Leaf shape is a key plant trait that varies enormously. The diversity of leaf shape, and the range of applications for data on this trait, requires frequent methodological developments so that researchers have an up-to-date toolkit with which to quantify leaf shape. We generated a dataset of 468 leaves produced by Ginkgo biloba, and 24 fossil leaves produced by evolutionary relatives of extant Ginkgo. We quantified the shape of each leaf by developing a geometric method based on elastic curves and a topological method based on persistent homology. Our geometric method indicates that shape variation in our modern sample is dominated by leaf size, furrow depth, and the angle of the two lobes at the base of the leaf that is also related to leaf width. Our topological method indicates that shape variation in our modern sample is dominated by leaf size and furrow depth. We have applied both methods to modern and fossil material: the methods are complementary, identifying similar primary patterns of variation, but also revealing some different aspects of morphological variation. Our topological approach distinguishes long-shoot leaves from short-shoot leaves and both methods indicate that leaf shape influences or is at least related to leaf area.

中文翻译：

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银杏叶形状变异的几何和拓扑方法

叶形是变化巨大的关键植物性状。叶子形状的多样性以及该特征数据的应用范围需要频繁的方法学开发，以便研究人员拥有最新的工具包来量化叶子形状。我们生成了由银杏产生的 468 片叶子和现存银杏的进化亲属产生的 24 片化石叶子的数据集。我们通过开发基于弹性曲线的几何方法和基于持久同源性的拓扑方法来量化每片叶子的形状。我们的几何方法表明，我们现代样本中的形状变化主要受叶片大小、犁沟深度以及叶片基部两个裂片的角度（也与叶片宽度有关）的影响。我们的拓扑方法表明，我们现代样本中的形状变化主要受叶片大小和犁沟深度的影响。我们已经将这两种方法应用于现代和化石材料：这些方法是互补的，识别出相似的主要变异模式，但也揭示了形态变异的一些不同方面。我们的拓扑方法将长枝叶与短枝叶区分开来，两种方法都表明叶形状影响或至少与叶面积有关。