Description Usage Arguments Details Value Author(s) References See Also Examples
kernelUD
is used to estimate the utilization distribution (UD)
of animals monitored by radiotracking, with the classical kernel method.
getvolumeUD
and kernel.area
provide utilities
for homerange size estimation.
getverticeshr
stores the
home range contour as objects of class area
in a list of class
kver
, with one component per animal.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  kernelUD(xy, id = NULL, h = "href", grid = 40, same4all = FALSE,
hlim = c(0.1, 1.5), kern = c("bivnorm", "epa"), extent = 0.5)
## S3 method for class 'khr'
print(x, ...)
## S3 method for class 'khr'
image(x, axes = FALSE, mar = c(0,0,2,0),
addcontour = TRUE, addpoints = TRUE, ...)
plotLSCV(x)
getvolumeUD(x)
kernel.area(xy, id, h = "href", grid = 40,
same4all = FALSE, hlim = c(0.1,1.5), kern = "bivnorm",
levels = seq(20,95, by = 5),
unin = c("m", "km"),
unout = c("ha", "km2", "m2"), extent = 0.5)
getverticeshr(x, lev = 95)

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

h 
a character string or a number. If 
grid 
a number giving the size of the grid on
which the UD should be estimated. Alternatively, this parameter may
be an object of class 
same4all 
logical. If 
hlim 
a numeric vector of length two. If 
kern 
a character string. If 
extent 
a value indicating the extent of the grid used for the
estimation (the extent of the grid on the abscissa is equal to

x 
an object of class 
axes 
logical. Whether the axes are to be plotted 
mar 
the margin parameter (see 
addcontour 
logical. If 
addpoints 
logical. If 
levels 
a vector of percentage levels for homerange size estimation 
unin 
the units of the relocations coordinates. Either 
unout 
the units of the output areas. Either 
lev 
the percentage level for home range contour estimation. 
... 
additionnal parameters to be passed to the generic
functions 
The Utilization Distribution (UD) is the bivariate function giving the
probability density that an animal is found at a point according to
its geographical coordinates. Using this model, one can define
the home range as the minimum area in which an animal has some
specified probability of being located. The
functions used here correspond to the approach described in Worton
(1995).
The kernel method has been recommended by many authors for the estimation of the utilization distribution (e.g. Worton, 1989, 1995). The default method for the estimation of the smoothing parameter is the ad hoc method, i.e. for a bivariate normal kernel
h = Sigma*n^(1/6)
where
Sigma = 0.5*(sd(x)+sd(y))
which supposes that the UD is
bivariate normal. If an Epanechnikov kernel is used, this value is
multiplied by 1.77 (Silverman, 1986, p. 86).
Alternatively, the smoothing parameter h may be
computed by Least Square Cross Validation (LSCV). The estimated value
then minimizes the Mean Integrated Square Error (MISE), i.e. the
difference in volume between the true UD and the estimated UD. Note
that the crossvalidation criterion cannot be minimized in some
cases. According to Seaman and Powell (1998) "This is a difficult
problem that has not been worked out by statistical
theoreticians, so no definitive response is available at this
time" (see Seaman and Powell, 1998 for further details and tricky
solutions). plotLSCV
allows to have a diagnostic of the
success of minimization of the cross validation criterion (i.e. to
know whether the minimum of the CV criterion occurs within the scanned
range). Finally, the UD is then estimated over a grid.
The default kernel is the bivariate normal kernel, but the
Epanechnikov kernel, which requires less computer time is also
available for the estimation of the UD.
The function getvolumeUD
modifies the UD component of the
object passed as argument, so
that the contour of the UD displayed by the functions contour
and image.khr
corresponds to the different percentage levels of
homerange estimation (see examples). In addition, this function is
used in the function kernel.area
, to compute the homerange
size. Note, that the function plot.hrsize
(see the help page
of this function) can be used to display the homerange size estimated
at various levels.
The class khr
is a class grouping three subclasses,
khrud
, kbbhrud
and khrudvol
:
kernelUD
returns a list of the class khrud
. This list
has one component per animal (named as the levels of argument
id
). Each component is itself a list, with the following
subcomponents:
UD 
an object of class 
h 
if

