The first two authors contributed equally to this study.
Minsung Kim, Faculty of Life Sciences, University of Manchester, Michael Smith Building, Oxford Road, Manchester M13 9PT, UK. Tel.: +44 161 275 1575; fax: +44 161 275 5082; e-mail: Minsung.Kim@manchester.ac.uk
The structure of compound leaves provides flexibility for morphological change by variation in the shapes, sizes and arrangement of leaflets. Here, we conduct a multilevel analysis of shape variation in compound leaves to explore the developmental plasticity and evolutionary potential that are the basis of diversification in leaf shape. We use the methods of geometric morphometrics to study the shapes of individual leaflets and whole leaves in 20 taxa of Potentilla (sensu lato). A newly developed test based on the bootstrap approach suggests that uncertainty in the molecular phylogeny precludes firm conclusions whether there is a phylogenetic signal in the data on leaf shape. For variation among taxa, variation within taxa, as well as fluctuating asymmetry, there is evidence of strong morphological integration. The patterns of variation are similar across all three levels, suggesting that integration within taxa may act as a constraint on evolutionary change.
The leaves of plants have a fantastic diversity of forms. Both genetic variation and phenotypic plasticity contribute to this variation, so that mutations have often dramatic effects on leaf morphology and even leaves on a single plant can have remarkably different forms (Jones, 1992; Kim et al., 2003a,b; Tsukaya, 2005; Bensmihen et al., 2008; Royer et al., 2009). In particular, the modular architecture of compound leaves, where the leaf blade is subdivided into multiple leaflets, provides many opportunities for developmental variation and associated morphological differences. It is therefore not surprising that variation in the form of compound leaves is particularly rich. Developmental genetic studies are rapidly providing information about the mechanisms that regulate this diversity of forms (e.g. Kim et al., 2001, 2003a; Blein et al., 2008; Efroni et al., 2010; Hasson et al., 2010; Koenig & Sinha, 2010). Yet, many aspects of how the shapes of compound leaves evolve remain unclear.
Here, we use this multilevel approach to investigate the patterns of morphological integration and allometry for shape variation in compound leaves. We consider three levels of variation of leaflets and whole leaves: evolutionary divergence among taxa, variation within taxa and fluctuating asymmetry (Klingenberg, 2008, 2010). We use the methods of geometric morphometrics to characterize shape variation (Dryden & Mardia, 1998; Zelditch et al., 2004; Klingenberg, 2010). We demonstrate this approach in an analysis in 20 taxa of cinquefoils (Potentilla and related genera, Rosaceae). Because the molecular phylogeny of Potentilla is poorly resolved and contains some inconsistencies (Dobeš & Paule, 2010; Töpel et al., 2011), we use a new method based on the bootstrap (Felsenstein, 1985a) to incorporate an assessment of phylogenetic uncertainty into tests of phylogenetic signal in morphometric data (Klingenberg & Gidaszewski, 2010). Comparisons of the patterns of variation across the different levels of variation address the question whether developmental plasticity defines the patterns of morphological integration within taxa and whether that integration acts as a constraint in the process of evolutionary diversification. We discuss the roles of plasticity and constraints in the evolution of leaf shape and relate the morphometric findings to information from developmental biology.
Materials and methods
Leaves of 20 taxa of Potentilla and related genera were collected in botanical gardens (Royal Edinburgh Botanic Garden; Botanic Garden of the University of Freiburg; Royal Botanic Gardens, Kew). The taxa were chosen to represent a range of leaf shapes, including both palmate and pinnate leaves (Fig. 1). Most taxa are distinct species, but two (Gibson’s Scarlet and Yellow Queen) are cultivars of P. atrosanguinea and a further one (P. goldbachii) turned out to be a synonym of P. thuringiaca (it can thus be considered a distinct accession for this species).
