Quantifying compositional variability in microbial communities with FAVA

Microbial communities vary across space, time, and individual hosts, presenting new challenges for the development of statistics measuring the variability of community composition. To understand differences across microbiome samples from different host individuals, sampling times, spatial locations, or experimental replicates, we present FAVA, a new normalized measure for characterizing compositional variability across multiple microbiome samples. FAVA quantifies variability across many samples of taxonomic or functional relative abundances in a single index ranging between 0 and 1, equaling 0 when all samples are identical and equaling 1 when each sample is entirely comprised of a single taxon. Its definition relies on the population-genetic statistic FST, with samples playing the role of "populations" and taxa playing the role of "alleles." Its convenient mathematical properties allow users to compare disparate data sets. For example, FAVA values are commensurable across different numbers of taxonomic categories and different numbers of samples considered. We introduce extensions that incorporate phylogenetic similarity among taxa and spatial or temporal distances between samples. We illustrate how FAVA can be used to describe across-individual taxonomic variability in ruminant microbiomes at different regions along the gastrointestinal tract. In a second example, a longitudinal analysis of gut microbiomes of healthy human adults taking an antibiotic, we use FAVA to quantify the increase in temporal variability of microbiomes following the antibiotic course and to measure the duration of the antibiotics influence on microbial variability. We have implemented this tool in an R package, FAVA, which can fit easily into existing pipelines for the analysis of microbial relative abundances. Significance statementStudies of microbial community composition across time, space, or biological replicates often rely on summary statistics that analyze just one or two samples at a time. Although these statistics effectively summarize the diversity of one sample or the compositional dissimilarity between two samples, they are ill-suited for measuring variability across many samples at once. Measuring compositional variability among many samples is key to understanding the temporal stability of a community across multiple time points, or the heterogeneity of microbiome composition across multiple experimental replicates or host individuals. Our proposed measure, FAVA, meets the need for a statistic summarizing compositional variability across many microbiome samples all at once.