Morphological Integration between Compartments

The level of covariation among compartments was typically quantified and evaluated by using GM. GM is a collection of algorithms that examine shape variation on a set of landmarks of the objects to be studied. A number of studies have adopted GM approaches to examine morphological integration between compartments, including the forewings and hindwings of bumblebees (Klingenberg et al., 2001), the anterior and posterior of Drosophila wing (Klingenberg and Zaklan, 2000), the face and braincase of birds skulls (Klingenberg and Marugán-Lobón, 2013), the arterial Circle of Willis and skull of laboratory mice (Jamniczky and Hallgrímsson, 2011), the face and cerebral capsule of human cranial skeletons (Mitteroecker and Bookstein, 2008), and the vault, face, and cranial base of human skulls (Bookstein et al., 2003).

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CHAPTER 3. QUANTIFIACTION OF FLORAL SHAPE IN THREE-DIMENSION

This chapter proposes a method to quantify the floral shape variations in an F2 cross of Sinningia speciosa by using 3D GM. Image processing algorithms were used to construct

3D floral images and improve the images quality. GM including generalized Procrustes analysis and principal component analysis were performed to evaluate the floral shape variation. The GM analysis demonstrated that corolla curvature, flower opening, and dorsoventral symmetry were principal shape variations of the flowers. To quantify the

extent of flower opening due to curvature and the degree of corolla asymmetry, two traits

— flower opening and corolla asymmetry were defined and quantified from the 3D floral

images. The 3D GM method proposed in this chapter was compared to typical 2D GM.

The 3D analysis was shown to be capable of observing shape variation that could not be identified by typical 2D approaches. The 3D GM approach opens new avenues to investigate floral shape variations.

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3.1 Material and Methods

3.1.1 Flower material

The flower samples were obtained by crossing two cultivars of S. speciosa, “Carangola”

and “Peridots Darth Vaders” (Fig. 2). These parental accessions were crossed to breed F1

plants. The F2 plants were generated by selfing a single F1 plant. All plants were grown in a greenhouse under natural lighting with 20% shade and 70%–80% humidity at 22–

28°C. We included only the flowers of the F2 plants with exactly 5 petal lobes because the flowers with different numbers of petal lobes were incomparable in shape (i.e., nonhomologous; Adams et al., 2004) and thus should be excluded from comparison. The flower samples were provided by Prof. Chun-Neng Wang and his team in the Institute of Ecology and Evolutionary Biology at the National Taiwan University.

Figure 2. Interbreeding process of S. speciosa flowers.

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3.1.2 Floral image acquisition

Three-dimensional flower images were acquired using a μCT scanner (SkyScan 1076, Bruker, Kontich, Belgium). The specimens of first-day fully bloomed fresh flowers were cut at the stalk near the bottom of the tube and placed in the scanner chamber. The specimens were fastened to the base in the chamber with gummed tape to prevent the movement of the specimens during scanning. The transverse diameter of the chamber was 68 mm and the single scan length was 20 mm in the travel direction. The number of scans

was dependent on the flower sizes. The X-ray source voltage, current, exposure time, and scanning resolution were set to 40 kV, 250 μA, 150 ms, and 35 μm, respectively. After

scanning was completed, the 3D raw images were reconstructed by using SkyScan NRecon (Bruker, Kontich, Belgium). We acquired 57 flower images from various F2

plants. The acquisitions were performed between August, 2012 and September, 2014.

3.1.3 Quality improvement of flower images

The raw images comprised flower specimens and the base for fastening the flower samples. Image processing algorithms were applied to segment the flowers from the background, reduce the noise of the images, and transform the images into an appropriate format for the subsequent analysis. During the process, the spatial resolution of the raw images was reduced by 50% to a voxel size of 70 μm on each side to expedite processing.