To avoid problems concerning the homology of leaflets, this study is limited to taxa with leaves that consist of five leaflets, excluding taxa with fewer or more leaflets per leaf (five is the most widespread number of leaflets in Potentilla). This study therefore excludes the discontinuous variation associated with differences in leaflet number. Except for this limitation, the taxa in our sample represent all the main features of leaf variation across Potentilla s. l. (Wolf, 1908).
As far as possible, rosette leaves from the outer whorl were collected. For each taxon, 10 leaves were collected, two each from five plants. Leaves were glued on paper, and landmarks were digitized from images obtained using a Nikon D3100.
For each leaf, the shape of the whole leaf was characterized by a set of 25 landmarks that indicate the relative sizes, approximate shapes and positions of the five leaflets (Fig. 2a). For each leaflet, landmarks were located at the base and the tip of the leaflet lamina and at the most basal tooth of the serrated part of the leaflet margin on each side. In addition, the insertion points of the petiolules of the leaflets (except the distal one) to the rachis and a landmark at the base of the petiole were also included. For palmate leaves, the landmarks at the insertion points of leaflet petiolules are located in the same point.
For 15 of the taxa (see Supporting Information), the shapes of the distal and lateral (basal) leaflets were studied in more detail. For each leaflet, a set of 15 landmarks was digitized (Fig. 2b). The landmarks are located as pairs on both margins: at the base of the leaflet, at the point where the leaflet widens to form the lamina, at the tips and in the notches associated with the first two teeth of the serrated part of the leaflet margin, at a level half-way between the second tooth and the tip of the leaflet and, finally, a single landmark at the tip of the leaflet (Fig. 2b).
To obtain a better phylogenetic resolution for the species in our study, we ran a detailed phylogenetic analysis of the species in described here and used Rosa majalis as an outgroup to root the tree. Three chloroplast DNA sequences (trnLuaa-trnFgaa IGS, trnSuga-ycf9 IGS and trnCgca-ycf6 IGS) and two nuclear sequences (ITS 5.8S rRNA gene and ETS 18S rRNA) were individually aligned using ClustalX (Larkin et al., 2007) and concatenated to form an alignment of 2992 nucleotides, which was used for subsequent analysis. A phylogenetic tree (Fig. 1) was estimated using RAxML (Stamatakis et al., 2008) under a model that partitioned the data into chloroplast and nuclear genes and allowed a different GTR + Γ model parameters and branch lengths for each partition. (Full details of phylogenetic analysis and model choice are provided in Appendix S1.) Uncertainty in the phylogenetic tree was assessed using a nonparametric bootstrap with 200 replicates (Felsenstein, 1985a; Stamatakis et al., 2008), and these trees were stored for use in later analyses.
Because no sequence data were available for some taxa, some of the relationships had to be inferred from other sources. Dasiphora parvifolia was entered as sister taxon to D. fruticosa, assuming monophyly of the genus Dasiphora. Because P. goldbachii is a synonym of P. thuringiaca, we treated the corresponding accessions as sister taxa. Likewise, we treated the two cultivars of P. atrosanguinea as sister taxa.
The morphometric analyses in this study are based on a definition of shape as all geometric aspects of a configuration of landmarks, except its size, position and orientation. Shape information is extracted from the landmark coordinates in a Procrustes superimposition (Rohlf & Slice, 1990; Goodall, 1991; Dryden & Mardia, 1998). The coordinates of the superimposed landmark configurations are then used in multivariate analyses to address specific biological questions.
Both the whole leaves and leaflets are bilaterally symmetric about their respective central axes (petiole/rachis or leaflet midrib). To take into account this symmetry and to gain information about asymmetry of shape, we used the method of shape analysis for object symmetry (Klingenberg et al., 2002). This method uses the landmark configurations and their reflected copies (with paired landmarks relabelled) in a joint Procrustes superimposition (Dryden & Mardia, 1998). A symmetric component of shape variation is obtained from the averages of original and reflected copies, and an asymmetric component is computed from the differences between original and reflected copies (Klingenberg et al., 2002).
