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Recent advances in bioinformatics have made high-throughput microbiome datawidely available, and new statistical tools are required to maximize theinformation gained from these data. For example, analysis of high-dimensionalmicrobiome data from designed experiments remains an open area in microbiomeresearch. Contemporary analyses work on metrics that summarize collectiveproperties of the microbiome, but such reductions preclude inference on thefine-scale effects of environmental stimuli on individual microbial taxa. Otherapproaches model the proportions or counts of individual taxa as responsevariables in mixed models, but these methods fail to account for complexcorrelation patterns among microbial communities. In this paper, we propose anovel Bayesian mixed-effects model that exploits cross-taxa correlations withinthe microbiome, a model we call MIMIX (MIcrobiome MIXed model). MIMIX offersglobal tests for treatment effects, local tests and estimation of treatmenteffects on individual taxa, quantification of the relative contribution fromheterogeneous sources to microbiome variability, and identification of latentecological subcommunities in the microbiome. MIMIX is tailored to largemicrobiome experiments using a combination of Bayesian factor analysis toefficiently represent dependence between taxa and Bayesian variable selectionmethods to achieve sparsity. We demonstrate the model using a simulationexperiment and on a 2x2 factorial experiment of the effects of nutrientsupplement and herbivore exclusion on the foliar fungal microbiome of$\textit{Andropogon gerardii}$, a perennial bunchgrass, as part of the globalNutrient Network research initiative.

MIMIX: a Bayesian Mixed-Effects Model for Microbiome Data from Designed Experiments