Testing the relationship among tepal area, length, and width using four Magnolia species

IF 2.1 3区农林科学 Q2 FORESTRY Trees Pub Date : 2025-01-13 DOI:10.1007/s00468-025-02600-6

Youying Mu, Peijian Shi, Jinfeng Wang, Weihao Yao, Lei Chen, Dirk Hölscher, Karl J. Niklas

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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.

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以4种木兰为研究对象，检验花被片面积、长度和宽度之间的关系

蒙哥马利方程假设花被片面积与花被片长度和宽度的乘积成正比关系，并使用从四种白玉兰中提取的数据进行验证。摘要单株花瓣或花被片面积(A)是衡量花非生殖大小的一个重要指标。Montgomery方程（ME）通过假设A与花瓣或花被片长度(L)和宽度(W)的乘积成正比关系（\(A \propto LW\)）来估计A，而幂律方程（PLE）假设A与异速生长关系（\(A \propto \left( {LW} \right)^{{{\upalpha }_{1} \ne 1}}\)）。如果W/L有一个小的变化，预计四个关系成立，即\(A \propto L^{2}\), \(A \propto L^{{{\upalpha }_{2} }}\), \(A \propto W^{2}\)和\(A \propto W^{{{\upalpha }_{3} }}\)，其中α1， α2和α3是要估计的缩放指数。为了评估这6个公式的有效性，我们测量了4种白玉兰250朵花的2031个花瓣状花被。使用均方根误差（RMSE）确定每个方程的拟合优度，使用百分比误差（PE）比较具有相同预测因子的任意两个方程，即LW， L和w。考虑到4个物种中有3个物种的RMSE为＆lt； 0.05, 1个物种的RMSE为＆lt； 0.07，因此验证了ME在物种水平和汇总数据上计算A的有效性。然而，在物种水平上，PLE比ME更稳健。对于合并的数据，ME和PLE在RMSE值上的差异可以忽略不计。这些结果表明，ME是测量本研究中检测的木兰物种a的有效和非破坏性工具，并且可能适用于其他更多样化的物种。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Trees 农林科学-林学

CiteScore

4.50

自引率

4.30%

发文量

113

审稿时长

3.8 months

期刊介绍： Trees - Structure and Function publishes original articles on the physiology, biochemistry, functional anatomy, structure and ecology of trees and other woody plants. Also presented are articles concerned with pathology and technological problems, when they contribute to the basic understanding of structure and function of trees. In addition to original articles and short communications, the journal publishes reviews on selected topics concerning the structure and function of trees.