Testing the Validity of the Montgomery-Koyama-Smith Equation for Calculating the Total Petal Area per Flower Using Two Rosaceae Species.

The size of floral organs is closely related to the successful reproduction of plants, and corolla size is, to some extent, indicative of the size of floral organs. Petals are considered to be homologous to leaves, so we also attempted to estimate the area of a single petal using the method that is typically employed for estimating single leaf area (i.e., the Montgomery equation). Additionally, we estimated the total petal area per flower (; i.e., the whole corolla area) using the method designed for estimating the total leaf area per shoot (i.e., the Montgomery-Koyama-Smith equation). The Montgomery equation (ME) estimates the leaf area by assuming that the leaf area is proportional to the product of leaf length and width. The Montgomery-Koyama-Smith equation (MKSE) assumes that the total leaf area per shoot is proportional to the product of the sum of individual leaf widths and the maximum individual leaf length. To test the validity of the ME for predicting petal area, a total of 1005 petals from 123 flowers of two Rosaceae species, which exhibit a certain variation in petal shape, were used to fit the relationship between the petal area () and the product of petal length () and width (). Two equations, including the MKSE and a power-law equation (PLE), were used to describe the relationship between the total petal area per flower and the product of the sum of individual petal widths and the maximum individual petal length. The root-mean-square error (RMSE) and the Akaike information criterion (AIC) were used to measure the goodness of fit and the trade-off between the goodness of fit and model's structural complexity for each equation. The results show that the ME has a low RMSE value and a high correlation coefficient when fitting the relationship between and for either of the two species. Additionally, the MKSE and the PLE exhibit low RMSEs and AICs for estimating the of both Rosaceae species. These results indicate that the ME, MKSE, and PLE are effective in predicting individual petal area and total corolla area, respectively.