\documentclass{article}
% \VignetteIndexEntry{adehabitatMA: tools for the analysis of mapped data}

\usepackage{graphicx}
\usepackage[colorlinks=true,urlcolor=blue]{hyperref}

\usepackage{color}
\usepackage{url}

\usepackage{Sweave}
\newcommand{\strong}[1]{{\normalfont\fontseries{b}\selectfont #1}}
\let\pkg=\strong

\title{Tools for the Analysis of Mapped Data:\\
the {\tt adehabitatMA} Package }
\author{Clement Calenge,\\
  Office national de la classe et de la faune
  sauvage\\
  Saint Benoist -- 78610 Auffargis -- France.}
\date{Mar 2019}

\begin{document}

\maketitle
\tableofcontents


<<echo=FALSE>>=
oldopt <- options(width=80, warn=-1)
.PngNo <- 0
wi <- 480
pt <- 20
@

<<label=afig,echo=FALSE,eval=FALSE>>=
.PngNo <- .PngNo + 1; file <- paste("Fig-bitmap-",
          .PngNo, ".png", sep="")
png(file=file, width = wi, height = wi, pointsize = pt)
@

<<label=zfig,echo=FALSE,eval=FALSE>>=
dev.null <- dev.off()
cat("\\includegraphics[height=7cm,width=7cm]{", file, "}\n\n", sep="")
@

<<label=zfigg,echo=FALSE,eval=FALSE>>=
dev.null <- dev.off()
cat("\\includegraphics[height=14cm,width=14cm]{", file, "}\n\n", sep="")
@


\section{History of the package adehabitatMA}

The package {\tt adehabitatMA} contains functions allowing the analysis of
mapped data that were originally available in the package {\tt
  adehabitat} (Calenge, 2006).\\

I developed the package {\tt adehabitat} during my PhD (Calenge, 2005)
to make easier the analysis of habitat selection by animals.  The
package {\tt adehabitat} was designed to extend the capabilities of
the package {\tt ade4} concerning studies of habitat selection by
wildlife.\\

Since its first submission to CRAN in September 2004, a lot of
work has been done on the management and analysis of spatial data in
R, and especially with the release of the package {\tt sp} (Pebesma
and Bivand, 2005).  The package {\tt sp} provides classes of data that
are really useful to deal with spatial data...\\

In addition, with the increase of both the number (more than 250
functions in Oct. 2008) and the diversity of the functions in the
package \texttt{adehabitat}, it soon became apparent that a reshaping
of the package was needed, to make its content clearer to the users.  I
decided to ``split'' the package {\tt adehabitat} into four packages:\\

\begin{itemize}
\item {\tt adehabitatMA} package provides methods for dealing
  with maps in R.
\item {\tt adehabitatHR} package provides classes and methods for dealing
  with home range analysis in R.
\item {\tt adehabitatHS} package provides classes and methods for dealing
  with habitat selection analysis in R.
\item {\tt adehabitatLT} package provides classes and methods for dealing
  with animals trajectory analysis in R.\\
\end{itemize}

We consider in this document the use of the package {\tt adehabitatMA} to
deal with the analysis of mapped data.  All the methods available in
\texttt{adehabitatMA} are also available in \texttt{adehabitat}, but the
classes of data returned by the functions of \texttt{adehabitatMA} are
completely different from the classes returned by the same functions
in \texttt{adehabitat}.  Indeed, the classes of data returned by the
functions of \texttt{adehabitatHR} have been designed to be compliant with
the classes of data provided by the package \texttt{sp}.  Note that
functions allowing the conversion from old classes of
\texttt{adehabitat} to new classes of \texttt{adehabitatMA} and
\texttt{sp} are described on the help page of the function
\texttt{kasc2spixdf}. We therefore suppose that the user is familiar
with this package.\\


Package {\tt adehabitatMA} is loaded by
<<echo=TRUE,print=FALSE>>=
library(adehabitatMA)
@

<<echo=FALSE,print=FALSE>>=
suppressWarnings(RNGversion("3.5.0"))
set.seed(13431)
adeoptions(shortprint=TRUE)
@


\section{The aim of the package}

\subsection{sp and adehabitatMA}

The package \texttt{sp} is really useful for the analysis of mapped
data, and for this reason, I encourage the user to become familiar
with this package.  However, the package \texttt{adehabitat}
originally contained functions which were also useful in spatial
analysis though not available in \texttt{sp}, and especially in the
field of analysis of animal space use. For this reason, I included
these functions in the package \texttt{adehabitatMA}. I demonstrate the use
of these functions in this document.\\

I will demonstrate the use of this package using the example dataset
\texttt{lynxjura}.

