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.