Leaf area is an important indicator of photosynthetic capacity in plants. Knowledge of the variation of leaf shape at an individual level or a population level can help by accurately calculate leaf area. Such calculations can help us to understand the life history strategies of plants, and allow us to better understand the influence of climate change on mean leaf area as an indicator of leaf size, which is closely related to stand yields and ecological ecosystem services. The Montgomery equation (ME), which describes a proportional relationship between leaf surface area and the product of leaf length and width, has been demonstrated to hold true for many broad-leaved plants. The Magnoliaceae family has 17 genera covering ca. 300 species, of which some plants play important roles in the landscape. Many Magnoliaceae plants have similar leaf shapes, and little is known about whether ME can act as a general formula to calculate leaf surface area for these plants. This paper provides the evidence that ME can be used to measure the leaf area of Magnoliaceae species. More than 2500 mature leaves of six species within two genera (Magnolia and Michelia) of the Magnoliaceae family were selected as samples. The data of leaf length, width, and area were obtained from the scanned images. We used four models to fit these data, including (1) ME (which is actually a direct proportional function of leaf area vs. the product of leaf length and width), (2) a power-law function between leaf area and the product of leaf length and width, (3) a power function with an exponent of 2 between leaf area and leaf length, and (4) a power function between leaf area and leaf length. We found that ME and the second function have similar root-mean-square error values that are both lower than those of the other two equations. However, ME is better than the second equation because of the simplicity of its structure. We documented the validity of ME for calculating leaf area at a species level, a genus level, and even for the 6-species pooled data set. The estimated Montgomery parameter (i.e., the proportional coefficient in ME) is approximately equal to 0.68, which means that leaf area of the six investigated species can be approximated by 68% of the area of a rectangle with the leaf’s length and width as its sides. This study provides a convenient and fast approach for leaf-area calculation. In addition, we found that the Montgomery parameter can act as an indicator for measuring the similarity of leaves among different species, which provides a measurement standard for leaf morphology.

叶面积是植物光合作用能力的重要指标。了解叶水平在个体水平或种群水平上的变化可以通过准确计算叶面积来提供帮助。这样的计算可以帮助我们了解植物的生命史策略，并让我们更好地了解气候变化对平均叶面积的影响，以此作为叶片大小的指标，这与林分产量和生态系统服务密切相关。蒙哥马利方程（ME）描述了叶片表面积与叶片长度和宽度的乘积之间的比例关系，已被证明对许多阔叶植物均成立。木兰科有17属。300种，其中一些植物在景观中起着重要作用。许多木兰科植物的叶片形状相似，关于ME是否可以作为计算这些植物叶片表面积的通用公式知之甚少。本文提供的证据表明，ME可以用于测量木兰科植物的叶面积。两个属中六个物种的2500多个成熟叶子（玉兰和含笑选择木兰科的）作为样品。叶的长度，宽度和面积的数据是从扫描图像中获得的。我们使用了四个模型来拟合这些数据，包括（1）ME（实际上是叶面积与叶长度和宽度的乘积的直接比例函数），（2）叶面积与乘积之间的幂律函数叶长度和宽度的函数，（3）叶面积和叶长度之间的幂函数为2，（4）叶面积和叶长度之间的幂函数。我们发现ME和第二个函数具有相似的均方根误差值，均低于其他两个方程式的均方根误差值。但是，由于其结构简单，ME比第二个方程更好。我们记录了ME在物种级别，属级别，甚至对于6种合并数据集。估计的蒙哥马利参数（即ME中的比例系数）大约等于0.68，这意味着所研究的六个物种的叶面积可以近似于以叶的长和宽为边的矩形的68％ 。这项研究为叶面积计算提供了一种方便快捷的方法。此外，我们发现蒙哥马利参数可以作为衡量不同物种之间叶片相似性的指标，这为叶片形态提供了测量标准。这意味着六个被调查物种的叶子面积可以近似于以叶子的长度和宽度为边的矩形面积的68％。这项研究为叶面积计算提供了一种方便快捷的方法。此外，我们发现蒙哥马利参数可以作为衡量不同物种之间叶片相似性的指标，这为叶片形态提供了测量标准。这意味着六个被调查物种的叶子面积可以近似于以叶子的长度和宽度为边的矩形面积的68％。这项研究为叶面积计算提供了一种方便快捷的方法。此外，我们发现蒙哥马利参数可以作为衡量不同物种之间叶片相似性的指标，这为叶片形态提供了测量标准。