Betadisper is significant, can I still do ADONIS and ANOSIM? I'm a grad student in microbial ecology and I'm comparing some bacterial communities in experimental man made ponds. I've run the PCoA, NMDS, and CCA to see how various variables effect or influence the communties. Next I'd like to actually assess the the similarity.
I'm running betadisper to check the homoscedasticity and I'm finding that within the entire 2 year experiment, the ponds' dispersions are different between years, but similar within years, for untreated and treated ponds. 
Am I still allowed to run ADONIS and ANOSIM on this data even though I'm getting significant values in anova and TukeyHSD?
Can anyone recommend any other tests I could use to assess community similarity or any other useful tests?
Thanks! I just joined the community and have been reading it alot! thank to all the contributors!
 A: Anderson and Walsh (2013) considered this issue. I'll summarise their findings with respect to your question.
ANOSIM is very sensitive to heterogeneity and the results of Anderson & Walsh would suggest that don't trust the ANOSIM results; they'll basically just tell you that there is some difference (be it in terms of location (differences in mean), dispersion (variances) or correlation structure), not that there is a location difference were a significant ANOSIM result be obtained.
PERMANOVA (which is basically adonis()) was found to be largely unaffected by heterogeneity in Anderson & Walsh's simulations but only for balanced designs.
For unbalanced designs PERMANOVA and ANOSIM were


*

*too liberal if the smaller group had greater dispersion, and

*too conservative if the larger group had greater dispersion.


This result was especially so for ANOSIM.
Basically, how much you can trust the results of your PERMANOVA depends on the balance in the design.
Anderson MJ, Walsh DCI. PERMANOVA, ANOSIM, and the Mantel test in the face of heterogeneous dispersions: What null hypothesis are you testing? Ecological monographs [Internet] 2013; 83: 557. Available from: http://doi.org/10.1890/12-2010.1
