Plant-pollinator specialization: Origin and measurement of curvature

AbstractA feature of biodiversity is the abundance of curves displayed by organs and organisms. Curvature is a widespread, convergent trait that has important ecological and evolutionary implications. In pollination ecology, the curvature of flowers and pollinator mouthparts (e.g. hummingbird bills) along the dorsiventral plane has been associated with specialization, competition, and species co-existence. Six methods have historically been used to measure curvature in pollination systems; we provide a solution to this inconsistency by defining curvature using well-established concepts from differential geometry. Intuitively, curvature is the degree to which a line is not straight, but more formally, it is the rate at which the tangent of a curve changes direction with respect to arc length. Here, we establish a protocol wherein a line is fitted against landmarks placed on an image of a curved organ or organism, then curvature is computed at many points along the fitted line and the sum taken. The protocol is demonstrated by studying the development of nectar spur curvature in the flowering plant genus Epimedium (Berberidaceae). By clarifying the definition of curvature, our aim is to make the language of comparative morphology more precise and broadly applicable to capture other curved structures in nature., Usage notesThis dataset is primarily an RStudio project. To run the .R files, we recommend first opening the .RProj file in RStudio and installing the package `here`. This will allow you to run all of the .R scripts without changing any of the working directories.【摘要】生物多样性的一大特征是各类器官与生物体所展现出的丰富曲线形态。曲率（curvature）是一种广泛存在且趋同演化的性状，具有重要的生态学与进化学意义。在传粉生态学领域，花朵与传粉者口器（如蜂鸟喙）沿背腹轴方向的曲率，曾被证实与物种特化、种间竞争及物种共存存在关联。过往针对传粉系统中的曲率测量，已存在六种不同方法；本研究借助微分几何（differential geometry）中的成熟概念对曲率进行明确定义，以此解决这一方法不统一的问题。直观而言，曲率即线条偏离直线的程度；而从严谨的学术定义来看，曲率是曲线的切线随弧长变化的方向变化率。本研究建立了一套标准化实验流程：先在弯曲器官或生物体的图像上标记地标点（landmarks），再基于这些地标点拟合一条直线，随后沿拟合直线在多个点位计算曲率并求取总和。本研究以小檗科（Berberidaceae）淫羊藿属（Epimedium）植物的花蜜距（nectar spur）曲率发育过程为例，对该流程进行了实例演示。本研究通过明确曲率的定义，旨在让比较形态学的学术表述更为精准，同时可广泛推广应用于自然界中其他弯曲结构的相关研究。 使用说明：本数据集本质为一个RStudio项目。若要运行其中的.R脚本文件，建议先在RStudio中打开该项目的.RProj文件，并安装`here`数据包。如此便可无需修改任何工作目录，直接运行所有.R脚本。