Fig. 1: Microbiome data is represented by relative abundances, thus differential abundance analysis should account for the bias introduced by across-sample variations in sampling fractions.

Sampling fraction is defined as the ratio of expected abundance in a sample to the corresponding absolute abundance in the ecosystem, which could be empirically estimated by the ratio of library size to the microbial load. a Differences in sampling fractions introduce false negatives. In this toy example, the microbial load for subject A in a unit volume of the ecosystem (e.g. a unit volume of gut) is 8 (4 blue + 4 red), while for subject B it is 12 (6 blue + 6 red). However, the samples taken from subject A and B have the same library size 4 (2 blue + 2 red), same observed abundance as well as the same relative abundance of blue and red taxa. Thus, one may mistakenly conclude that the blue and red taxa are not differentially abundant between two ecosystems, which is not the case in the two ecosystems. This false negative conclusion is caused by differences in the sampling fractions in the two samples. The sampling fraction in sample A is 1/2 and for B it is 1/3. b Differences in sampling fractions introduces false positives. Consider another subject C, who has the microbial load of 16 (12 blue + 4 red) in a unit volume of ecosystem. Given the same library size in sample C (3 blue + 1 red) as sample A, one may mistakenly conclude that both blue and red are differentially abundant between ecosystems A and C, while in fact, only the blue taxon is differentially abundant. Thus a normalization method must account for differences in sampling fractions to avoid such erroneous conclusions.