Geometric morphometrics is a collection of approaches that provide a mathematical description of biological forms according to geometric definitions of their size and shape. This mainly results from the still limited use of morphometric approaches in ecological and developmental studies of floral variation and also from the lack of user-friendly software for the statistical analysis of complex symmetry in biological shapes. In such systems, flowers are tightly arranged according to an overall spiral symmetry (Fibonacci sequence) while the flowers themselves have symmetries varying from bilateral symmetry (zygomorphy), left–right asymmetry, to rotational symmetry depending on their position relative to the centre of the capitulum (e.g., Carlson et al., 2011 Berger et al., 2016).ĭespite the ubiquity of floral symmetry and its widely acknowledged role in the evolutionary dynamics of flowers, very few studies have supplied quantitative characterisations of floral shapes and of their patterns of symmetric organisation. For instance, repeated gene duplication events are responsible for the complex ontogenetic patterning of the capitulum inflorescence, a structure thought to play a major role in the evolutionary diversification of angiosperms (Asteraceae and Dipsacaceae, Dipsacales) ( Carlson et al., 2011 Berger et al., 2016). Developmental genetic studies have started to unravel the origins of floral symmetry and identified specific genes known to play a role in the establishment of symmetry in corolla shape and related structures ( Almeida et al., 1997 Luo et al., 1999 Citerne et al., 2010 Berger et al., 2017 Spencer and Kim, 2018). It is involved in numerous facets of the adaptive evolution of flowers, from plant–pollinator interaction, shifts from outcrossing to selfing, to plasticity, and response to biotic and abiotic stresses ( Endress, 2001 Rodríguez et al., 2004 Sargent, 2004 Shipunov and Bateman, 2005 Bateman and Rudall, 2006 Gómez et al., 2006 Busch and Zachgo, 2007 Nattero et al., 2010 Frey and Bukoski, 2014 Vujić et al., 2015 Wang P. Symmetry has long been recognised as a key feature of the anatomical organisation and shape layout of the corolla of flowers. 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. 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. 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. 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). Principal Component Analysis is used to separate symmetric and asymmetric components of variation, respectively, quantifying variation among and within individuals. 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. 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 various spatial layout of petals can exhibit bilateral symmetry, rotational symmetry or more complex combination of symmetry types. The shape and symmetric organisation of corolla are key traits in the developmental and evolutionary biology of flowering plants. 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.
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