To visualize and test the separation of leaf shapes among taxa, we used canonical variate analysis (CVA) of the symmetric component of shape variation (Mardia et al., 1979; Campbell & Atchley, 1981). CVA maximizes the differences between taxa relative to the variation within taxa and is therefore the most efficient method for detecting separation among taxa. The statistical significance of pairwise differences in mean shapes was assessed with permutation tests using Mahalanobis distance as the test statistic (10 000 permutations per test).
To display the main patterns of variation in shape space, we used principal component analysis (PCA; e.g. Jolliffe, 2002). PCA, unlike CVA, does not distort the shape space and is therefore most suitable to display these patterns. The PCs are axes that successively maximize the variation for which they account, subject to the constraint that each PC must be orthogonal to all preceding PCs. The shape changes that correspond to the directions of the PCs in shape tangent space can be displayed graphically.
To take into account the considerable uncertainty in the estimated phylogeny (see bootstrap support values in Fig. 1), we used a new method based on the bootstrap. The bootstrap resampling provides an estimate of the statistical uncertainty under a process of random sampling from the data (DNA sequences in this case; Felsenstein, 1985a; Efron & Tibshirani, 1993). The variation in the outcome of analyses on the resulting bootstrap trees indicates the effects of uncertainty in the estimated phylogeny. Specifically, we used all 200 trees from the bootstrap analysis, mapped the shape data onto each tree and ran the permutation test for phylogenetic signal (with 250 rounds of permutation per tree). The resulting distribution of P-values provides an indication whether the results of the test are robust with regard to the statistical uncertainty of the estimated phylogenetic tree. This method is implemented in the MorphoJ software package (Klingenberg, 2011). For the shape of the whole leaves, where the permutation test provided some evidence against the null hypothesis of no phylogenetic signal, we computed independent contrasts of the shape and centroid size data (Felsenstein, 1985b).
We carried out PCAs at several different levels: among the average shapes of the species or independent contrasts (corresponding to evolutionary change), the pooled within-taxon covariance matrix of the symmetric component of variation (a common estimate for shape variation among leaves within the samples) and for fluctuating asymmetry (variation within each leaf; Klingenberg & McIntyre, 1998; Klingenberg et al., 2002). To avoid confounding effects from differences in directional asymmetry among taxa, the PCA for fluctuating asymmetry used the pooled within-taxon covariance matrix of the asymmetric component of variation.
To quantify the similarity of covariance structures at the different levels, we computed the matrix correlations between the corresponding covariance matrices. Because the relative amounts of variation at different landmarks are an important aspect of the covariance structure, we included the diagonal blocks of variances and covariances of coordinates of each landmark in the calculation of the matrix correlation (Klingenberg & McIntyre, 1998; Klingenberg et al., 2002). Matrix correlations were tested with a matrix permutation test, as adapted for geometric morphometrics, permuting the order of landmarks and not individual coordinates (Klingenberg & McIntyre, 1998; Klingenberg et al., 2002).
Allometry was analysed by multivariate regression of shape on size (Monteiro, 1999). We used log-transformed centroid size as a measure of size because preliminary analyses showed that it resulted in much better linear relationships than untransformed centroid size. The statistical significance of the regressions was assessed with permutation tests with 10 000 iterations for each test. To visualize allometric relationships, we plotted the regression scores (the projection of shape data onto the direction of the regression vector in the shape tangent space; Drake & Klingenberg, 2008). All morphometric analyses were carried out with the MorphoJ software package (Klingenberg, 2011).
The maximum-likelihood tree contains several branches with high bootstrap support, but many others have weak support, indicating substantial uncertainty concerning a large portion of the tree (Fig. 1). This agrees with previous reports of a poorly resolved ‘core Potentilla’ (Dobeš & Paule, 2010) or ‘Argentea’ clade (Töpel et al., 2011).
