Geometric morphometrics of nested symmetries unravels hierarchical inter- and intra-individual variation in biological shapes

Symmetry is a pervasive feature of organismal shape and the focus of a large body of research in Biology. Here, we consider complex patterns of symmetry where a phenotype exhibits a hierarchically structured combination of symmetries. We extend the Procrustes ANOVA for the analysis of nested symmetries and the decomposition of the overall morphological variation into components of symmetry (among-individual variation) and asymmetry (directional and fluctuating asymmetry). We illustrate its use with the Aristotle’s lantern, the masticatory apparatus of ‘regular’ sea urchins, a complex organ displaying bilateral symmetry nested within five-fold rotational symmetry. Our results highlight the importance of characterising the full symmetry of a structure with nested symmetries. Higher order rotational symmetry appears strongly constrained and developmentally stable compared to lower level bilateral symmetry. This contrast between higher and lower levels of asymmetry is discussed in relation to the spatial pattern of the lantern morphogenesis. This extended framework is applicable to any biological object exhibiting nested symmetries, regardless of their type (e.g., bilateral, rotational, translational). Such cases are extremely widespread in animals and plants, from arthropod segmentation to angiosperm inflorescence and corolla shape. The method therefore widens the research scope on developmental instability, canalization, developmental modularity and morphological integration

Savriama_Gerber_2018_Sc_Rep_Lantern3D

CT-Scan of the Aristotle’s lantern of the ‘regular’ sea urchin Paracentrotus lividus that is being displayed in the figures of this study. This model can be opened in software such as Meshlab and is ready for 3D printing