# miplot

##### Morisita Index Plot

Displays the Morisita Index Plot of a spatial point pattern.

- Keywords
- spatial, nonparametric

##### Usage

`miplot(X, ...)`

##### Arguments

- X
A point pattern (object of class

`"ppp"`

) or something acceptable to`as.ppp`

.- …
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 \(Q\) subsets (quadrats) of equal size and
shape. The numbers of points falling in each quadrat are counted.
Then the Morisita Index is computed as
$$
\mbox{MI} = Q \frac{\sum_{i=1}^Q n_i (n_i - 1)}{N(N-1)}
$$
where \(n_i\) is the number of points falling in the \(i\)-th
quadrat, and \(N\) is the total number of points.
If the pattern is completely random, `MI`

should be approximately
equal to 1. Values of `MI`

greater than 1 suggest clustering.

The *Morisita Index plot* is a plot of the Morisita Index
`MI`

against the linear dimension of the quadrats.
The point pattern dataset is divided into \(2 \times 2\)
quadrats, then \(3 \times 3\) 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.
**2**: 215--235.

##### See Also

##### Examples

```
# NOT RUN {
data(longleaf)
miplot(longleaf)
opa <- par(mfrow=c(2,3))
data(cells)
data(japanesepines)
data(redwood)
plot(cells)
plot(japanesepines)
plot(redwood)
miplot(cells)
miplot(japanesepines)
miplot(redwood)
par(opa)
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*