'Holey' niche! finding holes in niche hypervolumes using persistence homology

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.