1. Organisms often display multiple colour patches and for many analyses, it may be useful to take into account all these patches at the same time, and reconstruct the colour volume of the organisms. Stoddard and Prum (2008, The American Naturalist, 171, 755) proposed to use convex hulls to reconstruct the colour volume of a species. Convex hull volume has since then often been used as an index of colourfulness, and the intersection of multiple convex hulls is used to study the colour similarity between two objects.
2. In this article, I outline the limitations of convex hulls in this context. In particular, multiple studies have reported that the convex hull overestimates the actual colour volume. I argued for the use of a more general tool, developed as a more flexible extension of the convex hulls: α‐shapes. Depending on the parameter α, α‐shapes can reconstruct concave (i.e. non‐convex) volumes with voids or pockets that are better suited for the estimation of colour volumes.
3. To determine the optimal value of the parameter α, I point out two expected properties of multidimensional trait spaces, which translate into two conditions providing a lower and upper bound on α, and I propose technical tools to identify the α value satisfying these two conditions. Using colour data from the whole bird community from the biological station of the Nouragues, French Guiana, I show that using α‐shapes rather than convex hulls results in possibly major differences in the estimation of the colour volume.
4. I discuss possible future developments of this new framework in both colour science and other areas of ecology dealing with multidimensional trait spaces, such as community ecology where α‐shape volumes could serve as a replacement for the functional richness FRic, or morphometrics.

中文翻译：

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使用α形状将颜色体积估计为凹形超体积

1. 有机体通常会显示多个颜色斑块，并且对于许多分析而言，同时考虑所有这些斑块并重建生物体的颜色体积可能很有用。斯托达德和普鲁姆（2008，美国博物，171，755）提出了使用凸包来重建一个物种的颜色体积。从那时起，凸包的体积经常被用作色彩的指标，而多个凸包的交集被用来研究两个物体之间的颜色相似性。
2. 在本文中，我概述了在这种情况下凸包的局限性。特别是，多项研究报告说，凸包高估了实际的色彩量。我主张使用一种更通用的工具，该工具是作为凸包的更灵活的扩展而开发的：α形状。根据参数α，α形状可以重建具有更适合颜色体积估计的空隙或凹坑的凹（即非凸）体积。
3. 为了确定参数α的最佳值，我指出了多维特征空间的两个预期特性，它们转化为提供α上下限的两个条件，并且我提出了确定满足这两个条件的α值的技术工具。我使用来自法属圭亚那努尔阿盖斯生物站的整个鸟类群落的颜色数据，表明使用α形而不是凸包会导致颜色量估计上的重大差异。
4. 我讨论了这个新框架在色彩科学和其他涉及多维特征空间的生态学领域的未来发展，例如社区生态学，其中α形体积可以替代功能丰富性FRic或形态计量学。