Key message

Using more than 10,000 bamboo leaves, we found that the scaling between leaf surface area and length follows a uniform power law relationship mainly relying on the degree of variation in leaf shape (reflected by the ratio of leaf width to length).

Abstract

A recent study based on leaf data of different plant taxa showed that the scaling of leaf surface area (A) with linear leaf dimensions was best described by the Montgomery equation (ME) that describes A as the product of leaf length (L) and width (W). Following from ME, a proportional relationship between A and the square of L has been proposed, but the validity of this simplified equation strongly depends on leaf shape (W/L ratio). Here, we show that the simplified equation can be applied to a group of closely related plants sharing a similar W/L ratio with low degree of uncertainty. We measured A, L and W of more than 10,000 leaves from 101 graminoid taxa (subfamily Bambusoideae) having similar elongated leaf shapes. We found that ME applies to the leaves of all bamboo taxa investigated. The power law equation that was used to describe a scaling relationship of A vs. L also predicted leaf area with high accuracy, but the variability measured as the root-mean-square error (RMSE) was greater than that using ME, indicating that leaf width also plays an important role in predicting leaf area. However, the dependence of the prediction accuracy of A on W is intimately associated with the extent of the variation in W/L ratio. There was a strong positive correlation (r = 0.95 for the 101 bamboo taxa) between RMSE and the coefficient of variation in W/L ratio. Thereby, our results show that leaf area of bamboo plants can be calculated by the product of L and W with a proportionality coefficient ranging from 0.625 to 0.762, i.e., the leaf area of bamboo leaves approximately equals 70% of a rectangular area formed by L and W. The pooled data of ln(A) vs. ln(WL) of 101 bamboo taxa were located on or very close to the regression line without being affected by interspecific differences. However, interspecific differences in W/L ratio largely affected the scaling relationship of A vs. L, which led to large deviations of the data of ln(A) vs. ln(L) from the regression line. This implies that the square relationship between A and L does not apply to all species even if those are very closely related taxa.

中文翻译：

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叶片形状对竹植物叶片表面积和长度结垢的影响

关键信息

使用超过10,000片竹叶，我们发现叶表面积和长度之间的缩放关系遵循均匀的幂律关系，主要取决于叶形的变化程度（由叶宽与长的比率反映）。

抽象

基于不同植物分类单元的叶片数据的最新研究表明，蒙哥马利方程（ME）最好地描述了叶片表面积（A）与线性叶片尺寸的比例关系，该方程将A描述为叶片长度（L）和宽度的乘积（W）。根据ME，提出了A与L的平方之间的比例关系，但是此简化方程的有效性很大程度上取决于叶的形状（W / L比）。在这里，我们表明简化方程可以应用于一组具有相似的W / L比且不确定度较低的密切相关的植物。我们测量了A，101个革兰类类群（亚科Bambusoideae）的10,000片叶子的L和W具有类似的细长叶片形状。我们发现，ME适用于所调查的所有竹类分类单元的叶子。用来描述A与L的比例关系的幂定律方程还可以高精度地预测叶片面积，但是以均方根误差（RMSE）衡量的变异性大于使用ME的变异性，表明叶片宽度在预测叶面积方面也起着重要作用。但是，A的预测精度对W的依赖性与W / L比的变化程度密切相关。有很强的正相关性（ 对于RMSE和W / L比的变化系数之间的101个竹类分类单元，r = 0.95 。因此，我们的结果表明，竹子的叶面积可以通过L和W的乘积来计算，比例系数的范围为0.625至0.762，即竹叶的叶面积大约等于L形成的矩形面积的70％。和w ^。101个竹类类群的ln（A）vs. ln（WL）汇总数据位于回归线上或非常接近回归线，而不受种间差异的影响。然而，W / L比的种间差异在很大程度上影响了A vs. L，这导致ln（A）vs. ln（L）的数据与回归线有较大偏差。这意味着A和L之间的平方关系并不适用于所有物种，即使它们是密切相关的分类单元也是如此。