  Recent advances in bioinformatics have made high-throughput microbiome data
widely available, and new statistical tools are required to maximize the
information gained from these data. For example, analysis of high-dimensional
microbiome data from designed experiments remains an open area in microbiome
research. Contemporary analyses work on metrics that summarize collective
properties of the microbiome, but such reductions preclude inference on the
fine-scale effects of environmental stimuli on individual microbial taxa. Other
approaches model the proportions or counts of individual taxa as response
variables in mixed models, but these methods fail to account for complex
correlation patterns among microbial communities. In this paper, we propose a
novel Bayesian mixed-effects model that exploits cross-taxa correlations within
the microbiome, a model we call MIMIX (MIcrobiome MIXed model). MIMIX offers
global tests for treatment effects, local tests and estimation of treatment
effects on individual taxa, quantification of the relative contribution from
heterogeneous sources to microbiome variability, and identification of latent
ecological subcommunities in the microbiome. MIMIX is tailored to large
microbiome experiments using a combination of Bayesian factor analysis to
efficiently represent dependence between taxa and Bayesian variable selection
methods to achieve sparsity. We demonstrate the model using a simulation
experiment and on a 2x2 factorial experiment of the effects of nutrient
supplement and herbivore exclusion on the foliar fungal microbiome of
$\textit{Andropogon gerardii}$, a perennial bunchgrass, as part of the global
Nutrient Network research initiative.