Analysis of whole leaves
The CVA indicates that all taxa and accessions included in the analysis are clearly distinct from each other (Fig. 3). Mahalanobis distances range from 3.26 (P. goldbachii vs. P. pensylvanica) to 25.10 (P. dickinsii vs. P. neumanniana), and all permutation tests indicate that mean shapes differ significantly among taxa (all P <0.0001 in pairwise permutation tests between taxa). The Procrustes distances range from 0.0616 (P. recta vs. P. hirta) to 0.6136 (D. parvifolia vs. P. pensylvanica), and most are thus quite large shape differences. The scatter plot of canonical variate (CV) scores shows a gradient of pinnate to palmate leaves along the CV1, with a marked concentration of palmate groups at high CV1 scores (Fig. 3, horizontal axis). The CV2 contrasts, at one extreme, leaves with long petioles and narrow leaflets where the serrated edge extends from the tip along most of the length of the leaflets and, at the other extreme, leaves with broad leaflets where only the distal part is serrated (Fig. 3, vertical axis).
To visualize the phylogenetic history of shape change in the leaves, we projected the phylogeny (Fig. 1) into the shape tangent space by squared-change parsimony and plotted the resulting tree in the plane of the first two PCs of the taxon mean shapes (Fig. 4a). Closely related taxa are not necessarily close to each other in shape space and some remotely related taxa have similar leaf shapes, so that there are long branches that criss-cross the plot.
The permutation test for a phylogenetic signal in the symmetric component of leaf shape variation yielded a P-value of 0.059. This means that the test is not statistically significant according to the conventional threshold of 0.05 but still provides some evidence against the null hypothesis that variation of leaf shape is unrelated to phylogeny. The uncertainty in estimating the phylogeny is an important factor for the tests of the phylogenetic signal. For the 200 bootstrap trees, the P-values of the permutation test ranged from 0.004 to 0.36 (median 0.10). Because of this uncertainty, we conducted analyses of evolutionary change in leaf shape both with independent contrasts, accounting for phylogenetic structure, and based on the mean shapes of taxa.
In the PCA of the variation among the 20 taxa means, the PC1 accounts for more than 60% and is therefore clearly the dominant pattern of diversification of leaf shapes (Fig. 4b). The shape change associated with it is a contrast between the relative length of the petiole and the sizes of the leaflets (and also the spacing of the basal pair of leaflets relative to the other leaflets). In contrast, the PC2 mainly represents a concerted change in the shapes of the leaflets, concerning their relative length vs. width, how far the serrated part of the leaf margin extends towards the base and, to some extent, the orientation of the leaflets on either side of the leaf. The PCA of independent contrasts of leaf shapes gave very similar results, in terms of both the shape changes associated with the PC1 and PC2 and the amounts of variation taken up by the PCs (Fig. 5a).
To examine whether these patterns of diversification may relate to patterns observed within taxa, we used a PCA of the pooled within-taxon covariance matrix, which is a joint estimate of the covariance structure within taxa (Fig. 5b). The PC1, which accounts for just under half the total variance, is associated with a pattern of shape change that is primarily a contrast between relative petiole length and the size of all leaflets. The PC2 corresponds to a shape change that concerns the orientation of the leaflets on either side of the main axis. Many aspects of these shape changes relate to features seen in the corresponding PCs for divergence among taxa (Figs 4b and 5a). As a measure of overall similarity of the covariance structures within and among taxa, we computed the matrix correlations between the pooled within-taxa covariance matrix and the covariance matrices among taxon means and among independent contrasts of leaf shapes. Both matrix correlations were 0.91 and therefore very strong, and the matrix permutation tests were highly significant (P <0.0001).