<<>>=
data(lynxjura)
@

This dataset contains the results of the monitoring
of the lynx in the Jura mountains (France) by the French lynx network
of the \textit{Office national de la chasse et de la faune
  sauvage}. This dataset has two components: \texttt{\$locs} is a
\texttt{SpatialPointsDataFrame} containing the locations of presence
indices of the lynx, along with the date of collection and the type of
indices (attacks on livestocks, captured animal, tracks, etc.). Look
at the first rows of this object:

<<>>=
head(lynxjura$locs)
@

The component \texttt{\$map} of this dataset is a
\texttt{SpatialPixelsDataFrame} contains the maps of four
environmental variables measured on the study area:

<<>>=
lynxjura$map
@

The whole content of this object can be displayed using the function
\texttt{mimage}:

<<label=figu1,echo=FALSE,fig=FALSE,eval=FALSE>>=
mimage(lynxjura$map)
@

<<echo=TRUE,fig=FALSE,eval=FALSE>>=
<<figu1>>
@

\begin{center}
<<results=tex,echo=FALSE,fig=FALSE>>=
<<afig>>
<<figu1>>
<<zfig>>
@
\end{center}



\section{Working with raster maps only}

\subsection{Exploring a raster map interactively}

\texttt{adehabitatMA} provides one function allowing the exploration of
objects of class \texttt{SpatialPixelsDataFrame}, the function
\texttt{explore}. This allows to interactively explore a map, to find
the value of the variables at a given place, to measure the distance
between two points, to zoom on a given part. Note that this function
requires the package \texttt{tkrplot}:

<<eval=FALSE>>=
explore(lynxjura$map)
@

\includegraphics[keepaspectratio]{screenshot1.png}

This function also has an argument named \texttt{panel.last}, which
allows to pass an expression to be evaluated after plotting has taken
place. For example, we can use it to explore the distribution of lynx
indices in relationship with the maps. Copy and paste the following
expression:

<<eval=FALSE>>=
explore(lynxjura$map, panel.last=function() points(lynxjura$locs, pch=3))
@


\subsection{Labelling connected features on a map}

It is sometimes useful to identify automatically separated components
on a raster map. For example, consider the maps in the object
\texttt{lynxjura} loaded previously:

<<>>=
map <- lynxjura$map
@

Look at the values of the mapped variables:

<<label=sodssss,echo=FALSE,fig=FALSE,eval=FALSE>>=
hist(map)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<sodssss>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<sodssss>>
<<zfig>>
@
\end{center}


Consider the variable ``forets'', which represents the percentage of
forested area in each pixel of the map. We will consider areas with
at least 95\% of forests:

<<label=qsfddfdd,echo=FALSE,fig=FALSE,eval=FALSE>>=
forest <- map[,1]
forest[[1]][forest[[1]]<95] <- NA
image(forest, col="green")
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<qsfddfdd>>
@


\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<qsfddfdd>>
<<zfig>>
@
\end{center}

We may wonder how many forested areas are identified using this
criterium. in the present case, we can count them ourselves: 9
areas. However, the function \texttt{labcon} provides an efficient way
to do it:

<<label=ksdkksss,echo=FALSE,fig=FALSE,eval=FALSE>>=
lab <- labcon(forest)
image(lab)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<ksdkksss>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<ksdkksss>>
<<zfig>>
@
\end{center}

The resulting object is a \texttt{SpatialPixelsDataFrame} mapping
one integer vector taking a unique value per connected
component. Therefore, we can count the number of components in the
map.

<<>>=
lab
max(lab[[1]])
@

It is easy to measure the area of each component, because we know the
area covered by a pixel:

<<>>=
gridparameters(lab)
@

Therefore, the area covered by each component can be computed by:

<<>>=
table(lab[[1]])*500*500
@

The result is here returned in squared meters as the original units of
the maps were in meters.\\

We can also measure the average density of rivers (second variable,
names ``hydro'' in the object \texttt{map}) in the component 1. We
first have to transform the objects \texttt{lab} and \texttt{map} as
full grid to allow the comparison:

<<>>=
fullgrid(lab) <- TRUE
fullgrid(map) <- TRUE
@

Then we compute the mean of the density of rivers in the component 1:

<<>>=
mean(map[[2]][lab[[1]]==1], na.rm=TRUE)
@

Or getting the map of ``hydro'' for the first connected component in a
separate map:

