A Bayesian method for detecting pairwise associations in compositional data.

Area of Science:

• Ecology
• Statistics
• Bioinformatics

Background:

• Compositional data, common in ecology, are proportions summing to one, making correlation inference difficult due to information loss.
• Understanding correlations between features is crucial in fields like ecology but challenging with normalized data.

Purpose of the Study:

• To introduce a novel Bayesian framework, BAnOCC (Bayesian Analysis of Compositional Covariance), for robust correlation inference in compositional data.
• To enable uncertainty quantification for correlation matrices derived from compositional data.

Main Methods:

• Utilizing a Bayesian framework with a LASSO prior to estimate a sparse precision matrix.
• Employing Markov Chain Monte Carlo (MCMC) sampling to generate posterior distributions.
• Applying a first-order Taylor expansion to approximate the transformation from unobserved counts to compositions.

Main Results:

• BAnOCC accurately infers true networks on simulated data, matching existing methods while providing posterior inference.
• Performance evaluation on larger datasets demonstrates effective control of Type I and Type II error rates.
• Application to Human Microbiome Project data revealed novel competition-based roles for Proteobacteria.

Conclusions:

• BAnOCC offers a powerful Bayesian approach for analyzing correlations in compositional data, providing uncertainty quantification.
• The method successfully identifies ecological network structures and functional roles of microbial taxa.
• BAnOCC advances the analysis of high-dimensional compositional data in ecological and other scientific domains.