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The algorithms were implemented on the 2D slices of the 3D raw images along the travel direction. Region labeling (Haralick and Shapiro, 1992) was first applied to detect objects in the images. The base, the greatest object located at a fixed position in the slices, was automatically recognized and eliminated. The objects with pixel sizes smaller than a certain threshold (i.e., sparkles) were regarded as noise and were removed. The image contrast (i.e., gamma value) was adjusted appropriately to span the gray-level dynamic range. The resulting images, referred to as volumetric images (Fig. 3A), were then binarized. A morphological closing (Vincent, 1994) was applied to eliminate the hollow pixels within the flower petals. Surface images, which are composed of triangle meshes, were then generated (Hansen and Johnson, 2005; Fig. 3B). The mesh density was adjusted to maintain a reasonable resolution of the images. The image processing was performed using MATLAB (The Mathworks, Natick, MA, USA).

Figure 3. (A) Volumetric image, (B) surface image, and (C) flower landmarks.

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3.1.4 Landmark identification

Landmarks are categorized as primary and secondary (Zelditch et al., 2004). In this study, the primary landmarks were defined as the anatomically recognizable points of the corolla, including the intersections of adjacent lobes, endpoints of petal midribs, and boundary points of lobes and tubes on petal midribs (solid dots in Fig. 4). The secondary landmarks were equally distributed points between the two primary landmarks along the lobe contours or petal midribs (hollow dots in Fig. 4). In the landmark identification process, the lobe contours and petal midribs were identified using the Landmark software (Wiley et al., 2005). The landmarks were then determined using a program developed in MATLAB. Thus, 95 landmarks, including 15 primary and 80 secondary, were collected for each specimen (Fig. 3C). The lobes and tubes comprised 55 and 50 landmarks, respectively, with 10 landmarks in common. S. speciosa and various angiosperm species natively develop flowers with limited anatomical points that can serve as the primary landmarks. The proposed approach for selecting the secondary landmarks in 3D images effectively increases the number of homologous characteristic points of the flowers being studied, and thus improving the overall quality of describing and illustrating the flower shapes.

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Figure 4. Primary and secondary landmarks on a petal.

3.1.5 Shape variation quantification

GM was applied to the landmarks for identifying the major shape variations between the flowers. The GM procedure includes generalized Procrustes analysis and principal component analysis (PCA; Zelditch et al., 2004; Lawing and Polly, 2010). Generalized Procrustes analysis was first implemented to eliminate variations mainly irrelevant to shape (e.g., shifting, rotating, and scaling). PCA was then applied to obtain few principal components (PCs) that accounted for a major portion of the landmark variability between the flowers. The major floral shape variations then could be visualized by reconstructing flowers by using inverse PCA with altered PC values.

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3.1.6 Major morphological traits

The major shape variations identified by GM illustrated the transition between the zygomorphic and actinomorphic flowers. Morphological traits corresponding to the major shape variations were defined and quantified. These traits were physically measured in the volumetric images of the flowers using image processing and computer graphics and could genuinely and quantitatively represent the morphological characteristics of the flowers.

3.2 Results

3.2.1 Three-dimensional flower images and landmarks

Three-dimensional images of flowers were acquired. Image processing algorithms were used to segment the flower specimen from the background and to reduce noise in the images. Figure 5A and 5B show a flower image and its corresponding volumetric (μCT) image. Landmarks were selected following the proposed procedure. Figure 5C shows the landmarks and their identification numbers.

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Figure 5. (A) Image of a flower, (B) corresponding μCT image, and (C) landmarks on the flower image.

3.2.2 Identification and visualization of floral shape variations

PCs describing the primary floral shape variations were derived. The first three PC scores, PC1, PC2, and PC3, accounted for 38.8%, 16.3%, and 5.6% of the total shape variation.

Each of the remaining PC scores accounted for less than 4% of the total shape variation.

Because the first three PCs accumulated more than 60% of the total shape variation, we presented the results of the first three PCs only. Figure 6 displays the scatter plots of PCs.

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The PCs were standardized with zero means and unit variances. Unimodal distributions were observed for the first three PCs. Kolmogorov–Smirnov test indicated that the hypothesis that PC1, PC2, and PC3 were normally distributed could not be rejected (P = 0.94, 0.84, and 0.96).

