Let's say I have a between-sample distance matrix based on genetic similarity and I want to find out if structure in the matrix is correlated/explained by some environmental factors that I have information for (three factors, each with four groups/levels).

I run a PERMDISP analysis on each of the factors to test for homogeneity of multivariate dispersion. For one of the factors I return a significant result. I further perform a TukeyHSD pairwise analysis to identify between which pairs the significant dispersion result is coming from. Only one of the pairings returns a significant result.

I then run a PERMANOVA test on the same matrix. The factor that gave me a significant result in the PERMDISP analysis also gives me a significant result in the PERMANOVA with a considerable effect size (R2 value of 0.38).

Is there some way of quantifying (or estimating) how much of this effect size is due to the difference in group dispersion? The rationale being that if I can partition the variance apportioned to this factor by the PERMANOVA between 'effect' and dispersion differences, then I can make a more informed conclusion about the potential effect the factor could have on the genetic structure.