The PCA for fluctuating asymmetry shows that it is concentrated in relatively few dimensions, with just under half of the total variance in the PC1 alone (Fig. 5b). The PC1 combines a bending of the leaf and petiole with differences in the relative sizes of leaflets on either side of the main leaf axis (the lateral leaflets are smaller on the inside of the bend than on the outside). The PC2 mostly features asymmetry in the orientation of the lateral leaflets (Fig. 5b). The matrix correlation between the covariance matrix for fluctuating asymmetry and the pooled within-taxon covariance matrix for the symmetric component of variation is 0.57 (P <0.0001). The covariance matrix for fluctuating asymmetry is less similar to the pattern of divergence among taxa. The matrix correlation with the covariance matrix among taxon averages is 0.38 (P =0.0065), and the matrix correlation with the covariance matrix for independent contrasts is 0.39 (P =0.0048).
To examine whether allometry influences the patterns of variation, we regressed the independent contrasts of shape on the independent contrasts of log-transformed centroid size. The multivariate regression shows a clear relationship (Fig. 6a) that accounts for 51.4% of the shape variation and is statistically significant (P <0.0001). It thus indicates strong evolutionary allometry. The shape change associated with evolutionary allometry is a relative lengthening of the petiole and a slight apical shift of the basal pair of leaflets with increasing size. The pooled within-taxon regression accounts for 10.1% of the shape variation within taxa and is statistically significant (P <0.0001; Fig. 6b). This within-taxon allometry is associated with a shape change that is similar to that of evolutionary allometry, except for the basal pair of leaflets that shift towards the leaf base with increasing size (Fig. 6b). We used this within-taxon allometry to correct for the effects of size in the data by computing residuals. The results of the PCAs for these size-corrected data are similar to the analyses presented above, but the dominance of the PC1 in the analyses is less extreme. Importantly, the high and statistically significant matrix correlations between the different levels of variation remain almost the same.
Analysis of leaflets
Projecting the phylogenetic tree into plots of the first two PCs of the taxon means for the distal and lateral leaflets (Fig. 7a,b) shows that there are many branches that are relatively long and cross extensively (more so for the lateral leaflet, Fig. 7b, than for the distal leaflet, Fig. 7a). The permutation test for phylogenetic signal is nonsignificant for the distal leaflet (P =0.19) and the lateral leaflet (P =0.56). For the distal leaflet, P-values of the permutation test with the 200 bootstrap ML trees range from <0.004 to 0.83 (median 0.15) and therefore underscore that phylogenetic uncertainty makes a difference for the interpretation of the phylogenetic signal. In contrast, the P-values for the lateral leaflet range from 0.12 to 0.88 (median 0.42) and are therefore nonsignificant for all 200 bootstrap trees.
The PCAs of the taxon mean shapes show that the PC1s take up most of the variation – about 70% of the total variance (Fig. 7c,d). Comparing the shape changes associated with the first two PCs shared features in the analyses of the distal and lateral leaflets. The PC1s are associated with variation in the relative sizes of the proximal region (from the base to the first two teeth of the serrate margin) vs. the distal region. The PC2s combine variation between a more slender or broader leaflet shape with variation in the depth of the serration of the margin, but the direction of the association is different for the distal and lateral leaflets. Overall, the covariance structures for evolutionary divergence in both leaflets are similar, as indicated by the matrix correlation of 0.85 (P <0.0001 in the matrix permutation test).
The patterns of within-taxon variation of the symmetric component of shape variation are quite similar to the patterns of variation among taxa, as can be seen by comparing the shape changes associated with the first two PCs for the distal (cf. Figs 7a and 8a) and for the lateral leaflet (cf. Figs 7b and 8b). Also, the PC1 is dominant and accounts for more than 60% of the total variance in the within-taxon PCAs for both leaflets (Fig. 8a,b). The matrix correlation between the within- and among-taxon covariance matrices is 0.96 (P < 0.0001) for the distal leaflet and 0.89 (P < 0.0001) for the lateral leaflet. Furthermore, the patterns of integration in the distal and lateral leaflets are also closely related, as indicated by the matrix correlation of 0.90 between the pooled within-taxon covariance matrices for the symmetric component of shape variation (P <0.0001).
