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Bilateral symmetry of bilaterians was the first type of symmetry to be studied using the tools of geometric morphometrics (especially with Drosophila and the mouse as models). These studies are based on the methodological extension of fluctuating asymmetry analyses (Leamy 1984; Palmer and Strobeck 1986), originally based on the measurement of right–left differences of simple traits (linear measurements), to the study of shape as a highly multidimensional phenotypic trait (Klingenberg and McIntyre 1998; Mardia et al. 2000). Leamy et al. (2015), for example, using the fluctuating asymmetry in the size and shape of mouse mandibles to explore the genetic architecture of developmental instability. Quantitative trait locus (QTL) analysis underlines the epistatic genetic basis of fluctuating asymmetry, and suggests that the genes involved in the developmental stability of the mandible are the same as those controlling its shape and size.

The generalization of this morphometric framework to any type of symmetry has extended its scope to a wide variety of taxa and, in particular, to flowering plants (Savriama and Klingenberg 2011; Savriama 2018). Corolla symmetry is indeed 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.