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Floral symmetry and its evolution have attracted much attention in plant evolutionary and developmental biology (Coen, 1996; Endress, 2001; Citerne et al., 2010). Evolution of floral symmetry and its developmental basis have been investigated both on a microevolutionary scale (Kim et al., 2008) and across large clades (Zhang et al., 2010; Bartlett & Specht, 2011; Howarth et al., 2011; Busch et al., 2012). Traditionally, flower morphology has been assessed in a qualitative manner, but increasingly investigators are quantifying floral shape and symmetry with the methods of geometric morphometrics (Shipunov & Bateman, 2005; Gómez et al., 2006; Frey et al., 2007; Benitez-Vieyra et al., 2009; Gómez & Perfectti, 2010; Nattero et al., 2010; van der Niet et al., 2010; Kaczorowski et al., 2012). Because floral symmetry is important as a potential target of selection and because it is key to understanding the development and evolution of flowers, morphometric analyses of floral shape need to identify the patterns of symmetric variation and asymmetry and quantify them. Many flowers show complex symmetry, with multiple components of asymmetry (e.g. left–right, adaxial–abaxial, or asymmetry under rotation), which are challenging for morphometric analysis but offer opportunities for innovative studies in different biological contexts. So far, however, no morphometric study of floral shape has used methods that explicitly take symmetry into account and can separate the different components of symmetric variation and asymmetry.
Morphometric analyses of floral symmetry and asymmetry for zygomorphic flowers are relatively straightforward, because methods for analysing objects with bilateral symmetry are firmly established (Auffray et al., 1999; Mardia et al., 2000; Kent & Mardia, 2001; Klingenberg et al., 2002). Nevertheless, these methods have not yet been used for the study of floral symmetry (but for applications to leaf asymmetry, see Albarrán-Lara et al., 2010; Klingenberg et al., 2012). For other types of floral symmetry, morphometric analyses are more difficult. Frey et al. (2007) proposed a measure of rotational symmetry based on how close a single set of corresponding landmarks is to a regular polygon. Symmetry and asymmetry of algal cells with two perpendicular axes of reflection symmetry were studied with a generalization of the approach for bilateral symmetry (Potapova & Hamilton, 2007; Savriama et al., 2010). Savriama & Klingenberg (2011) offered a further generalization that is applicable to any type of symmetry, which constitutes a general framework for morphometric studies of floral symmetry and asymmetry. This approach is based on the theory of symmetry groups, which offers a rigorous and flexible mathematical foundation for the analysis of symmetric shapes (Weyl, 1952; Armstrong, 1988; Savriama & Klingenberg, 2011). The method is a generalization of the geometric morphometric methods devised for the study of bilateral symmetry (Klingenberg & McIntyre, 1998; Mardia et al., 2000; Kent & Mardia, 2001; Klingenberg et al., 2002). Depending on the type of symmetry under study, this method can separate a component of symmetric variation from one or more components of asymmetric shape changes and it can further resolve the asymmetric components into directional and fluctuating asymmetry (Savriama & Klingenberg, 2011). This paper aims to bring this new method to the attention of plant biologists and to demonstrate it in a first application to the study of floral shape.
Fluctuating asymmetry has been widely used as an indicator of stress or individual quality, with variable results (Møller & Swaddle, 1997; Møller & Shykoff, 1999; Perfectti & Camacho, 1999; Roy & Stanton, 1999; Freeman et al., 2003b; Raz et al., 2011). Fluctuating asymmetry is usually thought to originate from random variation in the developmental processes that produce the structures of interest (Palmer & Strobeck, 1986; Klingenberg, 2003). It is therefore a component of within-individual variation (Herrera, 2009) and is of nongenetic origin, although genetic factors may modulate the expression of fluctuating asymmetry (Queitsch et al., 2002; Klingenberg, 2003; Leamy & Klingenberg, 2005; Takahashi et al., 2011). Because fluctuating asymmetry arises from variation in developmental processes, it is patterned by those processes and the analysis of the patterns of fluctuating asymmetry offers an opportunity to investigate the developmental origin of phenotypic variation (Klingenberg, 2010; Klingenberg et al., 2012).
