Bayesian sparse principal coordinates analysis with delta-tolerant linear approximation for microbiome data

TL;DR

The paper introduces BSPCoA, a Bayesian method that approximates microbiome PCoA axes with sparse linear surrogates, enhancing interpretability and taxon identification.

Contribution

It develops a Bayesian sparse PCoA framework with a delta-tolerance diagnostic and global-local priors for taxa selection, applicable to various dissimilarities.

Findings

BSPCoA provides an approximately linear and interpretable ordination.

The method identifies influential taxa associated with seasonal variation.

Simulation studies confirm improved interpretability in microbiome data.

Abstract

Principal coordinates analysis (PCoA) is a standard exploratory tool for microbiome beta-diversity studies, but its axes are defined by pairwise dissimilarities and therefore do not directly identify the taxa driving an ordination. We propose Bayesian sparse principal coordinates analysis (BSPCoA), a post hoc framework that approximates the leading principal coordinates by a sparse linear surrogate in the observed taxa. A delta-tolerance diagnostic quantifies the discrepancy between the classical ordination and its best linear surrogate, clarifying when taxon-level interpretation is well supported. We place three-parameter beta normal global-local priors on the surrogate coefficients to induce row sparsity, obtain posterior uncertainty, and select influential taxa. The method reduces to sparse principal component analysis under Euclidean distance, while remaining applicable to ecologically meaningful dissimilarities such as Bray--Curtis and Hellinger distances. We conduct simulation studies to demonstrate that BSPCoA provides an approximately linear representation of the dominant ordination geometry while enhancing interpretability in sparse microbiome settings. In the Hadza gut microbiome data, the method produces an ordination close to that of classical PCoA while highlighting a parsimonious set of taxa associated with seasonal variation.