The PCAs of fluctuating asymmetry (computed from the pooled within-taxon covariance matrix of the asymmetric component of shape variation) feature asymmetric shifts of the serrations of the leaflet margin towards or away from the leaflet base, as well as lateral expansions or contractions that result in bending of the leaflet to one or the other side (Fig. 8c,d). There are also apparent correspondences between these patterns of asymmetry and those for the symmetric component of variation within taxa (compare the differences between the left and right sides of the leaflet diagram in Fig. 8c,d to the differences between the positive and negative scores of the corresponding PC in Fig. 8a,b). These similarities of symmetric variation and fluctuating asymmetry also are reflected in the matrix correlations between the covariance matrices for symmetric within-taxon variation and fluctuating asymmetry, which are 0.55 (P =0.0008) for the distal leaflet and 0.48 (P =0.0016) for the lateral leaflet. The covariance matrices of fluctuating asymmetry of the distal and lateral leaflets are very similar. Matrix correlation between them is 0.94 (P <0.0001).
As in the analysis for the whole leaf, allometry is an important factor for the variation of leaflet shapes. In the analyses for evolutionary allometry, regressions of species average shapes on log-transformed centroid size are statistically significant and account for 41.2% of the total shape variation in the distal leaflet (P =0.0017; Fig. 9a) and for 39.8% in the lateral leaflet (P =0.0045; Fig. 9b). Allometric shape changes associated with increasing size feature shifts of the two basal teeth of the serrated margin towards the leaflet base and relative expansions of the apical part of the leaflet (Fig. 9a,b). Pooled within-taxon regressions of leaflet shape on log-transformed centroid size account for 3.6% of the shape variation within taxa in the distal leaflet (P =0.0053; Fig. 9c) and for 3.5% in the lateral leaflet (P =0.0029; Fig. 9d). The allometric shape changes for the pooled within-taxon regression are similar to the corresponding shape changes for evolutionary allometry (compare Fig. 9a, c and 9b, d).
This study has used a multilevel approach to investigate the variation of leaf shapes in cinquefoils and their evolution (Fig. 1). The results are broadly similar for the analyses of the whole leaf and of the distal and lateral leaflets and show a substantial degree of developmental plasticity and evolvability, combined with strong integration.
CVA of leaf shapes shows that most taxa are clearly separated from each other (Fig. 3; CVAs of the leaflets yield similar results, not shown). Many large shape differences between taxa (Figs 4 and 7) underscore that there is a substantial evolutionary potential in the shapes of the whole leaf and single leaflets. This result is consistent with earlier analyses that found that taxa in Potentilla can be distinguished with morphological traits (Hansen et al., 2000), but also may relate to the considerable phenotypic plasticity found in various traits of Potentilla species (Huber, 1996; Stuefer & Huber, 1998).
Given this potential for evolutionary change, it may appear surprising that our analyses did not find a clear phylogenetic signal (marginally nonsignificant permutation test for the whole leaf and clearly nonsignificant tests for both leaflets). It is unlikely that these nonsignificant results are due to insufficient statistical power, because other studies with smaller numbers of taxa and less shape variation yielded significant results (Figueirido et al., 2010; Klingenberg & Gidaszewski, 2010). Uncertainty in estimating phylogeny, however, appears to play a major role. For both the whole leaf and the distal leaflet, the permutation tests of phylogenetic signal for the 200 bootstrap trees yield P-values ranging from very significant to clearly nonsignificant. Within the margins of uncertainty due to sampling of the DNA sequences, there are therefore trees that are associated with a significant match to these morphometric data and others that are not. Results of the permutation test for the ML tree for the original sequence data (Fig. 1) should therefore be interpreted with caution. The situation is different for the lateral leaflet, however, where the permutation tests both for the tree for the original sequence data and for all 200 bootstrap trees produce nonsignificant P-values. Therefore, regardless of phylogenetic uncertainty, there is no indication of any phylogenetic signal for the shape of the lateral leaflet.
