Table 1.

Normalization methods

Method	Description
none	Raw counts are not transformed.
tss	Total sum scaling. Raw counts are divided by the library size.
css	Cumulative sum scaling. As above, except that for each sample a quantile is calculated and the total sum is replaced by the sum up to and including that quantile.
rarefying	Each observation is subsampled to even depth. This method is implemented in the R package phyloseq [35]. We use the function rarefy_even_depth with sample.size=0.90*min(sample.size).
uBay	A standard Bayesian method that infers the posterior distribution of proportions as the product of the multinomial likelihood with a Dirichlet prior. Following [24], we set α=(1/2,…,1/2)T and convert raw counts to proportions by (6).
ALDEx2	A Bayesian method that infers the posterior distribution of proportions in the same way as uBay. However, rather than using the posterior mean, Monte–Carlo draws from the posterior distribution are used in downstream analysis [36].
eBay	The same as uBay, except that hyper-parameters of the Dirichlet prior are estimated from data by maximizing the marginal likelihood. We use the proposed empirical Bayes formula (9).
eBay-tree	The tree-based extension (15) of eBay.