Spatial Association and Dissociation

Spatial association might also be used to measure temporal change, for example
when the same species is sampled in the same traps on successive occasions.
This measures spatial instability - the rate of change of spatial distribution.

Spatial association is independent of the spatial pattern of each constituent population.
It should be measured after separate allowance for the two patterns.

As an example, consider the spatial patterns of a beetle and an aphid, sampled on
a 12 x 12 grid. The clustering indices of each species are contoured in the maps below.
Is there evidence of positive association or negative dissociation between the species?

x     y         count data
                       beetle     aphid
 0     0          0          8
15     0          0          4
30     0          0          2
45     0          0          1
  .      .          .           .

At each sample unit, the cluster indices of beetle and aphid are measures of their local
spatial pattern, into either patches or gaps, at that point. The extent to which the cluster
indices ‘agree’ at each point provides a measure of spatial association, locally.