CHE: A hypervolume approach to estimate the ecological niche that combines Convex Hulls and Elliptical envelopes

Methods that estimate the niche of a species by calculating a convex hull or an elliptical envelope have become popular due to their simplicity and interpretation, given Hutchinson's conception of the niche as an $d$-dimensional hypervolume. It is well known that convex hulls are sensitive to outliers and do not have the ability to differentiate between regions of low and high concentration of presences, while the elliptical envelopes may contain large regions of niche space that are not relevant for the species. Thus, when the goal is to estimate the niche of the species, both methods may overestimate the niche. We present a methodology that combines both the convex hull and the elliptical envelope methods producing an $n$-dimensional hypervolume that better fits the observed density of species presences, making it a better candidate to model the potential niche. Our method, called the CHE approach, allows defining regions of iso-suitability as a function of the significance levels inherited from the method (Mahalanobis distance model, minimum covariance determinant, or minimum volume ellipsoid) used to fit an initial elliptical envelope from which we then discard regions not relevant for the species by calculating a convex hull. We applied our approach to a case study of twenty-five species of bats present in the Iberian Peninsula, fitting a hypervolume for each species and comparing them to both the convex hulls and elliptical envelopes, as well as with other state-of-the-art methods obtained with the same data and different values of $d$. We show that as the number of variables used to define the niche space increases, both the convex hull and elliptical envelope models produce overly large hypervolumes, while the size of the hypervolume fitted with the CHE approach remains stable. As a consequence, similarity measures that account for the niche overlap among different species may be inflated when using convex hulls or elliptical envelopes to model the niche; something that does not occur under the CHE approach.