<<label=sldsss,echo=FALSE,fig=FALSE,eval=FALSE>>=
comp1 <- map[2]
comp1[[1]][map[[1]]<95] <- NA
comp1[[1]][lab[[1]]!=1] <- NA
image(comp1)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<sldsss>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<sldsss>>
<<zfig>>
@
\end{center}


\subsection{Computing the contour of a mapped area on a raster map}
\label{sec:contour}

Consider again the map of forested area built in the previous section:

<<label=skks,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(forest, col="red")
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<skks>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<skks>>
<<zfig>>
@
\end{center}

It may sometimes be useful to compute the coordinates of the vertices
of the contour polygon of the forested area:

<<echo=FALSE>>=
con <- getcontour(forest)
@

\begin{Schunk}
\begin{Sinput}
> con <- getcontour(forest)
\end{Sinput}
\begin{Soutput}
Warning message:
In getcontour(forest) :
  At least 3 pixels are required to compute a contour.
3 components erased
\end{Soutput}
\end{Schunk}

The resulting object is of the class \texttt{SpatialPolygons}. It can
therefore be handled with other functions of the package \texttt{sp},
and can be exported toward a GIS using the functions of the package
\texttt{sf} after conversion with \texttt{st\_as\sf} from this package.\\

However, note the warning here. To understand it, look at the
resulting object:

<<label=ssskkkq,echo=FALSE,fig=FALSE,eval=FALSE>>=
plot(con, col="green")
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<ssskkkq>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<ssskkkq>>
<<zfig>>
@
\end{center}

There are 6 polygons plotted here. However, we saw in the previous
section that there are 9 forested areas in the studied regions. Three
of the forested areas are built by less than three pixels, so that no
contour can be calculated for these ``small forests''.


\subsection{Mathematical morphology}

In the last case, we may be annoyed to ``loose'' these three small
forests. It is easy to understand that at least three points are
required to build a polygon, and that the function cannot find the
contour polygon of only one point (one pixel).\\

There is however a way to circumvent this drawback. We can use
the function \texttt{morphology}, which performs operations of
mathematical morphology: it allows to erode or to dilate the object
(see the help page of the function. In our case, we may dilate each
forested area by one pixel:

<<>>=
for1 <- morphology(forest, "dilate", nt=1)
for1
@

The resulting object is a \texttt{SpatialPixelsDataFrame}. Now
compare the area covered by the components of \texttt{for1} with the
area covered by the components of \texttt{forest}:

<<label=sdkskss,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(for1, col="blue")
image(forest, col="yellow", add=TRUE)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<sdkskss>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<sdkskss>>
<<zfig>>
@
\end{center}

Each forested area has been expanded by exactly one pixel on all
sides. Note that the components on the boundary of the map cannot be
expanded. Now if we use the function \texttt{getcontour}  again:

<<label=skkssss,echo=FALSE,fig=FALSE,eval=FALSE>>=
plot(getcontour(for1), col="green")
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<skkssss>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<skkssss>>
<<zfig>>
@
\end{center}


All forested areas are now present in this vectorized object. This
operation of course assume that the area increase caused by the use of
the function can be considered as negligible.\\

Note that the inverse operation (erosion) is also possible with the
function \texttt{morphology}.


\subsection{Changing the resolution of a map}

The package \texttt{adehabitatMA} provides a function allowing to change
the resolution of the map. For example, consider the map of the study
area used previously:

<<label=skdskdk,echo=FALSE,fig=FALSE,eval=FALSE>>=
map <- lynxjura$map
mimage(map)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<skdskdk>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<skdskdk>>
<<zfig>>
@
\end{center}

The parameters of this map are:

<<>>=
gridparameters(map)
@

We may want to change the resolution of this map so that pixels cover
5 $\times$ 5 km instead of 500 $\times$ 500 m. That is, we want to
merge together 10 pixels into one pixel. The function \texttt{lowres}
allows to perform this operation. We first define \texttt{map} as a
\texttt{SpatialPixelsDataFrame}:

<<label=sssshhh,echo=FALSE,fig=FALSE,eval=FALSE>>=
mimage(lowres(map, 10))
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<sssshhh>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<sssshhh>>
<<zfig>>
@
\end{center}

The function computes the average value in each pixel of the new
map. However, note that in some case, it is not sensible to compute an
average to summarize the values observed in a given pixel. For
example, imagine that we transform the variable ``forets'' in the
following way:

