The factorial decomposition of the Mahalanobis distances in habitat selection studies

The Mahalanobis distances have been introduced in habitat selection studies for the estimation of environmental suitability maps (ESMs). The pixels of raster maps of a given area correspond to points in the multidimensional space defined by the mapped environmental variables (ecological space). The Mahalanobis distances measure the distances in this space between these points and the mean of the ecological niche (i.e., the hypothesized optimum for the species) regarding the structure of the niche. The map of these distances over the area of interest is an estimated ESM. Several authors recently noted that the use of a single optimum for the niche of a species may lead to biased predictions of animal occurrence. They proposed to use instead a minimum set of basic habitat requirements, found by partitioning the Mahalanobis distances into a restricted set of biologically meaningful axes. However, the statistical approach they proposed does not take into account the environmental conditions on the area where the niche was sampled (i.e., the environmental availability), and we show that including this availability is necessary. We used their approach as a basis to develop a new exploratory tool, the Mahalanobis distance factor analysis (MADIFA), which performs an additive partitioning of the Mahalanobis distances taking into account this availability. The basic habitat requirements of a species can be derived from the axes of the MADIFA. This method can also be used to compute ESMs using only this small number of basic requirements, therefore including only the biologically relevant information. We also prove that the MADIFA is complementary to the commonly used ecological-niche factor analysis (ENFA). We used the MADIFA method to analyze the niche of the chamois Rupicapra rupicapra in a mountainous area. This method adds to the existing set of tools for the description of the niche.