Assessment of the Association between the Three-dimensional Shape of the Corolla and Two-dimensional Shapes of Petals Using Fourier Descriptors and Principal Component Analysis in Eustoma grandiflorum

The shapes of the petal curvature and two-dimensional (2D) petal shape of Eustoma flowers were quantitatively evaluated by Fourier transform analysis. Petal curvature was traced along the abaxial surface of petal midribs observed in the lateral view. The curved lines were transformed to Fourier coefficients and then subjected to principal component analysis. Petal curvature could be described using the first three principal components (PC), which accounted for 95% variation of overall PCs. The first and second PC described the opening angle of the flower and inward curvature of the middle the part of the petals, respectively. Petal shape could be described using the first two PCs, representing petal width and the position of the weighted center, respectively. A total of 122 cultivars and breeding lines were clustered based on Self-Organization Maps (SOMs) using the Fourier coefficients of petal curvature and petal shape. The SOM characterized four typical corolla shapes; 1) bowl-shaped, 2) tall-cup-shaped, 3) trumpet-shaped, and 4) funnel-shaped corolla. The second PC of petal curvature showed a high correlation with the first PC of the 2D petal shape, indicating that the formation of petal curvature observed in bowl- and tall-cup-shaped corollas is associated with the wide shape of the petals.