Figure 6. Scatter plots of the first three principal components.

Figure 7 illustrates the degree of floral shape variations caused by changes in the PCs. In the visualization process, the mean and standard deviation (STD) of the PCs were calculated. Reconstructed landmarks were calculated using an inverse PCA with a specific PC value being manipulated, whereas other PC values were maintained at mean values. The manipulated PC values were set at the mean or mean ± 2 STD. Flower shapes were then reconstructed using the resulting landmarks. The flowers were shown in 3D

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images by using a thin-plate spline approach (Rohlf and Slice, 1990) to reveal the degree of shape transformation. In Figure 7, the mean flower shape is indicated in gray, and the reconstructed flowers with the manipulated PCs are illustrated in beige. Red arrows at the landmarks show the direction and degree of transformation from the mean shape to another. Major transformation was observed at the distal lobes (PC1 and PC2), boundary between the lobe and tube (PC2), margin between the tube and sepal (PC2), and tube chamber (PC3). Figure 8 shows the front (or face) and side views of the flowers.

Figure 7. Illustration of flower shape variations caused by changes in PCs.

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The shape variation associated with each PC was examined. We observed that PC1 primarily corresponded to corolla curvature and flower opening. Figures 7 and 8 indicate that petal curvature in the boundary region between the lobe and tube changes drastically for the flowers with different PC1 values. The lobes of the flower with a high PC1 value bent outward at a considerable degree (the curves connecting L1-T8 and L25-T16 in Figure 8B). This large curvature produced a wide opening in the flower. The landmarks on lobe contours (from L1 to L33 in Figure 8A) spread out from the center. By contrast, the flower with a low PC1 value was associated with a moderate degree of opening (Figure 8B). In the front-view images, the lobes of the flower with a narrow opening (mean − 2 STD) exhibited a high degree of overlapping compared with the lobes of the flower with a wide opening (mean + 2 STD) in which the lobes were distinctly separated.

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(A)

(B)

Figure 8. (A) Front-view and (B) side-view illustration of the flower shape variations.

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We observed that PC2 mainly corresponded to the degree of corolla dorsoventral symmetry (Citerne et al., 2010). The flower with a low PC2 value was zygomorphic. The distances from either side of the petal base (lines connecting T1–T4 and T9–T12 in Figure 8B) to the center of the tube were balanced. By contrast, the flower with a high PC2 value was actinomorphic. The end of the tube (lines connecting T1–T4 and T9–T12) bent upward, resulting in a visible asymmetry between the dorsal and ventral petals. In addition, PC2 corresponded to the degree of overlapping between the ventral and lateral lobes in the front view (Fig. 8A). Compared with the actinomorphic flower, the zygomorphic flower developed a ventral lobe bent downward at a higher degree (Fig. 8B). Because of the aforementioned changes, the flowers with various PC2 values displayed distinct front views (Fig. 8A) for pollinators.

We observed that PC3 particularly corresponded to the size of the tube chamber. The flower with a low PC3 value was associated with a chamber dilated around landmark T5 (Fig. 8B). Furthermore, the flower with a small PC3 value was associated with widely opened lateral lobes (L9 and L33 in Figure 8A).

3.2.3 Morphological traits: flower opening and corolla asymmetry

The GM analysis revealed that flower opening (i.e., corolla curvature) and dorsoventral symmetry were the leading shape variations. Two traits, flower opening and corolla

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asymmetry, were defined and identified directly in the 3D flower images. Flower opening was defined as the ratio of the diameters of the lobe-widening circle to the tube-opening circle (Fig. 9A). The lobe-widening circle was defined as the smallest circle that comprised the lobe contour. The tube-opening circle was defined as the optimally fitted circle of the 5 lobe intersections. Corolla asymmetry was defined as the sine value of the asymmetry angle. The asymmetry angle (θ in Figure 9B) was the angle between the long axis of the corolla tube and the normal vector of the tube-opening circle. On the basis of these definitions, the two traits were unaffected by the size, translation, or rotation of the 3D flower images.

