Key message
The Montgomery equation, which assumes a proportional relationship between the tepal area and the product of the tepal length and width, is validated using data drawn from four Magnolia species.
Abstract
An important metric of floral non-reproductive size is individual petal or tepal area (A). The Montgomery equation (ME) estimates A by assuming a proportional relationship between A and the product of petal or tepal length (L) and width (W), i.e., \(A \propto LW\) , whereas the power-law equation (PLE) assumes the allometric relationship \(A \propto \left( {LW} \right)^{{{\upalpha }_{1} \ne 1}}\) . If W/L has a small variation, four relationships are expected to hold true, i.e., \(A \propto L^{2}\) , \(A \propto L^{{{\upalpha }_{2} }}\) , \(A \propto W^{2}\) , and \(A \propto W^{{{\upalpha }_{3} }}\) , where α1, α2, and α3 are scaling exponents to be estimated. To assess the validity of these six formulae, 2031 the petal-like tepals of 250 flowers from four Magnolia species were measured. The root-mean-square error (RMSE) was used to determine the goodness of fit of each equation, and the percentage error (PE) was used to compare any two equations with the same predicator, i.e., LW, L and W. The ME was validated for calculating A at the species level and for the pooled data given that three of the four species had < 0.05 RMSEs and one had a < 0.07 RMSE. However, the PLE was more robust than the ME at the species level. For the pooled data, the ME and PLE had a negligible difference in RMSE values. These results show that the ME is a valid and non-destructive tool for measuring A for the Magnolia species examined in this study and likely holds true across other more diverse species.
