[Paper Review] Microbiome association diversity reflects proximity to the edge of instability

Rubén Calvo, Adrián Roig+4 more|arXiv (Cornell University)|Jan 30, 2026

Gut microbiota and health0 citations

TL;DR

The paper introduces an interacting stochastic logistic model (ISLM) with random balanced interactions to explain how microbiomes exhibit broad pairwise associations and operate near the edge of instability; it provides a method to estimate distance to instability (g) from empirical covariances and applies it to environmental and human gut microbiomes, showing healthy guts sit closer to the edge than dysbiotic states.

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.

Motivation & Objective

• Motivate the need to move beyond single-species macroecological laws to explain interspecific correlations in microbiomes.
• Develop a minimal interacting stochastic logistic model (ISLM) with balanced random interactions that preserves single-species statistics.
• Map the ISLM phase diagram (stable, chaotic, unbounded) and identify an effective stability parameter linked to openness to perturbations.
• Derive a finite-size correction framework to infer distance to instability from empirical pairwise covariances.
• Apply the framework to environmental microbiomes and human gut data to assess proximity to criticality and dysbiosis.
• Highlight implications for May’s stability theory and ecosystem resilience in complex microbial communities.

Proposed method

• Formulate ISLM as a generalized Lotka-Volterra system with multiplicative environmental noise.
• Construct an ensemble of sparse, balanced interaction matrices A=D+σM that preserve fixed-point carrying capacities while introducing interactions.
• Use random-matrix theory to show the May-like instability line g=σ√C=1 and apply dynamical mean-field theory (DMFT) to derive an effective one-species process with emergent noise.
• Derive beyond-DMFT 1/S corrections to estimate the width of pairwise covariance distributions Δ and connect Δ to the stability parameter g via an explicit formula.
• Infer g from empirical short-time covariances and match simulated covariance histograms to data to select representative networks within the ensemble.
• Apply the pipeline to seawater, river, glacier, and lake microbiomes, and to human gut cohorts, to compare proximity to the edge of instability across environments and health conditions.

Figure 1: From ideal-gas-like descriptions to interacting ensembles. Non-interacting models such as the SLM capture marginal statistical patterns of empirical data (Grilli’s laws) but fail to reproduce interspecific associations, while Bayesian inference can fit both at the cost of losing interpreta

Experimental results

Research questions

• RQ1 Can a minimal interacting stochastic logistic model reproduce both single-species macroecological laws and observed interspecific associations in microbiomes?
• RQ2 How do network sparsity and interaction heterogeneity influence the phase behavior (stable, chaotic, unbounded) of microbial communities?
• RQ3 Can an effective stability parameter g, inferred from empirical covariances, quantify distance to the edge of instability in real microbiomes?
• RQ4 Do healthy and dysbiotic gut microbiomes occupy different regions relative to the edge of instability, and can this be used to discriminate conditions like IBD, IBS, CRC, or CDI?

Key findings

• An interacting stochastic logistic model with balanced Gaussian interaction ensembles reproduces single-species laws while generating broad pairwise associations seen in data.
• Random-matrix analysis yields a May-like instability line g=1 that marks the transition from stable to chaotic regimes in the ISLM.
• Finite-size corrections show that proximity to the edge of instability (higher g) broadens the distribution of pairwise associations, matching empirical patterns.
• Fitting covariances with the ISLM framework yields g values close to 1 (edge of instability) across diverse environmental biomes, with variation reflecting network realization differences.
• In human gut data, healthy individuals have higher average g (~0.86) and broader, more heterogeneous associations, whereas dysbiosis-associated states show lower g (~0.74–0.77) and more stable regimes, enabling discrimination across conditions such as IBD, IBS, CRC, and CDI.
• The approach links macroecological laws, interaction-network ensembles, and May’s stability theory, suggesting complex communities may benefit from operating near a dynamical phase transition.

Figure 2: The synthetic model exhibits fixed-point, chaotic, and unbounded dynamical phases. A . Heat map of the largest Lyapunov exponent (LLE) as a function of $\sigma$ and $C$ (negative values are plotted as zero for clarity). Three regimes can be distinguished: a fixed-point phase (FP), a chaoti