Figure 9. (A) Tube-opening and lobe-widening circles for calculating the opening score and (B) the asymmetry angle.

Analysis was conducted to determine if PC1 and PC2 were linearly correlated to flower opening and corolla asymmetry, respectively. Figure 10 shows the scatter plots of the

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analysis. The data were normalized with zero means and unit variances. Moderate

correlation was observed. The correlation coefficient between PC1 and the flower opening score was −0.53, and the correlation coefficient between PC2 and the asymmetry

score was 0.61. This indicates that the two defined flower traits can generally represent the principal shape variations.

(A) (B)

Figure 10. Scatter plots of (A) PC1 and flower opening, and (B) PC2 and the asymmetry score.

3.2.4 Transition between the zygomorphic and actinomorphic flowers

Figure 11 shows the distributions of flower opening and corolla asymmetry. The mean and STD of flower opening were 1.74 and 0.12, respectively. The mean and STD of corolla asymmetry were 0.07 and 0.28 (the corresponding asymmetry angles were 4.19°

and 16.19°), respectively. Figure 11A and 11C show the flower images with extreme flower opening values (1.43 and 1.98). Figures 11D and 11F show the flower images with the extreme corolla asymmetry values (0.14 and 0.44).

-3 -2 -1 0 1 2 3

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The two traits could be unimodally and continuously distributed (Fig. 11). The hypothesis that flower widening and corolla asymmetry were normally distributed could not be

Figure 11. (A) Flower of the smallest opening value, (B) histogram of flower opening, (C) flower of the largest opening value, (D) flower of the smallest corolla asymmetry, (E) histogram of corolla asymmetry, and (F) flower of the largest corolla asymmetry.

3.2.5 Comparison of shape variation analyses performed using 2D and 3D images

The performance of the proposed approach was compared with that of the conventional method, which determines the floral shape variations by using 2D images (Hsu et al.,

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2015). The 2D images were obtained by projecting the 3D flower images onto 2D planes.

In the projection, the view angle of a flower was set according to its tube-opening circle (Fig. 9A) and dorsoventral planes to capture the front-view and side-view images of the flower (Fig. 12). This projection process mimicked the action of acquiring 2D flower images by using a camera. Subsequently, landmarks were identified on the images by following the procedure stated in a previous study (Hsu et al., 2015). All the front-view landmarks were located on the lobe contours, whereas all the side-view landmarks were located on the tube contours (Fig. 12). This limitation was because of the challenge of accurately determining landmarks on the tubes from front views and on the lobes from side views. Thus, 30 front-view and 15 side-view landmarks were collected for each specimen (Fig. 12).

(A) (B)

Figure 12. 2D (A) front-view and (B) side-view images of a flower. Red dots indicate landmarks selected along the contours.

To quantify the floral shape variation, two GM analyses were conducted using the front-view and side-front-view landmarks, respectively. This procedure followed the typical

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approach used for 2D images (Kawabata et al., 2009; Hsu et al., 2015). The first two PCs obtained from the front-view landmarks, referred to as F-PC1 and F-PC2, accounted for 19.0% and 14.5% of the total shape variation. The first two PCs obtained from the side-view landmarks, referred to as S-PC1 and S-PC2, accounted for 44.0% and 16.2% of the total shape variation. Figure 13 displays the floral shape variation caused by the changes in the first two PCs. We observed that F-PC1 and F-PC2 primarily corresponded to the ventral lobe extension and the degree of overlapping between the lobes. Furthermore, S-PC1 and S-PC2 principally corresponded to the dorsoventral asymmetry and the opening of the tube chamber. The flower opening (i.e., corolla curvature) characteristic shown in the 3D GM analysis was not observed in the 2D GM analysis.

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(A)

(B)

Figure 13. (A) Front-view and (B) side-view illustrations of the floral shape variation quantified using 2D images.

