鹅掌楸属植物叶片两侧对称性测量的泰勒幂法则

Taylor's power law of the leaf bilateral symmetry measure of Liriodendron trees

【目的】泰勒幂法则是一种重要的生物学统计规律,反映了特定生物学测量值的均值和方差,呈现出幂函数的关系,鹅掌楸叶形复杂,但明显呈两侧对称的特征,本研究旨在验证鹅掌楸叶片两侧对称性测量是否符合泰勒幂法则。【方法】选取了2种鹅掌楸及其杂交种(Liriodendron chinense、L.tulipifera和L.chinense×L.tulipifera)的叶片(以下表述为3种鹅掌楸叶片),每种200片以上,将每片叶子沿垂直于中轴方向划分出1 000对等距的左右部分,计算左右部分差值之绝对值的均值和方差,使用对数转置的均值和方差数据进行线性拟合,检验3条直线斜率(即泰勒幂指数)的估计值是否具有显著性差异,同时将3种鹅掌楸的数据进行汇总,计算其直线的斜率。【结果】3种鹅掌楸叶片对称性测量均符合泰勒幂法则,但3个斜率的估计值没有显著性差异,根据汇总数据计算得到的泰勒幂指数的估计值为1.777。【结论】研究证实了基于叶面积测量的两侧对称性差异能够反映出泰勒幂法则,良好的尺度比例关系可以提高幂函数的拟合优度。尽管不同类群植物叶形差异较大,但两侧对称性测量的均值和方差的对数转置数据都分布在一条理论回归直线上。考虑到叶形的两侧对称性变异程度能够反映植物地上部分建筑学结构对光获取和利用的影响,研究结果对于分析植物地上部分的拓扑结构对植物光合作用的影响具有一定的参考价值。

【Objective】Taylor’s power law(TPL) is an important biological statistical law that describes the power-law relationship between the mean and variance of a particular biological measure. The leaves of tulip trees exhibit a certain complexity but are bilaterally symmetric. The aim of this study was to examine whether TPL could apply to leaf bilateral symmetry measures.【Method】The leaves of two extant species of tulip trees and their hybrid(Liriodendron chinense, L. tulipifera, and L. chinense ×L. tulipifera) were picked from healthy plants. We will refer to the two species of tulip trees and their hybrid as three species of tulip trees for simplicity. For each species,≥ 200 leaves were used. For a leaf, 1 000 equidistant strips that are perpendicular to the median axis(i.e., the straight line passing through the apex and base of the leaf) were generated from the apex to base of the leaf, assuming that leaf surface is on a plane. Then, 1 000 areal differences between the intersection(of the left side of the leaf and strips) and that(of the right side of the leaf and strips) were obtained. We calculated the mean and variance of the absolute values of the above 1 000 areal differences, resulting in at least 200 pairs of the data of variance vs. mean(corresponding to 200 leaves) for each species. We used reduced major axis to carry out a linear fit to the log-transformed data of variance vs. mean for each species and also for the pooled data to estimate the slopes of the straight lines(i.e., the exponents of TPL). And then we used the bootstrap percentile method to test whether there was a significant difference in the estimated exponents of TPL among different species.【Result】We found that bilateral symmetry measures of the three species of tulip trees all followed TPL, and there were no significant differences in the estimated exponents of TPL among the three species. The estimated exponent of TPL for the pooled data was equal to 1.777.【Conclusion】This study shows that leaf area, which has a scaling relationship with leaf weight, can be used for depicting TPL. The goodness of fit for TPL is improved if the scaling relationship of leaf weight vs. area is strong. In addition, there was a large variation in leaf shape across different plant groups. The log-transformed data of variance vs. mean that measured the extent of leaf bilateral symmetry could be well described by a linear equation. Variation in leaf bilateral symmetry is associated with the influence of above-ground plant architecture on light interception and utilization;thus, results of this study can improve our understanding of the effect of above-ground plant topology on the photosynthetic potentials of leaves.