Uncertainty in estimating phylogeny is one possible cause of the lack of a phylogenetic signal, but it is not the only one. In Potentilla and its relatives, hybridization and polyploidization have been reported and may be widespread (e.g. Goldblatt & Johnson, 1979; Lundberg et al., 2009; Töpel et al., 2011). Such events may cause abrupt changes in morphological traits and therefore may be a factor for the evolution of leaf shape. Also, a phylogenetic tree cannot accurately represent an evolutionary history that includes hybridization events and may therefore produce a nonsignificant phylogenetic signal. Furthermore, vegetative parts such as leaves have long been known to have a high degree of phenotypic plasticity and evolutionary malleability and therefore may provide little information on phylogenetic relatedness (e.g. Darwin, 1859). Unfortunately, with the available evidence, it is not possible to determine conclusively why no significant phylogenetic signal for leaf or leaflet shape was found.
For all PCAs of the whole leaf and the two leaflets, the PC1 takes up at least about half of the variation, far more than any other PC (Figs 4, 5, 7 and 8). This indicates that the shape variation in each data set is highly concentrated in a single direction. Moreover, the shape changes associated with the PC1s are remarkably consistent across all three levels of analysis: evolutionary divergence among taxa (analyses with taxon means or independent contrasts), variation of the symmetric component of variation among leaves within taxa and fluctuating asymmetry of leaves (shape differences between the two halves of each leaf; Fig. 4, 5, 7 and 8). This correspondence is also apparent from the very high matrix correlations between the covariance matrices for within-taxon variation and evolutionary divergence and the moderately high ones for the covariance matrices of within-taxon variation and fluctuating asymmetry (it should be noted that only the paired landmarks can be used in the comparison of covariance matrices between the symmetric and asymmetric components of variation, and that these matrix correlations are therefore based on less information; see Klingenberg et al., 2002).
Shape variation at the three levels originates from different sources: divergence among taxa results from evolution by selection and drift or processes such as hybridization and polyploidization. The symmetric component of variation within taxa is due to genetic variation and phenotypic plasticity, and the asymmetric component of shape variation reflects the combined effects of phenotypic plasticity and developmental instability. The strong dominance of a single PC and the consistency of patterns across all three levels suggest that a common process may channel variation at all three levels in a single direction of phenotypic space. Because variation within taxa is concentrated to a large extent in a single dimension of the shape spaces, evolutionary changes are also most likely in that direction. It is thus possible that the PC1s, both for leaflets and for whole leaves, act as ‘lines of least resistance’ that acts as a relative constraint or bias for evolutionary change (Schluter, 1996; Arthur, 2001; Hunt, 2007; Klingenberg, 2010).
The symmetric component of within-taxon variation is of both genetic and environmental origins. In contrast, fluctuating asymmetry originates entirely from nongenetic causes. It is a mix of developmental instability, the imprecision in developmental processes based on the same genome and environmental conditions and phenotypic plasticity due to microenvironmental differences between the left and right halves of each leaf (e.g. shading; shown experimentally by Freeman et al., 2003). Note that this is different from motile organisms, such as most animals, where it can be assumed that the movement eliminates microenvironmental differences by ‘averaging out’ their effects and where therefore fluctuating asymmetry can be interpreted as originating exclusively from developmental instability (Klingenberg, 2003b). For uses of fluctuating asymmetry as indicators of whole-plant developmental instability, measuring the asymmetry of several leaves provides a different way of averaging out the local microenvironment of individual leaves (e.g. Puerta-Piñero et al., 2008; Albarrán-Lara et al., 2010). These possible microenvironmental effects on leaf asymmetry preclude the interpretation of correlated asymmetries as indicating direct developmental interactions (Klingenberg, 2003a, 2008). Nevertheless, fluctuating asymmetry provides information about the patterns of variation that are produced by the developmental system spontaneously or in response to effects of the environment (Breuker et al., 2006; Drake & Klingenberg, 2010). That these patterns are similar to those for the other two levels in the analysis, evolutionary divergence and within-taxon variation suggests that the developmental system has a strong effect in modulating the expression of variation from multiple origins. Furthermore, the strong integration of fluctuating asymmetry, indicated by the large proportion of the total variance for which the PC1s account (Figs 5b and 8c,d), suggests that the developmental modulation is channelling variation strongly into the corresponding direction and is therefore an important integrating factor for individual leaflets and the whole leaf.
