kerneloverlap {adehabitatHR}  R Documentation 
Spatial Interaction between Animals Monitored Using RadioTracking
Description
These functions implements all the indices of kernel homerange 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 
x 
an object of class 
method 
the desired method for the estimation of overlap (see details) 
percent 
the percentage level of the home range estimation 
conditional 
logical. If 
... 
additional arguments to be passed to the function

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 clement.calenge@ofb.gouv.fr, based on a work of John Fieberg
References
Fieberg, J. and Kochanny, C.O. (2005) Quantifying homerange 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)