Betadisper and adonis in R: Am I interpreting my output correctly? I am currently analyzing next generation sequencing bacterial data and trying to figure out whether bacterial communities differ between regions (seems to exhibit this in nMDS).
When running adonis (vegan package) I got an r2 = 0.45, and p = 0.001. When I ran the betadisper and ran a subsequent permutation test I got an F = 1 and p = 0.3.
From my understanding my results are saying that there is an effect of region on bacterial communities and that the communities from each region display similar homogeneity. I'm not sure if that is correct or even if it would be "expected" or appropriate to have a significant adonis but insignificant betadisper. For both permutation tests I used the obligatory 999 permutations. Let me know if you need more information and thanks in advance for your help!
 A: This question was answered on another forum by Jaime Pinzon from the University of Alberta. Here is answer:
A non-significant result in betadisper is not necessarily related to a significant/non-significant result in adonis. The two tests are testing different hypothesis. The former tests homogeneity of dispersion among groups (regions in your case), which is a condition (assumption) for adonis. The latter tests no difference in 'location', that is, tests whether composition among groups is similar or not. You may have the centroids of two groups in NMS at a very similar position in the ordination space, but if their dispersions are quite different, adonis will give you a significant p-value, thus, the result is heavily influenced not by the difference in composition between groups but by differences in composition within groups (heterogeneous dispersion, and thus a measure of betadiversity).  In short, your results are fine, you are meeting the 'one assumption'  for adonis (homogeneous dispersion) and thus you are certain that results from adonis are 'real' and not an artifact of heterogeneous dispersions. For more information you can read Anderson (2006) Biometrics 62(1):245-253 and Anderson (2006) Ecology Letters 9(6):683-693. Hope this helps!
