Institute of Mathematics, University of Aberdeen, King's College, Aberdeen, AB24 3FX, Scotland.
School of Biological Sciences, University of Aberdeen, Zoology Building, Tillydrone Ave, Aberdeen, AB24 2TZ, Scotland.
J Math Biol. 2022 Jun 9;84(7):58. doi: 10.1007/s00285-022-01763-x.
Living organisms are limited in the range of values of ecological factors they can explore. This defines where animals exist (or could exist) and forms an ecological fingerprint that explains species' distribution at global scales. Species' ecological fingerprints can be represented as a n-dimensional hypervolume - known as Hutchinson's niche hypervolume. This concept has enabled significant progress in our understanding of species' ecological needs and distributions across environmental gradients. Nevertheless, the properties of Hutchinson's n-dimensional hypervolumes can be challenging to calculate and several methods have been proposed to extract meaningful measurements of hypervolumes' properties. One key property of hypervolumes are holes, which provide important information about the ecological occupancy of species. However, to date, current methods rely on volume estimates and set operations to identify holes in hypervolumes. Yet, this approach can be problematic because in high-dimensions, the volume of region enclosing a hole tends to zero. We propose the use of persistence homology (PH) to identify holes in hypervolumes and in ecological datasets more generally. PH allows for the estimates of topological properties in n-dimensional niche hypervolumes independent of the volume estimates of the hypervolume. We demonstrate the application of PH to canonical datasets and to the identification of holes in the hypervolumes of five vertebrate species with diverse niches, highlighting the potential benefits of this approach to gain further insights into animal ecology. Overall, our approach enables the study of a yet unexplored property of Hutchinson's hypervolumes, and thus, have important implications to our understanding of animal ecology.
生物体在其能够探索的生态因子值范围内是有限的。这决定了动物的存在位置（或可能存在的位置），并形成了一种生态指纹，解释了物种在全球范围内的分布。物种的生态指纹可以表示为 n 维超体积——即 Hutchinson 的生态位超体积。这一概念极大地促进了我们对物种在环境梯度上的生态需求和分布的理解。然而，Hutchinson 的 n 维超体积的性质可能难以计算，已经提出了几种方法来提取超体积性质的有意义的测量值。超体积的一个关键性质是孔，它提供了关于物种生态占据的重要信息。然而，迄今为止，当前的方法依赖于体积估计和集合运算来识别超体积中的孔。然而，这种方法可能存在问题，因为在高维空间中，包围孔的区域的体积趋于零。我们建议使用持久同调（PH）来识别超体积和更一般的生态数据集中的孔。PH 允许在 n 维生态位超体积中独立于超体积的体积估计来估计拓扑性质。我们展示了 PH 在典型数据集和五个具有不同生态位的脊椎动物物种的超体积中孔的识别中的应用，突出了这种方法在动物生态学中获得进一步见解的潜力。总的来说，我们的方法使研究 Hutchinson 的超体积的一个尚未探索的性质成为可能，因此对我们理解动物生态学具有重要意义。
