Microbiome association diversity reflects proximity to the edge of instability

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.

💡 Research Summary

Recent metagenomic surveys have revealed striking macro‑ecological regularities across microbial communities: species‑level abundance fluctuations follow a Gamma distribution, mean abundances are log‑normally distributed, and variance scales roughly as the square of the mean (Taylor’s law). These “laws” are reproduced by the stochastic logistic model (SLM), an ecological analogue of an ideal gas in which species evolve independently under environmental noise. However, real microbiomes display a much broader distribution of pairwise correlations than predicted by the SLM, indicating that inter‑species interactions play a crucial role.

To bridge this gap, the authors introduce the interacting stochastic logistic model (ISLM), which minimally extends the SLM by adding a random interaction matrix while preserving the single‑species statistics. The interaction matrix is constructed as A = D − σ G D, where D encodes log‑normally distributed carrying capacities (ensuring the mean‑abundance law), G is a sparse Gaussian matrix with connectivity C, zero diagonal, and row‑balance (∑j G{ij}=0). The parameter σ controls the overall strength of interactions, and the product g = σ√C serves as an effective stability parameter.

Random matrix theory shows that, in the limit of a large number of species S, the eigenvalues of G fill a disk of radius √C in the complex plane (circular law). Adding the deterministic term −I shifts the spectrum of the effective Jacobian τA_eff = −I + σG so that the disk is centered at –1. Linear stability is lost when the disk first touches the origin, i.e., when g = 1, reproducing May’s classic criterion for the stability of large random ecosystems. Thus g quantifies the distance of a community from the “edge of instability” (or edge of chaos).

To go beyond linear analysis, the authors employ dynamical mean‑field theory (DMFT). In the thermodynamic limit (S → ∞), the high‑dimensional stochastic dynamics collapse onto a single effective stochastic differential equation for a representative species:

  ẋ(t) = x(t)