<<label=sqkdksssq,echo=FALSE,fig=FALSE,eval=FALSE>>=
map[[1]] <- as.numeric(cut(map[[1]],3))
image(map, 1)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<sqkdksssq>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<sqkdksssq>>
<<zfig>>
@
\end{center}

The map is now a factor with three classes. In such a case, it does
not make sense to compute a mean to summarize the values of the
pixels. In such a case, the function \texttt{lowres} assigns to the
pixel the most frequent level.  When several levels are equally
represented in the pixel, the function randomly samples one of these
levels. We have to indicate to the function which variable(s) in the
object are factors thanks to the argument \texttt{which.fac}:

<<label=sdskkkk,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(lowres(map, 10, which.fac=1))
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<sdskkkk>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<sdskkkk>>
<<zfig>>
@
\end{center}


\subsection{Subsetting a map}


Consider again the map of the forests:

<<label=skssjdx,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(forest, col="green")
box()
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<skssjdx>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<skssjdx>>
<<zfig>>
@
\end{center}

The forested areas are located in the eastern part of the area. We can
use the function \texttt{subsetmap} to get that part of the map:

<<eval=FALSE>>=
for2 <- subsetmap(forest)
@

Then click on the map to indicate the lower-left and upper-right
boundaries of the new map:

<<echo=FALSE>>=
for2 <- subsetmap(forest, xlim=c(850254.2, 878990.2),
                  ylim=c(2128744, 2172175))
@

<<label=skksks,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(for2, col="green")
box()
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<skksks>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<skksks>>
<<zfig>>
@
\end{center}


\section{Working with points and maps}

We now consider the case where we work with points and raster maps.
Remember that the functions of \texttt{adehabitatMA} were originally
available in \texttt{adehabitat} to study issues related to habitat
selection by animals. Issues involving both points and maps are
extremely frequent in this field. The points may be the relocations of
animals collected using radio-tracking, or presence indices of animals
on an area (as is the case for the \texttt{lynxjura} data).  The maps
therefore represent the environment of the animals.\\

We programmed two commonly used functions to deal with points and
maps:\\
\begin{itemize}
\item \texttt{count.points} allows to count the number of points in
  each pixel of the raster map;

\item \texttt{join} allows to identify the values of mapped variables
  at specified locations.\\
\end{itemize}

Although the function \texttt{overlap} of the package \texttt{sp}
could easily be used to perform these operations, we prefered to
provide specific functions, as these operations are very common in the
field of habitat selection studies.


\subsection{Counting the number of points in pixels}

Consider the data on the lynx in the Jura mountains:

<<>>=
data(lynxjura)
map <- lynxjura$map
class(map)
locs <- lynxjura$loc
class(locs)
@

Display the image:

<<label=flkqskqfkjc,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(map, 1)
points(locs, pch=3)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<flkqskqfkjc>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<flkqskqfkjc>>
<<zfig>>
@
\end{center}

We can count the number of points in each pixel of the map:

<<echo=FALSE>>=
cp <- count.points(locs, map)
@

\begin{Schunk}
\begin{Sinput}
> cp <- count.points(locs, map)
\end{Sinput}
\begin{Soutput}
Warning message:
In count.points(locs, map) :
  several columns in the SpatialPointsDataFrame, no id considered
\end{Soutput}
\end{Schunk}

Note the warning message. We will talk about it later. Now, display
the result:

<<label=ssckcc,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(cp)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<ssckcc>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<ssckcc>>
<<zfig>>
@
\end{center}

The warning returned by the functions is explained by the object
containing the points. Indeed, this object should be, according to the
help page, an object of class \texttt{SpatialPoints}, or
\texttt{SpatialPointsDataFrame} \textit{with one column}.  In the
latter case, the column is considered as a factor giving, for each
point, the membership of the point to a set (e.g. the identity of the
animal). In this case, the \texttt{SpatialPointsDataFrame} contains
more than one column:

<<>>=
head(locs)
@

The function does not know which column should be considered as the
variable defining the membership of points to a set. Therefore, it
treats the object as a \texttt{SpatialPoints} object (which is the
desired behaviour). However, we could have wanted to compute several
maps, with one map per type of index, indicating the number of indices
of each type in each pixel of the map:

<<>>=
cpr <- count.points(locs[,"Type"], map)
cpr
@

The results can be displayed:

<<label=sdkkckck,echo=FALSE,fig=FALSE,eval=FALSE>>=
mimage(cpr)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<sdkkckck>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<sdkkckck>>
<<zfigg>>
@
\end{center}


There is one map per type of points.


