kernelUD {adehabitat} | R Documentation |
kernelUD
is used to estimate the utilization distribution (UD)
of animals monitored by radio-tracking, with the classical kernel method.
getvolumeUD
and kernel.area
provide utilities
for home-range size estimation.
getverticeshr
stores the
home range contour as objects of class area
in a list of class
kver
, with one component per animal.
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
xy |
h |
a character string or a number. If h is set to
"href" , the ad hoc method is used for the smoothing parameter
(see details). If h is set to
"LSCV" , the least-square cross validation method is
used. Note that "LSCV" is not available if kern = "epa" .
Alternatively, h may be set to any given numeric value |
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 asc , or a list of objects of class
asc , with named elements corresponding to each level of the
factor id (see examples) |
same4all |
logical. If TRUE , the same grid
is used for all animals. If FALSE , one grid per
animal is used |
hlim |
a numeric vector of length two. If h = "LSCV" ,
the function minimizes the cross-validation criterion for values of
h ranging from hlim[1]*href to hlim[2]*href , where
href is the smoothing parameter computed with the ad hoc
method (see below) |
kern |
a character string. If "bivnorm" , a bivariate
normal kernel is used. If "epa" , an Epanechnikov kernel is
used. |
extent |
a value indicating the extent of the grid used for the
estimation (the extent of the grid on the abscissa is equal to
(min(xy[,1]) + extent * diff(range(xy[,1]))) ). |
x |
an object of class khr returned by kernelUD . |
axes |
logical. Whether the axes are to be plotted |
mar |
the margin parameter (see help(par) ) |
addcontour |
logical. If TRUE , contours are drawn on the
graphics |
addpoints |
logical. If TRUE , the animal relocations are
drawn on the graphics |
levels |
a vector of percentage levels for home-range size estimation |
unin |
the units of the relocations coordinates. Either "m" for
meters (default) or "km" for kilometers |
unout |
the units of the output areas. Either "m2" for
square meters, "km2" for square kilometers or "ha" for
hectares (default) |
lev |
the percentage level for home range contour estimation. |
... |
additionnal parameters to be passed to the generic
functions print and image |
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 cross-validation 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
home-range estimation (see examples). In addition, this function is
used in the function kernel.area
, to compute the home-range
size. Note, that the function plot.hrsize
(see the help page
of this function) can be used to display the home-range size estimated
at various levels.
The class khr
is a class grouping three sub-classes,
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
sub-components:
UD |
an object of class asc , with the values of density
probability in each cell of the grid |
h |
if LSCV is not used, the value of the smoothing
parameter. if
LSCV is used, a list with three components:
|
locs |
The relocations used in the estimation procedure. |
hmeth |
The argument h of the function kernelUD |
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 clement.calenge@oncfs.gouv.fr
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 home-range studies. Ecology, 70, 164–168.
Worton, B.J. (1995) Using Monte Carlo simulation to evaluate kernel-based 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. ftp://ftp.im.nbs.gov/pub/software/CSE/wsb2695/KERNELHR.ZIP.
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.
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 home-range) ## udvol describes, for each cell of the grid, ## the smaller home-range to which it belongs ## Calculation of the 95 percent home range ver <- getverticeshr(ud, 95) elev <- getkasc(puechabon$kasc, "Elevation") # Map of the area image(elev) plot(ver, add=TRUE) legend(696500, 3166000, legend = names(ver), fill = rainbow(4)) ## Example of estimation using LSCV udbis <- kernelUD(loc, id, h = "LSCV") image(udbis) ## Compare the estimation with ad hoc and LSCV method ## for the smoothing parameter (cuicui1 <- kernel.area(loc, id)) ## ad hoc plot(cuicui1) (cuicui2 <- kernel.area(loc, id, h = "LSCV")) ## LSCV plot(cuicui2) ## Diagnostic of the cross-validation plotLSCV(udbis) ## Use of the same4all argument: the same grid ## is used for all animals udbis <- kernelUD(loc, id, same4all = TRUE) image(udbis) ## Estimation of the UD on a map ## (e.g. for subsequent analyses on habitat selection) elev <- getkasc(puechabon$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