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3.4 Discussion

3.4.1 Advantages of 3D floral shape analysis

The 3D analysis explored the additional aspects of the corolla shape variation that was not observed using the conventional 2D methods. Our proposed approach can identify corolla curvature (i.e., flower opening). The 3D GM analysis revealed that the corolla curvature corresponded to the major portion of the total shape variation (i.e., PC1).

However, this was not identified by the 2D GM analysis (Fig. 13). Corolla curvature has been demonstrated to act as a mechanical nectar guide, which facilitates direct flower handling for plant–pollinator interactions (Campos et al., 2015). The corolla curvature is perhaps an essential trait for the development and evolution of flower shape

Three-dimensional images enables quantification of flower traits. Flower shape is complex, and the principal shape variations are often presented qualitatively (e.g., GM analysis results). By using 3D images, flower traits corresponding to the leading shape variations can be further defined and measured with high accuracy. In this study, the traits of the corolla, such as the tube-opening circle, lobe-widening circle, and long axis, were quantified. Subsequently, the flower opening and corolla asymmetry scores were derived.

These traits of flowers are physically measured and can quantitatively represent the flower shapes. Furthermore, these traits are crucial parameters that illustrate the transition between the zygomorphic and actinomorphic flowers. By contrast, these flower traits

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could be difficult to assess or quantify with a high level of uncertainties when 2D images are used. These traits can be used in future studies that address topics such as genotype–

phenotype association or plant–pollinator interactions.

Graphics using 3D information are more powerful tools that illustrate flower shapes. With 3D coordinates, the corollas could be observed from various view angles in more detail (e.g., midribs). In addition, the lobe and tube of a corolla could be illustrated together in a 3D image (Fig. 7), whereas a 2D image could only demonstrate the lobe or tube of a corolla (Fig. 13). The partial information obtained in 2D images may result in the misinterpretation of the floral shape variations. For example, the 2D graphical illustration (Fig. 13a) could lead to a false interpretation of the shape variation corresponding to F-PC1 as the degree of overlapping for the ventral lobe, whereas the same shape variation was clearly observed as dorsoventral asymmetry in the 3D graphical illustration (Fig. 7).

3.4.2 Reasons for 3D analysis outperforming 2D analysis

Three-dimensional images inherently contain more anatomical details (e.g., midribs).

Landmarks must be situated on the homologous loci in all specimens and are typically identified on the basis of these anatomical details. By contrast, a large portion of geometric details are not available in 2D images. Thus, less shape variations can be quantified using 2D images. In addition, certain 2D landmarks are identified on the lobe

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or tube contours (Fig. 12). These contours are projections on 2D planes and are subjected to the view angle of a camera. Thus, uncertainties can be introduced in the contours when the flower images are taken. Subsequently, these uncertainties propagate to the landmark coordinates. Moreover, a 3D flower image comprises both the lobe and tube landmarks of the same flower. The lobe and tube landmarks are subjected to the GM analysis simultaneously; therefore, the association between the two compartments can be retained.

However, a 2D image comprises only the lobe or tube landmarks (Fig. 13). Conducting the shape analysis by using only one of the datasets separately leads to a loss of association between the two compartments, therefore failing to retain the inherent shape information.

3.4.3 Biological implications of flower shape variations

Our 3D GM analysis facilitated in identifying the flower opening and corolla asymmetry (indicated by the asymmetry angle) as the two major traits for the petal shape variations in the transition between actinomorphic and zygomorphic flowers. Wide flower opening and bilateral symmetry in the zygomorphic F2 individuals allow only those pollinators that enter flowers in a certain direction, thus facilitating pollen deposition on these visitors.

Narrow flower opening and radial symmetry in the actinomorphic F2 individuals indicates that the flowers are unable to restrict pollinators entering from any direction. Flowering

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plants with bilateral symmetry have been demonstrated greatly in facilitating plant–

pollinator interactions or coevolution.

3.5 Concluding Remarks

3.5 Concluding Remarks