The developmental processes that are responsible for establishing floral symmetry and asymmetry have been investigated with the tools of developmental genetics and are known in increasing detail (Coen, 1996; Endress, 2001; Citerne et al., 2010). These studies have revealed regulatory networks that play a major role in conferring adaxial or abaxial identities to floral organs (e.g. Coen, 1996; Almeida & Galego, 2005; Busch & Zachgo, 2007; Preston & Hileman, 2009; Citerne et al., 2010). Mutations of genes belonging to these networks can disrupt adaxial–abaxial polarity, but do not affect left–right symmetry (e.g. Preston & Hileman, 2009). By contrast, flowers with left–right asymmetry are relatively rare and no specific developmental pathways are known that establish this type of symmetry (Endress, 2001; Jesson & Barrett, 2002a; Marazzi & Endress, 2008). From this information, it appears that adaxial–abaxial and left–right asymmetries are the result of distinct sets of developmental processes, and therefore it is important to distinguish and characterize the patterns of fluctuating asymmetry for both components of asymmetry. The new morphometric methods for complex symmetry provide the tools for quantifying these components of fluctuating asymmetry and dissecting their patterns of variation.
We illustrate this approach by analysing symmetric and asymmetric components of floral shape variation in a population of Erysimum mediohispanicum grown under natural conditions (Gómez et al., 2006). As usual for the Brassicaceae, flowers of this species have four petals separated by two perpendicular axes of symmetry: one axis divides the petals of the left side from the right side and the other axis bisects the flower into adaxial and abaxial parts. Closer examination, however, reveals that there are many deviations from this ground plan (Fig. 1). A range of different symmetries occur even within single populations, there is a genetic basis for floral shape and symmetry, and different pollinators favour different floral symmetries (Gómez et al., 2006, 2008, 2009a,b,c; Gómez & Perfectti, 2010; Ortigosa & Gómez, 2010). Therefore, Erysimum flowers are a particularly interesting and relevant model for studying shape variation and the evolution of floral symmetry. Here we demonstrate the new morphometric approach to quantify the different components of symmetry and asymmetry and to investigate the patterns of variation associated with them. The case study demonstrates the utility of specifically quantifying symmetry and asymmetry for studies of floral morphology in evolutionary, functional and developmental perspectives (Breuker et al., 2006a; Klingenberg, 2010; Murren, 2012).
Figure 1. Floral shape diversity in a wild population of Erysimum mediohispanicum (Brassicaceae). (a) Example of a flower that is almost perfectly symmetric about both the left–right and adaxial–abaxial axes. The configuration of landmarks used in the analysis is also shown. (b) Example of a flower with adaxial–abaxial asymmetry that is symmetric in the left–right direction (zygomorphy). (c) Example of a flower with left–right asymmetry, but with little adaxial–abaxial asymmetry. (d) Example of a completely asymmetric flower, both in the adaxial–abaxial and left–right directions.
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In this example, we have demonstrated the new morphometric approach for investigating floral shapes with complex symmetry. The results of this case study are useful to highlight some of the possibilities of this method, but they also raise some issues of general relevance for morphometric studies of symmetry and asymmetry in plants.
PCA and Procrustes ANOVA indicate that just under half of the total corolla shape variation consists of completely symmetric shape changes. This component represents the variation among flowers that affects the shapes and relative positions of all four petals equally (Fig. 3a). The other half of the total variation is asymmetry, mostly fluctuating asymmetry and a relatively small amount of directional asymmetry.
Directional asymmetry is statistically highly significant in all three components of asymmetry, but it is very subtle (Table 1). This result indicates that there are systematic differences among the four quadrants of the flowers. For the adaxial–abaxial component, this is a differentiation as it is characteristic for zygomorphic flowers, and corresponds to a tendency reported for this population before (Gómez et al., 2006). In contrast, directional asymmetry in the other two components of asymmetry is much harder to interpret. Directional asymmetry in all three components is quite subtle and, as a contribution to the asymmetries of individual flowers, is negligible by comparison to the magnitude of fluctuating asymmetry. This result corresponds to findings from animals, including humans, where most studies using geometric morphometrics have observed subtle but statistically significant directional asymmetry (Klingenberg et al., 1998, 2002, 2010; Debat et al., 2000; Schaefer et al., 2006; Ercan et al., 2008; Savriama & Klingenberg, 2011). Whether such subtle directional asymmetry of flower shape is widespread—clearly relevant for topics such as the evolution of zygomorphy and completely asymmetric flowers—needs to be studied further.
