On the Interpretation of PERMANOVAs R2.

TOday I want to share one of my common multivariate stats headaches. Few days ago I was working on a project with paired samples. I had samples collected before and after a two treatments. To test the effect of treatments on beta diversity I, like I usually do, used a PERMANOVA. While doing my analysis, I was a little confused by the interpretation of such results.

I had three groups and I wanted to compare which group was compositionally more similar to the original (pre-treatment) group. So I did a pairwise-PERMANOVA calculated on bray curtis dissimilarities, my idea was to compare the R2. A higher R2 between two pairs would indicate a bigger variation in the community, I thought. Nevertheless I also compared the bray-Curtis dissimilarities among the groups, calculating dissimilarities before and after the two treatments. I would expect that the two groups having higher R2 also would show higher mean BC dissimilarities. Nevertheless this was not the case. Here below is a simulation of a similar distance matrix (well exaggerated case).

These are the results of the permanovas:

What we can see is that, even if treatment B has much higher dissimilarities from group A, it clusters much worse together compared to group A. Hence, the PERMANOVA throws out a higher R2 whenever treatment A is involved.

A higher R2 value in PERMANOVA doesn't necessarily imply a larger variation in the community itself. Instead, it indicates that a greater proportion of the total variation observed in your data can be explained by the factors included in your model.

It can be thought more of a indicator of how well communities cluster togheter in your groups. It is important to keep this in mind, especially when dealing with paired or grouped designs. If somehow a treatment causes communities to go all over the place, PERMANOVA might not even be significant as they do not cluster together before and after treatment.

Code here.