Allometry is well known as a factor contributing to morphological integration (Klingenberg, 2009), and it has a substantial effect on shape variation in the whole leaf and in both leaflets (Figs 6 and 9). Shape changes associated with the within- and among-taxon allometries are clearly similar. Such agreements between levels of allometry have been reported before (Cheverud, 1982; Klingenberg & Zimmermann, 1992), but the modular architecture of plants makes this a particularly promising area for further analyses (Preston & Ackerly, 2004). The allometric shape changes also coincide with the PC1 patterns of shape variation at all three levels analysed in this study (Figs 4, 5, 7 and 8). It is therefore plausible that the process responsible for the common pattern of shape variation is related to size variation and growth. However, analyses correcting for allometry by regression (not shown) do not eliminate the coherent patterns of shape variation, so that allometry is clearly not the only source of integration.
The strong integration and common pattern of variation at multiple levels suggest a shared mechanism underlying this variation and raise the question what its nature may be. Developmental genetic studies have identified a number of pathways that are involved in the patterning and growth of compound leaves (Efroni et al., 2010; Hasson et al., 2010; Koenig & Sinha, 2010). NAM/CUC3 and KNOX genes have conserved gene expression patterns and are likely to be involved in the initiation of leaflets and leaf dissection (Hareven et al., 1996; Janssen et al., 1998; Hay & Tsiantis, 2006; Blein et al., 2008). The expression domain of the transcription factor PHANTASTICA specifies the spacing of leaflets that defines pinnate and palmate leaves even in groups that independently evolved compound leaves (Kim et al., 2003a). Despite the apparent conservation of these mechanisms at a very broad phylogenetic scale, some authors caution that no single explanation can account for the available data across taxa (Efroni et al., 2010). From the point of view of integration, it is interesting to note that the molecular pathways of leaf patterning involve plant hormones such as auxin and gibberellin (Hay et al., 2006; Koenig et al., 2009; Hasson et al., 2010; Koenig & Sinha, 2010), and experiments have demonstrated that even messenger RNA can be transported over long distances in tomato plants to influence leaf morphology (Kim et al., 2001). Such transport of growth regulators may be a direct physiological basis for morphological integration over extended distances in the leaflets and entire leaves, as it appears in our morphometric analyses. It is premature, however, to invoke specific molecular mechanisms as explanations for specific changes in leaf shape within or among species. Studies that combine specific genetic changes with the quantitative analysis of shape are a step in that direction (Langlade et al., 2005; Bensmihen et al., 2008; Klingenberg, 2010).
We would like to thank Royal Edinburgh Botanic Garden, Botanic Garden of the University of Freiburg, Royal Botanic Gardens, Kew, for providing Potentilla leaves and C. Grossmann for helping with Potentilla leaf preparation and Prof. N. Sinha, Prof. E. Coen, Dr. N. Langlade, Dr. A. Green and Dr. D. Chitwood for critical discussion. T. A. Dickinson and an anonymous reviewer provided helpful comments on an earlier version of the manuscript. This project was supported by Royal Society Research Grant (2009/R111035).