Among the components of asymmetric shape variation, adaxial–abaxial asymmetry accounts for the biggest share of variation (Table 1, Fig. 3b). This feature corresponds to variation in the degree of zygomorphy of the flowers, which has been found to be a prime aspect of phenotypic and genetic variation of flower shape in this species (Gómez et al., 2006, 2008, 2009b). This type of asymmetry also has been implicated in natural selection on Erysimum flower shape (Gómez et al., 2006); indeed, it is an important aspect of floral evolution in Brassicaceae and throughout angiosperms (Busch & Zachgo, 2009; Citerne et al., 2010; Knapp, 2010; Busch et al., 2012). Developmental genetic studies have demonstrated a network of regulatory genes that establish adaxial and abaxial identities of flower organs, and changes in the expression of the respective genes have been associated with evolutionary transitions to and from zygomorphy (Busch & Zachgo, 2007; Kim et al., 2008; Citerne et al., 2010; Zhang et al., 2010; Bartlett & Specht, 2011; Howarth et al., 2011; Busch et al., 2012). Variation in the activities of these regulatory networks may contribute to the observed level of variation in adaxial–abaxial asymmetry.
A further component of asymmetric shape variation is left–right asymmetry (Table 1, Fig. 3c). Left–right asymmetry is somewhat intriguing because the developmental mechanisms that are responsible for it are unknown (note, however, that the fact that no mechanism is known does not imply that no mechanism exists). Examples of such asymmetry include enantiostyly, where the style points to the left or right side of the flower, and asymmetries that involve the entire flower (Tucker, 1999; Jesson et al., 2003; Etcheverry et al., 2008; Marazzi & Endress, 2008). There is evidence that left- or right-sidedness in enantiostyly has a genetic basis in some instances (Jesson & Barrett, 2002a,b), but no specific genes or molecular pathways have been discovered that control any of these asymmetries.
The last component of asymmetry consists of shape changes that are asymmetric under reflection about both the left–right and adaxial–abaxial axes, but symmetric under rotation by 180°. This component includes some variation that is symmetric under rotation by 90°, but does not appear in the PC patterns, and includes phenomena such as flower contortion (Endress, 1999). The corresponding shape changes are twisting or diagonal deformations of the flower (Fig. 3d). The amount of fluctuating asymmetry for this component is distinctly smaller than those for adaxial–abaxial or left–right asymmetry (Table 1). There are known mechanisms that can produce this type of asymmetry. In Arabidopsis thaliana, mutations in α-tubulin genes have been shown to cause twisted growth of the petals in response to cytoskeletal defects, which led to rotational symmetry of flowers and reflection asymmetry (Furutani et al., 2000; Thitamadee et al., 2002). Twisting of petals and other floral organs is also involved in the development of completely asymmetric flowers (e.g. Etcheverry et al., 2008; Marazzi & Endress, 2008).
The three components of floral asymmetry appear to relate to different biological processes. Because these components occupy orthogonal subspaces in shape tangent space, separating and quantifying the phenotypic outputs of these processes are straightforward. Combination of such morphometric analyses of asymmetry with developmental genetic and comparative study designs will be a powerful and promising strategy for investigating the evolution and development of floral shape.
Fluctuating asymmetry is generally considered to originate from developmental noise, that is, from random perturbations of the developmental processes involved in producing a structure. Such perturbations produce differences between repeated parts, for instance different petals or left and right sides, even if parts are genetically identical and develop in the same environment (e.g. Klingenberg, 2003). Environmental stresses and genetic factors can affect the predisposition to fluctuations in developmental processes or influence how such variation is expressed in the phenotype (Klingenberg & Nijhout, 1999; Roy & Stanton, 1999; Queitsch et al., 2002). Even though these external factors can mediate the expression of developmental noise, the actual asymmetries arise from random differences among repeated parts in the activities of developmental processes. It may therefore be possible to relate the patterns and amounts of fluctuating asymmetry, as well as shape variation among flowers, to the mechanisms of flower development. Several studies of this kind have been conducted in animal models such as Drosophila (Breuker et al., 2006b; Debat et al., 2006, 2011) or mice (Klingenberg et al., 2003; Willmore et al., 2006; Jamniczky & Hallgrímsson, 2009). In flowers, analyses of the different components of fluctuating asymmetry can provide additional information that is unique to structures with complex symmetry. This is an application of morphometric approaches that is so far unexplored, but holds considerable potential.
