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.