Habitat Suitability Mapping with Mahalanobis Distances.

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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

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mahasuhab(x, pts, type = c("distance", "probability"))

Arguments

x

a raster map of class SpatialPixelsDataFrame

pts

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

type

a character string. Whether the raw "distance" should be returned, or rather the "probability" (see details).

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

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## 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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