Let assume that a set of locations of the species on an area is available
(gathered on transects, or during the monitoring of the population,
etc.). If we assume that the probability of detecting an individual
is independent from the habitat variables, then we can consider that
the habitat found at these sites reflects the habitat use by the animals.
The Mahalanobis distances method has become more and more popular
during the past few years to derive habitat suitability maps. The
niche of a species is defined as the probability density function of
presence of a species in the multidimensionnal space defined by the
habitat variables. If this function can be assumed to
be multivariate normal, then the mean vector of this distribution
corresponds to the optimum for the species.
The function mahasuhab first computes this mean vector as well
as the variance-covariance matrix of the niche density function, based
on the value of habitat variables in the sample of locations.
Then, the *squared* Mahalanobis distance from this optimum is computed
for each pixel of the map. Thus, the smaller this squared
distance is for a given pixel, and the better is the habitat in this
pixel.
Assuming multivariate normality, squared Mahalanobis distances are
approximately distributed as Chi-square with n degrees of freedom,
where n equals the number of habitat characteristics (see the section
note below on this question). If the
argument type = "probability", maps of these p-values are
returned by the function. As such these are the probabilities of a
larger squared Mahalanobis distance than that observed when x is
sampled from the niche.