Influence of leaf shape on the scaling of leaf surface area and length in bamboo plants
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Influence of leaf shape on the scaling of leaf surface area and length in bamboo plants Pei‑Jian Shi1,2 · Yi‑Rong Li1 · Ülo Niinemets3,4 · Edward Olson2 · Julian Schrader5,6 Received: 11 December 2019 / Accepted: 31 October 2020 © The Author(s) 2020
Abstract 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. Keywords Montgomery equation · Power law · Principle of similitude · Ratio of leaf width to length · Scaling · Bambusoideae
Introduction
Communicated by H. Roaki Ishii. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00468-020-02058-8) contains supplementary material, which is available to authorized users. * Julian Schrader jsch
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