A method for quantifying rotational symmetry

Here, a new approach for quantifying rotational symmetry based on vector analysis was described and compared with information obtained from a geometric morphometric analysis and a technique based on distance alone. A new method was developed that generates a polygon from the length and angle data of a structure and then quantifies the minimum change necessary to convert that polygon into a regular polygon. This technique yielded an asymmetry score (s) that can range from 0 (perfect symmetry) to 1 (complete asymmetry). Using digital images of Geranium robertianum flowers, this new method was compared with a technique based on lengths alone and with established geometric morphometric methods used to quantify shape variation. Asymmetry scores (s) more clearly described variation in symmetry and were more consistent with a visual assessment of the images than either comparative technique. This procedure is the first to quantify the asymmetry of radial structures accurately, uses easily obtainable measures to calculate the asymmetry score and allows comparisons among individuals and species, even when the comparisons involve structures with different patterns of symmetry. This technique enables the rigorous analysis of polysymmetric structures and provides a foundation for a better understanding of symmetry in nature.