This discussion has focussed on the traditional view that fluctuating asymmetry of flowers is the expression of intrinsic instability in development, so that it is present even in a completely homogeneous environment (Møller & Shykoff, 1999; Freeman et al., 2003b). Another possible source of fluctuating asymmetry, however, is plasticity in response to localized variation in the immediate surroundings of developing flowers. This mechanism is well established for variation among whole flowers, leaves or fruits within individual plants (reviewed by Herrera, 2009), but might also apply to asymmetry within these structures. Asymmetry can arise from plastic responses to heterogeneity, for instance, in the solar irradiation or in the flow of sap to different parts of the flower bud. Because plants are sessile, their parts are thus exposed to heterogeneity in their microenvironment constantly throughout development and plasticity is a mechanism that can produce fluctuating asymmetry, in addition to developmental instability. This is different from fluctuating asymmetry in motile animals, which move through their environment so that, over the entire period of development, differences between sides cancel out and both sides experience effectively the same environment (Klingenberg, 2003). There is experimental evidence that plasticity in response to light can produce asymmetry in leaves (Freeman et al., 2003a) and can therefore contribute to the substantial levels of fluctuating asymmetry often observed in leaf shape (Klingenberg et al., 2012). If this reasoning also applies to asymmetry of flower shape, the patterns of asymmetry induced by such plasticity would reflect the spatial distribution of heterogeneity of the relevant microenvironmental factors. Unfortunately, it is not possible to separate or quantify the contributions of plasticity and developmental noise to the fluctuating asymmetry observed in our data. The contribution of plasticity to fluctuating asymmetry in plants needs to be demonstrated and quantified in studies designed for this specifically; the morphometric methods for complex symmetries are promising tools for this purpose.
Analyses in Erysimum (Gómez et al., 2006, 2008, 2009a,c; Gómez & Perfectti, 2010) and other plants (Herrera, 1993; Benitez-Vieyra et al., 2009; Nattero et al., 2010; Gaskett, 2012; Kaczorowski et al., 2012) suggest that pollinators exert selection on floral shape. Symmetry is important in plant–pollinator interactions because insects can perceive, and appear to prefer, left–right symmetry (Møller, 1995; Giurfa et al., 1999; Rodríguez et al., 2004; but see Plowright et al., 2011). Also, some plant–pollinator systems favour flowers where adaxial and abaxial petals are differentiated and may perform different functions, for instance if abaxial petals function as a landing platform or to guide pollinating insects. These aspects of floral asymmetry concern two different components of shape asymmetry and occupy two separate subspaces of shape tangent space. Accordingly, analyses of selection on these two aspects of asymmetry can be conducted separately, using the appropriate component of asymmetry. The new morphometric methodology allows investigators to conduct analyses that specifically target particular components of variation.
The results presented here resemble those from earlier analyses of overall corolla shape without a priori separation into components of variation according to symmetry and asymmetry. The shape features captured in the first few PCs in our analysis (Fig. 3) resemble those of the corresponding PCs in the same data (Gómez et al., 2006), for other data sets for this species (Gómez et al., 2008, 2009b) and even for data from other species of Erysimum (Ortigosa & Gómez, 2010; our unpublished analyses of the data of Abdelaziz et al., 2011). The resemblance of shape features among corresponding PCs is particularly close for the analyses with the largest sample sizes (Gómez et al., 2009b; Fig. 2). This consistency of the main patterns of shape variation, obtained by applying different morphometric methods to several independent data sets, indicates that symmetry and asymmetry are fundamental for floral shape variation in Erysimum. This outcome is not universal, however, as is evident from another study where the shape changes associated with PCs of overall floral shape do not show identifiable types of symmetry or asymmetry (Nattero et al., 2010). In such cases, morphometric methods that specifically take into account floral symmetry are the only way to separate the different components of variation.
The limitations of the approach are that the user needs to specify the type of symmetry and the correspondence of landmarks. Because the type of symmetry is clear for most flowers, the requirement to choose a specific type of symmetry is not likely to cause difficulties in practice. By contrast, finding landmarks that clearly correspond across the different parts of each flower and among the flowers included in a study can be challenging. It may seem tempting to use outline methods to avoid this difficulty, but each algorithm used for analysing outline data also makes assumptions about the correspondence of points along the outline, even though they may not always be apparent to the user (Klingenberg, 2008). In principle, the approach of using copies that are transformed and relabelled according to the symmetry group is also applicable for semilandmarks and similar approaches (Bookstein, 1997; McCane & Kean, 2011), although there may be difficulties in practice. In many instances, however, landmarks can be found, as is clear from the growing number of studies using landmark methods for investigating floral shape.
In conclusion, the new morphometric method for complex symmetries is promising for studies of floral shape. It can quantify biologically meaningful components of symmetric and asymmetric shape variation and analyse the patterns of variation associated with each component. Different components of symmetric variation and asymmetry are of interest for investigating selection by pollinators, developmental instability and plasticity, as well as for taxonomic studies. We have demonstrated this type of analysis for one example, but we stress that it can accommodate any possible type of symmetry (Savriama & Klingenberg, 2011). The morphometric tools demonstrated here are opening a range of new possibilities for studying floral shape in evolutionary, developmental and ecological contexts.