Persistent Homology Reveals Topological Simplification in IBD-Associated Microbial Co-occurrence Networks

Background. Conventional diversity metrics are insensitive to the loop-level structure of microbialco-occurrence networks. Persistent homology, from topological data analysis (TDA), trackshow loops and other higher-order features form and dissolve across all correlation thresholdssimultaneously. Methods. We applied persistent homology to Spearman co-occurrence networks from 3,409American Gut Project (AGP) stool samples (CLR-transformed; top-80 prevalent taxa). A pairedbootstrap (200 iterations, n = 100/group) yielded distributions of six H1 scalar features. Significance was assessed via sign-flip permutation (500 shuffles; primary) and Wilcoxon signed-rank(confirmatory), with Benjamini–Hochberg correction across 18 tests per subset. All analyses wererepeated in age/sex/BMI-matched subsamples and at taxon-set sizes N ∈ {50,80,120}. The AGPfinding was independently validated in the IBDMDB multi-omics cohort and grounded againstfecal calprotectin. A leave-one-out topological attribution identified per-taxon contributions toloop structure. Classification benchmarking compared topological features against Shannondiversity under 5-fold cross-validation. Results. IBD (n = 165 vs. n = 3,084 healthy) was associated with systematically lower topologicalcomplexity across all six features (Cohen’s |d| = 0.75–2.38; pFDR < 0.005 at all taxa sizes), fullypreserved after covariate matching. In IBDMDB (cross-platform, WGS), a one-sample-persubject sensitivity check reveals that the full-dataset IBD vs. non-IBD comparison is driven byoverrepresentation of active-disease timepoints; the within-IBD calprotectin comparison, which isunaffected by this sampling bias, confirms that loop structure tracks a continuous inflammationbiomarker. Leave-one-out attribution identified Oscillospira and Blautia as the dominant loopanchors in healthy AGP networks, with cross-dataset replication of Bacteroides-clade importancein IBDMDB. An extended classification benchmark against α- and β-diversity established thatAitchison-PCoA (phylogeny-free compositional β-diversity) is the strongest single predictor(AUC = 0.734, logistic regression), while topology scalars outperform Shannon under randomforest and provide mechanistic interpretability that distance-based embeddings do not supply.Plant-based diet showed moderately longer-lived loops (d = 0.65, pFDR = 0.004); antibioticrecency produced limited signal. Conclusions. IBD-associated microbiomes are topologically simpler than healthy controls acrosstwo independent cohorts and two sequencing technologies, and this simplification tracks a clinical inflammation biomarker. Persistent homology provides a structurally informative complementto existing microbiome metrics, with taxon-level attribution bridging topological statistics andnamed biological interactions.