There are currently two published method for power in microbiome data. Which you want to use depends on your analysis, and what you want to know.
Micropower (
Kelly, et al, 2015) would be my current first choice for doing this analysis. It's recent, and more likely to be directly relevant to what you're doing. Micropower estimates sample size based on permanova for beta diversity. I've not run micropower, but they have a
GitHub page, and that might be a way to reach out. I assume, based on reading the paper, that you calculate an effect size statistic and that's either compared against a bootstrap of your data, or an existing power curve.
The other option is to use the dirichlet multinomial model from
La Rosa et al, 2012. This works based on the assumption you've done taxonomic analysis using their method. Again, I've not used this package, so I don't know how easy or hard it is to use.
Not sure if that helps make anything clearer.
Happy Holidays,
Justine