Revisiting niche fundamentals with Tukey depth

The first attempts to describe species ecological niches were simple geometric procedures that depict the niche boundaries directly from environmental data. The convex hull was one of such procedures, popular for its simplicity, clear ecological rational and precise definition of the niche. However, it lacked the ability to differentiate areas of the niche with different probabilities of occurrence according to environmental suitability. We incorporate the Tukey depth, a mathematical tool to measure the centrality of a point within a cloud of points on a multidimensional space, in the convex hull approach to (i) propose a new procedure (CH-Tukey) to estimate species’ environmental suitability, and (ii) estimate niche overlap coherently. In addition to a clear ecological rational and simplicity the CH-Tukey procedure has a number of attractive features: use of presence-only data; independence from background data; invariance to scale; robustness to outliers; and the decomposition of the niche into a finite number of iso-suitability levels, permitting the computation of consistent overlap indices. We illustrate the use of CH-Tukey, using occurrence data of the main Quercus species and subspecies from Western Mediterranean Europe, comparing its outputs with BIOCLIM and MaxEnt. Results showed distinct niche geometries among the different approaches. BIOCLIM produced rectilinear niches reflecting the assumption that ecological variables are independent in their action on the species. CH-Tukey, relaxing this assumption, adjusts niche outer boundary and the inner suitability levels to the known occurrences. MaxEnt produced unbounded niche geometries, showing abrupt shifts in the species response to the environmental variables. The niche predictions obtained with geometric approaches, BIOCLIM and CH-Tukey, are simpler but better aligned with Hutchinson's niche concept than those obtained with MaxEnt, this latter showing ecologically implausible relationships with the environmental variables. CH-Tukey and the related overlap measures provide an adequate tool to explore niche properties and species–environment relationships.