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.