Microbiome association diversity reflects proximity to the edge of instability

TL;DR

This paper introduces an interacting stochastic logistic model to analyze microbiome stability, revealing that healthy gut communities operate near the edge of instability, which can distinguish health states from disease conditions.

Contribution

The study develops a new model incorporating species interactions and derives an estimator for community stability, linking macroecological laws with May's stability theory.

Findings

Healthy microbiomes are near the edge of instability.

Dysbiotic states are more stable and farther from the edge.

The model accurately predicts community behavior from empirical data.

Abstract

Recent advances in metagenomics have revealed macroecological patterns or "laws" describing robust statistical regularities across microbial communities. Stochastic logistic models (SLMs), which treat species as independent -- akin to ideal gases in physics -- and incorporate environmental noise, reproduce many single-species patterns but cannot account for the pairwise covariation observed in microbiome data. Here we introduce an interacting stochastic logistic model (ISLM) that minimally extends the SLM by sampling an ensemble of random interaction networks chosen to preserve these single-species laws. Using dynamical mean-field theory, we map the model's phase diagram -- stable, chaotic, and unbounded-growth regimes -- where the transition from stable fixed-point to chaos is controlled by network sparsity and interaction heterogeneity via a May-like instability line. Going beyond mean-field theory to account for finite communities, we derive an estimator of an effective stability parameter that quantifies distance to the edge of instability and can be inferred from the width of the distribution of pairwise covariances in empirical species-abundance data. Applying this framework to synthetic data, environmental microbiomes, and human gut cohorts indicates that these communities tend to operate near the edge of instability. Moreover, gut communities from healthy individuals cluster closer to this edge and exhibit broader, more heterogeneous associations, whereas dysbiosis-associated states shift toward more stable regimes -- enabling discrimination across conditions such as Crohn's disease, inflammatory bowel syndrome, and colorectal cancer. Together, our results connect macroecological laws, interaction-network ensembles, and May's stability theory, suggesting that complex communities may benefit from operating near a dynamical phase transition.