# Habitat Suitability Mapping with Mahalanobis Distances.

### Description

This function computes the habitat suitability map of an area for a species, given a set of locations of the species occurences (Clark et al. 1993). This function is to be used in habitat selection studies, when animals are not identified.

### Usage

1 |

### Arguments

`x` |
a raster map of class |

`pts` |
a data frame with two columns, giving the coordinates of the species locations |

`type` |
a character string. Whether the raw |

### Details

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-1 degrees of freedom,
where n equals the number of habitat characteristics. 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.

### Value

Returns a raster map of class `SpatialPixelsDataFrame`

.

### Note

The computation of the squared Mahalanobis distances inverts the
variance-covariance matrix of the niche density function (see
`?mahalanobis`

).
It is therefore important that the habitat variables considered
are not too correlated among each other. When the habitat variables
are too correlated, the variance-covariance matrix is singular and
cannot be inverted.

Note also that it is recommended to scale the variables before the computation, so that they all have the same variance, and therefore the same weight in the analysis (see examples below).

### Author(s)

Clement Calenge clement.calenge@oncfs.gouv.fr

### References

Clark, J.D., Dunn, J.E. and Smith, K.G. (1993) A multivariate model of
female black bear habitat use for a geographic information
system. *Journal of Wildlife Management*, **57**, 519–526.

### See Also

`madifa`

and `dunnfa`

for factor
analyses of the Mahalanobis distances, `domain`

for
another method of habitat suitability mapping,
`mahalanobis`

for
information on the computation of Mahalanobis distances.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
## loads the data
data(lynxjura)
ma <- lynxjura$map
lo <- lynxjura$locs[,1:2]
## We first scale the maps
slot(ma, "data") <- dudi.pca(slot(ma, "data"), scannf=FALSE)$tab
## habitat suitability mapping
hsm <- mahasuhab(ma, lo, type = "probability")
image(hsm)
title(main = "Habitat suitability map for the Lynx")
points(lo, pch = 3)
``` |

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