\subsection{Finding the value of mapped variables at specified locations}

The other possible approach consists to perform a spatial join: in
other words, to find the value of mapped variables at specified
locations For example:

<<>>=
df <- join(locs, map)
@

The result is a data frame containing the value of the variables at
the specified locations:

<<>>=
head(df)
@

This data frame can then be used in further analyses of habitat selection.


\subsection{Generating a raster map from points data}

In some cases it may be useful to generate a grid of pixels from a set
of points. The package \texttt{sp} contains a function named
\texttt{makegrid}, which generates a regular grid of points. However,
I also included in \texttt{adehabitatMA} a function which computes directly
a \texttt{SpatialPixelsDataFrame} from a set of points. This function
allows to specify either the size of the pixel or the number of
rows/columns of the grid. For example, to generate a
\texttt{SpatialPixelsDataFrame} object from the set of locations of
presence indices of the lynx, with a pixel size of 5000 m $\times$ 5000
m:

<<>>=
asc <- ascgen(locs, cellsize=5000)
asc
@

The resulting object is an object of class
\texttt{SpatialPixelsDataFrame}, with one column containing the number
of points in the pixels of the map.

<<label=llldcvdv,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(asc)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<llldcvdv>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<llldcvdv>>
<<zfig>>
@
\end{center}



\section{Computing buffer regions}

\texttt{adehabitatMA} provides a function allowing the computation of
buffer region. Buffer regions can be computed from points, lines or
polygons. For example, consider the presence indices of the lynx of
type ``sighting'' (labelled "O" in the data)

<<>>=
po <- locs[locs[["Type"]]=="O",]
@

We may want to identify all areas located within 3000 m from a lynx
presence index:

<<label=sfjkfc,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(buffer(po, map, 3000))
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<sfjkfc>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<sfjkfc>>
<<zfig>>
@
\end{center}

Now consider again the vector map of forested areas that we built in
the section \ref{sec:contour} (map \texttt{con}):

<<label=sdskwkl,echo=FALSE,fig=FALSE,eval=FALSE>>=
plot(con)
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<sdskwkl>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<sdskwkl>>
<<zfig>>
@
\end{center}

We may want to identify all the areas located within 3000 metres from
one of these forested areas:

<<label=dfkwkfckj,echo=FALSE,fig=FALSE,eval=FALSE>>=
image(buffer(con, map, 3000))
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<dfkwkfckj>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<dfkwkfckj>>
<<zfig>>
@
\end{center}

Alternatively, we may have wanted to identify the ``ecotone''
(boundary habitat) between the forest and the open areas... for
example, to identify all the areas located within 500 metres from the
boundary:

<<label=qksdk,echo=FALSE,fig=FALSE,eval=FALSE>>=
sl <- as(con, "SpatialLines")
image(buffer(sl, map, 500))
@

<<results=tex,echo=TRUE,fig=FALSE,eval=FALSE>>=
<<qksdk>>
@

\begin{center}
<<results=tex,echo=FALSE>>=
<<afig>>
<<qksdk>>
<<zfig>>
@
\end{center}


\section{Conclusion}

I included in the package \texttt{adehabitatMA} several functions
adding to the existing set of tools available in R to perform spatial
analyses. Originally, these functions were included in the package
\texttt{adehabitat} to allow the study of very specific ecological
issues related to habitat selection, but as most users who sent me
questions/suggestions concerning these functions were using them to
study issues in other fields (e.g. biogeography, landscape ecology,
etc.), I decided to include them in a separate package much more
compliant with existing packages for spatial analysis within R.\\

However, readers interested in the study of animal space use and
habitat selection should also have a look at the brother packages. All
the packages \texttt{adehabitat**} contain a vignette similar to this
one, which explains not only the functions, but also in some cases the
philosophy underlying the analysis of animal space use.


\section*{References}
\begin{description}
\item Calenge, C. 2005. Des outils statistiques pour l'analyse des
  semis de points dans l'espace ecologique. Universite Claude Bernard
  Lyon 1.
\item Calenge, C. 2006. The package adehabitat for the R software: a
  tool for the analysis of space and habitat use by
  animals. Ecological modelling, 197, 516--519.
\item Pebesma, E. and Bivand, R.S. 2005. Classes and Methods for
  Spatial data in R. R News, 5, 9--13.

\end{description}

<<echo=FALSE>>=
options(oldopt)
@

\end{document}


% vim:syntax=tex
