kerneloverlap {adehabitatHR}

Spatial Interaction between Animals Monitored Using Radio-Tracking

Description

These functions implements all the indices of kernel home-range overlap reviewed by Fieberg and Kochanny (2005). kerneloverlap computes these indices from a set of relocations, whereas kerneloverlaphr computes these indices from an object containing the utilization distributions of the animals.

Usage

kerneloverlap(xy, method = c("HR", "PHR", "VI", "BA", "UDOI",
              "HD"), percent = 95, conditional = FALSE, ...)

kerneloverlaphr(x, method = c("HR", "PHR", "VI", "BA", "UDOI", "HD"),
                percent = 95, conditional = FALSE, ...)

Arguments

xy

an object of class SpatialPointsDataFrame containing only one column (which is a factor indicating the identity associated to the relocations))

x

an object of class estUDm containing several home-ranges for which the overlap is to be calculated

method

the desired method for the estimation of overlap (see details)

percent

the percentage level of the home range estimation

conditional

logical. If TRUE, the function sets to 0 the pixels of the grid over which the UD is estimated, outside the home range of the animal estimated at a level of probability equal to percent. Note that this argument has no effect when meth="HR".

...

additional arguments to be passed to the function kernelUD for the kernel estimation of the utilization distribution.

Details

Fieberg and Kochanny (2005) made an extensive review of the indices of overlap between utilization distributions (UD) of two animals. The function kerneloverlap implements these indices. The argument method allows to choose an index.

The choice method="HR" computes the proportion of the home range of one animal covered by the home range of another one, i.e.:

HR_{i,j} = A_{i,j} / A_i

, where A_{i,j} is the area of the intersection between the two home ranges and A_i is the area of the home range of the animal i.

The choice method="PHR" computes the volume under the UD of the animal j that is inside the home range of the animal i (i.e., the probability to find the animal j in the home range of i). That is:

PHR_{i,j} = \int \int_{A_i} UD_j(x,y) dxdy

where UD_j(x,y) is the value of the utilization distribution of the animal j at the point x,y.

The choice method="VI" computes the volume of the intersection between the two UD, i.e.:

VI = \int_x \int_y min(UD_i(x,y),UD_j(x,y)) dxdy

Other choices rely on the computation of the joint distribution of the two animals under the hypothesis of independence UD[i](x,y) * UD[j](x,y).

The choice method="BA" computes the Bhattacharyya's affinity

BA = \int_x \int_y \sqrt{UD_i(x,y)} \times \sqrt{UD_j(x,y)}

The choice method="UDOI" computes a measure similar to the Hurlbert index of niche overlap:

UDOI = A_{i,j} \int_x \int_y UD_i(x,y) \times UD_j(x,y)

The choice method="HD" computes the Hellinger's distance:

HD = \int_x \int_y ((\sqrt UD_i(x,y) - \sqrt UD_j(x,y))^2 dxdy)^{1/2}

Value

A matrix giving the value of indices of overlap for all pairs of animals.

Author(s)

Clement Calenge [e-mail], based on a work of John Fieberg

References

Fieberg, J. and Kochanny, C.O. (2005) Quantifying home-range overlap: the importance of the utilization distribution. Journal of Wildlife Management, 69, 1346–1359.

See Also

kernelUD for additional information on kernel estimation of home ranges

Examples

## Not run: 
data(puechabonsp)

kerneloverlap(puechabonsp$relocs[,1],
              grid=200, meth="VI", conditional=TRUE)

## Identical to
kud <- kernelUD(puechabonsp$relocs[,1],
                grid=200, same4all=TRUE)
kerneloverlaphr(kud, meth="VI", conditional=TRUE)

## other indices
kerneloverlap(puechabonsp$relocs[,1],
              grid=200, meth="HR")

kerneloverlap(puechabonsp$relocs[,1],
              grid=200, meth="PHR")

kerneloverlap(puechabonsp$relocs[,1],
              grid=200, meth="BA")

kerneloverlap(puechabonsp$relocs[,1],
              grid=200, meth="UDOI")

kerneloverlap(puechabonsp$relocs[,1],
              grid=200, meth="HD")

## End(Not run)