`Q-niche': topology-preserving niche hypervolumes built using a quantum mechanics modelling analogue.

Abstract

Hutchinson's n-dimensional niche hypervolume underlies many ecological analyses, yet estimating hypervolumes from finite occurrence data remains challenging, particularly when niches contain non-convex structure such as separated regions or internal holes. Here, we introduce Q-niche, a quantum-mechanics-inspired algorithm for ecological hypervolume estimation. Using an inverse Schrodinger formulation, Q-niche transforms an occurrence-derived Gaussian field into a potential surface whose low-potential regions define a hypervolume represented by a stochastic point cloud. We evaluated Q-niche against Gaussian kernel density estimation and one-class support vector machine hypervolume estimators using synthetic niches, virtual species and empirical Acacia occurrence data. Across controlled synthetic benchmarks, Q-niche preserved imposed topological features more consistently than either alternative and showed closer overall topological agreement with occurrence clouds. This preservation remained robust across the tested parameter settings. Virtual-species analyses showed that stronger preservation of environmental topology did not necessarily produce greater overlap with the known geographical distribution, showing that topology and geographical range are not necessarily coupled. The empirical Acacia dataset revealed that the inferred size and topology of a niche hypervolume is estimator-dependent, favouring the use of Q-niche when hypervolume topology is the focus of research due to its topology preservation performance. Overall, Q-niche provides a practical tool for reconstructing complex niche hypervolumes and investigating how their geometry and topology relate to potential geographical distributions.