Fig. 3

Performance of tmap in detecting linear and nonlinear patterns of simulated microbiome associations. Four scenarios of associations between metadata and synthetic microbiome (generated with SparseDOSSA [37]) are simulated. a–d Gaussian mixture with three symmetric centers; Gaussian mixture with three asymmetric centers; Gaussian mixture with two symmetric centers; linear association. Simulation of nonlinear associations is based on mapping the Gaussian mixtures to the first two PCs of the PCoA (principal coordinates analysis) of synthetic microbiome. Linear associations between metadata and synthetic microbiome are simulated based on linear function of the first two PCs. Arrow indicates a linear projection of the values of simulated metadata (scaled by R-squared using envfit). Significance levels and effect sizes of envfit (p value and R²) and tmap (p value and SAFE enriched score) are depicted. SAFE enriched scores are normalized (divided by the sum of SAFE scores). Color legend (from blue to red) indicates values of metadata (from small to large). e Receiver operating characteristic (ROC) curves of the performance of tmap (red) and envfit (green), adonis (yellow), and ANOSIM (blue) in detecting microbiome-associated metadata. Three scenarios of association are examined, including linear-only (dash-dot line), nonlinear-only (dotted line), and a mix (solid line) of both. The shaded areas indicate 95% confidence intervals (100 repeats). Performance is measured by ROC AUC (mean ± sd) for each method and simulation