Yan Chunxiu, Shi Peijian, Yu Kexin, Guo Xuchen, Lian Meng, Miao Qinyue, Wang Lin, Yao Weihao, Zheng Yiwen, Zhu Fuyuan, Niklas Karl J
National Key Laboratory of Smart Farm Technologies and Systems, College of Plant Protection, Northeast Agricultural University, Harbin 150030, China.
Southern Modern Forestry Collaborative Innovation Center, College of Ecology and Environment, Nanjing Forestry University, Nanjing 210037, China.
Ann Bot. 2024 Dec 31;134(7):1151-1164. doi: 10.1093/aob/mcae165.
The Montgomery-Koyama-Smith (MKS) equation predicts that total leaf area per shoot is proportional to the product of the sum of individual leaf widths and maximum individual leaf length, which has been validated for some herbaceous and woody plants. The equation is also predicted to be valid in describing the relationship between the total stomatal area per micrograph (AT) and the product of the sum of individual stomatal widths (denoted as LKS) and maximum individual stomatal length (denoted by WKS) in any particular micrograph.
To test the validity of the MKS equation, 69 931 stomata (from 720 stomatal micrographs from 12 Magnoliaceae species) were examined. The area of each stoma was calculated using empirical measurements of stomatal length and width multiplied by a constant. Six equations describing the relationships among AT, LKS and WKS were compared. The root mean square (RMSE) and the Akaike information criterion (AIC) were used to measure the goodness of fit and the trade-off between the goodness of fit and the structural complexity of each model, respectively.
Analyses supported the validity of the MKS equation and the power-law equation AT ∝ (LKSWKS)α, where α is a scaling exponent. The estimated values of α at the species level and for the pooled data were all statistically smaller than unity, which did not support the hypothesis that AT ∝ LKSWKS. The power-law equation had smaller RMSE and AIC values than the MKS equation for the data from the 12 individual species and the pooled data.
These results indicate that AT tends to scale allometrically with LKSWKS, and that increases in AT do not keep pace with increases in LKSWKS. In addition, using LKSWKS is better than using only one of the two variables to calculate AT.
蒙哥马利 - 小山 - 史密斯（MKS）方程预测，每个枝条的总叶面积与单叶宽度之和与最大单叶长度的乘积成正比，这已在一些草本植物和木本植物中得到验证。该方程还被预测可有效描述任何特定显微照片中每张显微照片的总气孔面积（AT）与单个气孔宽度之和（记为LKS）和最大单个气孔长度（记为WKS）的乘积之间的关系。
为检验MKS方程的有效性，研究人员检查了69931个气孔（来自12种木兰科植物的720张气孔显微照片）。每个气孔的面积通过气孔长度和宽度的实测值乘以一个常数来计算。比较了六个描述AT、LKS和WKS之间关系的方程。分别使用均方根误差（RMSE）和赤池信息准则（AIC）来衡量拟合优度以及每个模型在拟合优度与结构复杂性之间的权衡。
分析支持了MKS方程和幂律方程AT ∝ (LKSWKS)α的有效性，其中α是一个标度指数。在物种水平和汇总数据中，α的估计值在统计学上均小于1，这并不支持AT ∝ LKSWKS的假设。对于来自12个单独物种的数据和汇总数据，幂律方程的RMSE和AIC值均小于MKS方程。
这些结果表明，AT倾向于与LKSWKS呈异速生长关系，并且AT的增加与LKSWKS的增加不同步。此外，使用LKSWKS比仅使用两个变量之一来计算AT更好。
