  The advent of high-throughput sequencing technologies has made data from DNA
material readily available, leading to a surge of microbiome-related research
establishing links between markers of microbiome health and specific outcomes.
However, to harness the power of microbial communities we must understand not
only how they affect us, but also how they can be influenced to improve
outcomes. This area has been dominated by methods that reduce community
composition to summary metrics, which can fail to fully exploit the complexity
of community data. Recently, methods have been developed to model the abundance
of taxa in a community, but they can be computationally intensive and do not
account for spatial effects underlying microbial settlement. These spatial
effects are particularly relevant in the microbiome setting because we expect
communities that are close together to be more similar than those that are far
apart. In this paper, we propose a flexible Bayesian spike-and-slab variable
selection model for presence-absence indicators that accounts for spatial
dependence and cross-dependence between taxa while reducing dimensionality in
both directions. We show by simulation that in the presence of spatial
dependence, popular distance-based hypothesis testing methods fail to preserve
their advertised size, and the proposed method improves variable selection.
Finally, we present an application of our method to an indoor fungal community
found with homes across the contiguous United States.
