The SADIE approach to spatial association

A reasonable assessment of overall positive spatial association is given by the extent
to which the red patches of the beetle overlap onto similar clusters of the aphid,
and likewise the degree to which the blue gaps of both insects cover the same areas.

Conversely, if red patches of the beetle generally coincide with blue gaps of the aphid,
and vice-versa (as for these beetle and aphid data), then this indicates spatial dissociation.

This can be measured through the correlation between the cluster indices of the two sets.
This correlation is calculated from summing components, one from each sample unit
The component from each local unit is proportional to the product of the two cluster indices. If the cluster indices 'agree' then the component is positive; if they 'disagree' it is negative.

As an example, consider once again the beetle and aphid data:

  x     y          cluster index
                    beetle   aphid       association locally
  .      .           .            .                .
  .      .           .            .                .
  .      .           .            .                .
60     60        2.6         0.1        negligble
60     75        2.2         1.9        strongly positive
60     90        1.9         1.8        strongly positive
60     105      1.6        -1.9        moderately negative
60     120      1.5        -2.0        strongly negative
  .      .           .            .                .
  .      .           .            .                .
  .      .           .            .                .
                                             _____________
overall association,                   strongly negative
calculated from the
sum total over all
local contributions


It is the cluster indices, not the abundances of each set that are the basis for calculations.
Therefore, as required, this method automatically compares the spatial pattern of the two
sets, not their numerical properties.