locs 
The relocations used in the estimation procedure. 
hmeth 
The argument 
getvolumeUD
returns a list of class khrvol
,
with the same components as lists of class khrud
.
kernel.area
returns a data frame of subclass hrsize
,
with one column per animal and one row per level of
estimation of the home range.
getverticeshr
returns an object of class kver
.
Clement Calenge [email protected]
Silverman, B.W. (1986) Density estimation for statistics and data analysis. London: Chapman \& Hall.
Worton, B.J. (1989) Kernel methods for estimating the utilization dirstibution in homerange studies. Ecology, 70, 164–168.
Worton, B.J. (1995) Using Monte Carlo simulation to evaluate kernelbased home range estimators. Journal of Wildlife Management, 59,794–800.
Seaman, D.E. and Powell, R.A. (1998) Kernel home range estimation program (kernelhr). Documentation of the program.
asc
for additionnal informations on
objects of class asc
, mcp
for estimation of home
ranges using the minimum convex polygon, and for help on the function
plot.hrsize
. kver
for information on objects of
class kver
, kernelbb
for an alternative approach
of the kernel estimation for trajectory data.
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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101  data(puechabon)
loc < puechabon$locs[, c("X", "Y")]
id < puechabon$locs[, "Name"]
## Estimation of UD for the four animals
(ud < kernelUD(loc, id))
image(ud) ## Note that the contours
## corresponds to values of probability density
udvol < getvolumeUD(ud)
image(udvol)
## Here, the contour corresponds to the
## home ranges estimated at different probability
## levels (i.e. the contour 90 corresponds to the 90 percent
## kernel homerange)
## udvol describes, for each cell of the grid,
## the smaller homerange to which it belongs
## Calculation of the 95 percent home range
ver < getverticeshr(ud, 95)
elev < getkasc(puechabon$kasc, "Elevation") # Map of the area
image(elev)
plot(ver, add=TRUE)
legend(696500, 3166000, legend = names(ver), fill = rainbow(4))
## Example of estimation using LSCV
udbis < kernelUD(loc, id, h = "LSCV")
image(udbis)
## Compare the estimation with ad hoc and LSCV method
## for the smoothing parameter
(cuicui1 < kernel.area(loc, id)) ## ad hoc
plot(cuicui1)
(cuicui2 < kernel.area(loc, id, h = "LSCV")) ## LSCV
plot(cuicui2)
## Diagnostic of the crossvalidation
plotLSCV(udbis)
## Use of the same4all argument: the same grid
## is used for all animals
udbis < kernelUD(loc, id, same4all = TRUE)
image(udbis)
## Estimation of the UD on a map
## (e.g. for subsequent analyses on habitat selection)
elev < getkasc(puechabon$kasc, "Elevation")
opar < par(mfrow = c(2, 2), mar = c(0, 0, 2, 0))
cont < getcontour(elev)
for (i in 1:length(udbis)) {
image(elev, main = names(udbis)[i], axes = FALSE)
points(udbis[[i]]$locs, pch = 21, bg = "white", col = "black")
}
## Measures the UD in each pixel of the map
udbis < kernelUD(loc, id, grid = elev)
opar < par(mfrow = c(2, 2), mar = c(0, 0, 2, 0))
for (i in 1:length(udbis)) {
image(udbis[[i]]$UD, main = names(udbis)[i], axes = FALSE)
box()
polygon(cont[, 2:3])
}
par(opar)
## Estimation of the UD with a list of objects of class "asc" passed as
## argument grid (useful for large datasets)
## For example, consider the following limits:
lim < rbind(c(697901,701061,3160198,3162604),
c(698936,701089,3159969,3162518),
c(698461,701928,3157362,3160427),
c(698265,701369,3157219,3162661))
gro < lapply(1:4, function(i) {
subsetmap(elev, xlim = lim[i,1:2], ylim=lim[i,3:4])
})
names(gro) < levels(id)
## show the data:
opar < par(mfrow=c(2,2), mar=c(0.1,0.1,2,0.1))
lapply(1:4, function(i) {
image(gro[[i]], main=names(gro)[i], axes=FALSE)
points(loc[id==names(gro)[i],])
box()
})
gro
## The map has been subset to fit the relocations.
## Now, estimate the UD:
ud.one.per.grid < kernelUD(loc, id, grid = gro)
image(ud.one.per.grid)
## The UD can then be matched to habitat maps

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