FIGURE 8.

Workflow for shape analysis of T. undulatum exhibiting bilateral symmetry combined with rotational symmetry of order 3 (by 120°) (case study 4). (A) First, an original configuration is considered, then all transformed relabelled copies in the symmetry group are produced with functions ‘C1v’ and ‘Cn.’ A GPA is applied to this dataset. The mean shape (consensus) is symmetric. (B) A PCA unambiguously separates the four categories of shape variation and indicates how much their associated PCs account for the total variance. The first PC of each category is displayed. The shape changes for pairs of PCs with equal eigenvalues that first appear as totally asymmetric are further revealed by appropriately rotating them using function ‘RotatePC.’ The outline soft wireframes of flowers are as in Figure 6. A scatterplot of the PC scores for the first two PCs shows a distribution that is symmetric under reflection combined with rotation of order 3. Each point in the plot corresponds to transformed copies of a given flower’s configuration of landmarks. Credit: photograph by Nicholas A. Tonelli, distributed under a cc-by-2.0 licence.