# Floral symmetry and scaling relationships between tepal mass and area in the daylily (Hemerocallis fulva)

## TL;DR

This study examines the symmetry and scaling relationships of daylily flowers, comparing tepal mass and area to better understand floral symmetry.

## Contribution

The study provides new insights into transitional floral symmetry by analyzing tepal mass, area, and shape in Hemerocallis fulva.

## Key findings

- There were no significant differences in most metrics between inner or outer tepals within their respective whorls.
- Significant differences were found between inner and outer whorl tepals in terms of mass, area, and shape metrics.
- Scaling relationships of tepal mass vs. area suggest congruence with the 'diminishing returns' phenomenon and serial homology.

## Abstract

Floral symmetry plays an important role in the evolution and ecology of flowering plants, yet quantifying the symmetry of the perianth remains challenging. Here, we quantify the floral symmetry of the daylily (Hemerocallis fulva) with a focus on tepal mass, area, and shape. H. fulva was selected for this study because its perianth exhibits weak bilateral symmetry, providing a unique opportunity to investigate floral forms that are transitional between radial and bilateral symmetry. Toward this end, the tepal fresh mass (FM), dry mass (DM), tepal area (A), and the ratio of tepal width to length (W/L) of 136 flowers of H. fulva were quantified. In addition, the tepal roundness index (RI) and the standardized index for bilateral asymmetry (SI) were calculated. For the purpose of comparison, the FM, DM, and A of 202 leaves were measured and calculated. Reduced major axis regression protocols were then used to fit the scaling relationships of mass vs. area for tepals and leaves. With the exception of W/L, there were no significant differences in the means of FM, DM, A, RI, and ln(SI) between any two of the three inner whorl tepals or between any two of the three outer whorl tepals. However, there were significant differences in the means of these six measures between inner and outer whorls of tepals. The 95% confidence intervals of the scaling exponents of FM vs. A and DM vs. A of the outer whorl included unity. In contrast, the lower bounds of the 95% confidence intervals of the scaling exponents of FM vs. A and DM vs. A of the inner whorl and leaves of H. fulva exceeded unity. Different metrics for size (i.e., tepal mass vs. area) and shape (i.e., the degree of deviation from a standard circle and the degree of bilateral symmetry) yield different assessments of H. fulva perianth morphometrics (i.e. radial vs. bilateral symmetry), thereby highlighting the challenge of assessing symmetry. The scaling relationships of perianth parts and leaves are statistically congruent and consistent with the phenomenon called “diminishing returns” and the classical hypothesis of serial homology.