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\name{miplot}
\alias{miplot}
\title{Morisita Index Plot}
\description{
Displays the Morisita Index Plot of a spatial point pattern.
}
\usage{
miplot(X, ...)
}
\arguments{
\item{X}{
A point pattern (object of class \code{"ppp"}) or something
acceptable to \code{\link[spatstat.geom]{as.ppp}}.
}
\item{\dots}{Optional arguments to control the appearance of the plot.}
}
\details{
Morisita (1959) defined an index of spatial aggregation for a spatial
point pattern based on quadrat counts. The spatial domain of the point
pattern is first divided into \eqn{Q} subsets (quadrats) of equal size and
shape. The numbers of points falling in each quadrat are counted.
Then the Morisita Index is computed as
\deqn{
\mbox{MI} = Q \frac{\sum_{i=1}^Q n_i (n_i - 1)}{N(N-1)}
}{
MI = Q * sum(n[i] (n[i]-1))/(N(N-1))
}
where \eqn{n_i}{n[i]} is the number of points falling in the \eqn{i}-th
quadrat, and \eqn{N} is the total number of points.
If the pattern is completely random, \code{MI} should be approximately
equal to 1. Values of \code{MI} greater than 1 suggest clustering.
The \emph{Morisita Index plot} is a plot of the Morisita Index
\code{MI} against the linear dimension of the quadrats.
The point pattern dataset is divided into \eqn{2 \times 2}{2 * 2}
quadrats, then \eqn{3 \times 3}{3 * 3} quadrats, etc, and the
Morisita Index is computed each time. This plot is an attempt to
discern different scales of dependence in the point pattern data.
}
\value{
None.
}
\references{
M. Morisita (1959) Measuring of the dispersion of individuals and
analysis of the distributional patterns.
Memoir of the Faculty of Science, Kyushu University, Series E: Biology.
\bold{2}: 215--235.
}
\seealso{
\code{\link[spatstat.geom]{quadratcount}}
}
\examples{
miplot(longleaf)
opa <- par(mfrow=c(2,3))
plot(cells)
plot(japanesepines)
plot(redwood)
miplot(cells)
miplot(japanesepines)
miplot(redwood)
par(opa)
}
\author{\adrian
and \rolf
}
\keyword{spatial}
\keyword{nonparametric}
|
