involved in multiple aspects of the evolution of flowering plants, and morphometrics allows the statistical testing of adaptive hypotheses. For example, in Erysimum mediohispanicum, Gómez and Perfectti (2010) have shown the impact of the shape of the corolla (and its deviation from the expected symmetry) on the selective value of the plant: pollinators (bees, bombyliids) significantly prefer flowers with bilaterally symmetric corollas (zygomorphism).
The decomposition of the variation into symmetric and asymmetric components can also be relevant in systematics. For example, Neustupa (2013) demonstrated the possible discrimination of different species of Micrasterias (single-cell green algae of the Desmidiales order) according to the share of symmetric and asymmetric components, relative to the two orthogonal planes of symmetry that characterize the cell shape.
Measures of fluctuating asymmetry are also used to infer patterns of developmental integration, in other words, the modular organization of phenotypes resulting from differential interactions between developmental processes (Klingenberg 2008).
Savriama et al. (2016) quantified the fluctuating “translational” asymmetry in order to assess the developmental cost of segmented modular organization in eight species of soil centipedes (Geophilomorpha). The results did not show any impact of the degree of modularity (number of segments) on developmental precision, rejecting the hypothesis of a “cost” of modularity.
Finally, the architecture of some organisms or organic structures may combine several hierarchically arranged patterns of symmetry. This is, for example, the case for Aristotle’s lantern, the masticatory apparatus of sea urchins, which, in regular sea urchins, combines bilateral and rotational symmetries (Savriama and Gerber 2018). The lantern exhibits the fifth-order rotational symmetry that is typical of echinoderms, and results from the repetition of a composite skeletal unit (hemipyramids + epiphyses) with bilateral symmetry. Analysis of the symmetric architecture of the lantern revealed a torsion (directional asymmetry) of the hemipyramids, contributing to the functioning of the lantern, and patterns of fluctuating asymmetry reflecting the spatialization of the skeletal precursors during the morphogenesis of the lantern.
1.8. Conclusion
The symmetry of biological forms, initially an object of curiosity and fascination, has become an important research topic in several branches of biological sciences in recent decades. The understanding of the developmental processes involved in the morphogenesis of symmetric phenotypes is a major issue in developmental and evolutionary biology (see Citerne et al. (2010), for example). In parallel to these genetic and developmental approaches, morphometrics has established a rigorous methodological framework for the analysis of symmetric shapes. Beyond the characterization of the symmetry of shapes, these approaches also quantify the deviations from the symmetric expectation. Their statistical analysis allows inferences to be made with regards to the architecture of complex phenotypes (genetic modularity, developmental modularity) and their variational properties (evolutionary modularity, evolvability). Coupled with molecular and developmental approaches, the recent generalization of the morphometric framework to all types of symmetry thus opens up new ways to describe, study and understand the origin and evolution of symmetries in the living world.
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