ABSTRACT Studying the avian egg, its shape, and other aspects of its morphology, has recently undergone a renaissance. Yet most studies rely solely on 2, albeit multicomponent, metrics for the quantification of egg shape: elongation and asymmetry. The difficulty of quantifying an additional trait, the curvature, of an eggshell has yielded many attempts, including several with complex equations or spatial modeling techniques based on digitized images. Yet most of these approaches have lacked an independent single-variable metric, hampering comparative studies especially. We propose a metric for one common quality of egg shape, conicality, which is notably variable across different species' calcareous shells, including shorebirds and non-avian theropods. This metric utilizes multiple measurements of the slope along an egg's profile to produce a distribution of angular measurements, which can be analyzed with a kurtosis value. We tested this metric with sets of computer-generated and 3-dimensional-printed egg forms, where elongation, the percentage of conicality, and the relative curvature of the shell profile were systematically manipulated. For applicability to natural eggs and their diversity across taxa, the kurtosis value was used to quantify the gradient of conicality across a focal avian family, Alcidae, where the extreme ranges of kurtosis values successfully identified eggs qualitatively described as most conical in previous studies. Given the significance of egg morphology and profile curvature to eggshells' structural integrity, surface area-to-volume ratio, mobility/stability, nesting behavior, embryonic development, and individual recognition, our proposed measure of conicality could prove a useful variable to the study of avian and non-avian egg-producing species. LAY SUMMARY Avian eggs are shaped in diverse ways and the form of bird's eggshell can be influenced by its nesting requirements, parenting strategies and flight abilities. Most previous studies used only 2 metrics to study avian egg shape: (1) the width-to-length ratio and (2) the position along its length where the widest part of the egg is located (asymmetry). We propose a novel metric (conicality) for quantifying how straight/curved the profile of an eggshell is between its outermost dimensions by assessing how much either half of the profile resembles a cone. The novel conicality measure was also applied to a group of closely related birds with eggs that ranged from more elliptical to more conical. This new conicality metric successfully predicted the relative level of curvature known from casual observations of each species, which supports the method's validity.

中文翻译：

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禽蛋的形状：评估一种用于量化蛋壳圆锥度的新指标

摘要 对禽蛋、其形状及其形态的其他方面的研究最近经历了复兴。然而，大多数研究仅依赖于 2 个（尽管是多组分）量化蛋形的指标：伸长率和不对称性。量化蛋壳的附加特征曲率的困难已经产生了许多尝试，包括一些具有复杂方程或基于数字化图像的空间建模技术的尝试。然而，这些方法中的大多数都缺乏独立的单变量指标，尤其阻碍了比较研究。我们为一种常见的卵形状质量提出了一个度量标准，即圆锥度，它在不同物种的钙质外壳中显着变化，包括水鸟和非鸟类兽脚亚目动物。该指标利用对鸡蛋斜率的多次测量' s 轮廓以生成角度测量值的分布，可以使用峰度值对其进行分析。我们用一组计算机生成的和 3 维打印的鸡蛋形式测试了这个指标，其中系统地操纵了伸长率、圆锥度百分比和蛋壳轮廓的相对曲率。为了适用于天然鸡蛋及其在整个分类群中的多样性，峰度值用于量化焦点鸟类家族 Alcidae 的圆锥度梯度，其中峰度值的极端范围成功地确定了在以前的研究中定性描述为最圆锥形的鸡蛋。鉴于鸡蛋形态和轮廓曲率对蛋壳结构完整性、表面积与体积比、流动性/稳定性、筑巢行为、胚胎发育和个体识别的重要性，我们提出的圆锥度测量可以证明是研究鸟类和非鸟类产卵物种的有用变量。产蛋总结 鸟蛋的形状多种多样，鸟蛋壳的形状会受到其筑巢要求、养育策略和飞行能力的影响。大多数先前的研究仅使用 2 个指标来研究禽蛋的形状：(1) 宽长比和 (2) 沿其长度的鸡蛋最宽部分所在的位置（不对称）。我们提出了一种新的度量标准（圆锥度），通过评估轮廓的任何一半与圆锥的相似程度来量化蛋壳轮廓在其最外层尺寸之间的直线/弯曲程度。新的圆锥度测量方法还应用于一组密切相关的鸟类，它们的蛋从椭圆形到圆锥形不等。