Application of the Montgomery Equation in Morphometric Analysis of Tepals: A Case Study of Liriodendron × sinoamericanum

Distinctions between plant perianths are often defined by structural variations, which makes it critical to understand species evolution through the lens of morphological differentiation. Additionally, the size of the perianth is often closely related to the successful reproduction of plants, and the perianth area is generally considered one of the indicators of perianth size. The Montgomery equation (ME) hypothesizes that the individual leaf area is proportional to the product of leaf length and width, with the proportionality coefficient referred to as the Montgomery parameter (MP). To test the validity of the ME for calculating the tepal area, a total of 541 tepals (including petaloid and sepaloid tepals, which have similar shapes but different colors) from 60 <i>Liriodendron</i> × <i>sinoamericanum</i> P.C. Yieh ex C.B. Shang & Z.R. Wang flowers were used to fit the relationship between the tepal area (<i>A</i>) and the product of the tepal length (<i>L</i>) and width (<i>W</i>). Furthermore, this study compared whether there were significant differences in MPs between the two types of tepals, as well as differences in the fitting performance of the ME for each type. The root-mean-square error (RMSE) and mean absolute percentage error (MAPE) were used to assess the goodness of fit. The results revealed that the ME had low RMSE values (<0.05) and MAPE values (<5%), along with a high correlation coefficient (>0.95), when fitting the relationship between <i>A</i> and <i>LW</i> for either of the two different types of tepals. These findings indicate that the ME is effective in predicting the tepal area. Furthermore, there was a difference between the MPs of the two types of tepals. However, since the ME fitting of the data for each tepal type individually, as well as the combined data, all yielded a good fitting performance, the difference between the two types of tepals can be considered negligible in terms of its impact on the fitting results. Therefore, based on the combined morphology and ME fitting results of the two types of tepals, the tepals in <i>L</i>. × <i>sinoamericanum</i> do not show obvious differentiation. This study provides new insights into the understanding of the differentiation of similar organs during the evolution of angiosperms.