Mathematical contributions to link biota with environment

Hutchinson's pioneering work on the niche concept, dating from 1957, inspired the development of many ecological models. The first proposals, BIOCLIM and HABITAT, were simple geometric approximations to the shape of the niche. Despite their simplicity, they combine two features that make them adequate for the purpose of exploring the niche: they fit a predefined shape to the empirical data; and produce binary or ordinal predictions rather than continuous predictions. Thus, both explicitly delineate a precise boundary for the niche. However, the two methods present some limitations: BIOCLIM assumes that the variables are independent in their action on the species; and HABITAT, although not having that limitation, only delineates the boundaries of the niches without distinguishing levels of suitability for the species. We propose, discuss and illustrate: (1) the use of depth functions to identify regions with distinct suitability inside the niche; and (2) a general framework to assess overlap of the niches of two species, which can be applied to predictions from models that decompose the niche into a finite number of measurable regions.