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.
1 2 3 4 5 6  kerneloverlap(xy, id = NULL,
method = c("HR", "PHR", "VI", "BA", "UDOI", "HD"),
lev = 95, conditional = FALSE, ...)
kerneloverlaphr(x, method = c("HR", "PHR", "VI", "BA", "UDOI", "HD"),
lev=95, conditional=FALSE)

xy 
a data frame with two columns (x and y coordinates of the animal relocations) 
id 
a factor giving the animals identity associated to

x 
an object of class 
method 
the desired method for the estimation of overlap (see details) 
lev 
the level of the home range estimation 
conditional 
logical. If 
... 
additional arguments to be passed to the function

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] = integral_over_x integral_over_y 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 = integral_over_x integral_over_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 = integral_over_x integral_over_y sqrt(UD[i](x,y)) * sqrt(UD[j](x,y))
The choice method="UDOI"
computes a measure similar to the
Hurlbert index of niche overlap:
UDOI = A[i,j] integral_over_x integral_over_y UD[i](x,y) * UD[j](x,y)
The choice method="HD"
computes the Hellinger's distance:
HD = integral_over_x integral_over_y ((sqrt(UD[i](x,y)  sqrt(UD[j](x,y)))^2 dxdy)^(1/2))
A matrix giving the value of indices of overlap for all pairs of animals.
Clement Calenge clement.calenge@oncfs.gouv.fr, based on a work of John Fieberg
Fieberg, J. and Kochanny, C.O. (2005) Quantifying homerange overlap: the importance of the utilization distribution. Journal of Wildlife Management, 69, 1346–1359.
kernelUD
for additional information on kernel
estimation of home ranges
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31  ## Not run:
data(puechabon)
kerneloverlap(puechabon$locs[,c("X","Y")], puechabon$locs$Name,
grid=200, meth="VI", conditional=TRUE)
## Identical to
kud < kernelUD(puechabon$locs[,c("X","Y")], puechabon$locs$Name,
grid=200, same4all=TRUE)
kerneloverlaphr(kud, meth="VI", conditional=TRUE)
## Other indices:
kerneloverlap(puechabon$locs[,c("X","Y")], puechabon$locs$Name,
grid=200, meth="HR")
kerneloverlap(puechabon$locs[,c("X","Y")], puechabon$locs$Name,
grid=200, meth="PHR")
kerneloverlap(puechabon$locs[,c("X","Y")], puechabon$locs$Name,
grid=200, meth="BA")
kerneloverlap(puechabon$locs[,c("X","Y")], puechabon$locs$Name,
grid=200, meth="UDOI")
kerneloverlap(puechabon$locs[,c("X","Y")], puechabon$locs$Name,
grid=200, meth="HD")
## End(Not run)

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