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Using dynamical mean-field theory on stochastic Generalized Lotka-Volterra dynamics, this work establishes an analytical framework to determine the stability regimes of species-rich communities directly from abundance time series. The approach reduces high-dimensional, disordered interactions to an effective single-species stochastic process with a Gamma-distributed steady state, proving that environmental noise systematically destabilizes coexistence into intermittent, near-extinction dynamics. Formulated as a multivariate regression, the method extracts collective interaction statistics and quantifies extinction risk across empirical datasets without requiring pairwise interaction network reconstruction.
High-dimensional complex systems can be analytically mapped into distinct dynamical stability regimes directly from macroscopic time series without ever reconstructing their underlying interaction graphs.
The stability of an ecological community is conventionally defined through species interactions, which quantify how species affect one another. Interaction strengths are notoriously difficult to measure in species-rich assemblages. Long-term monitoring of species-rich communities, however, provides species abundance time series, increasingly available across habitats and taxa but not yet connected to the stability properties of the communities they describe. Here we develop a statistical framework that infers stability regimes in large ecological communities directly from abundance time series. We study stochastic Generalized Lotka--Volterra dynamics with random interactions and environmental fluctuations using dynamical mean-field theory, reducing the multispecies system to an effective stochastic process for a representative species. The theory predicts three stability regimes (stable coexistence, intermittent dynamics close to extinction, and unbounded growth) separated by analytical boundaries, and shows that environmental stochasticity systematically destabilizes coexistence by promoting intermittent low-abundance dynamics. The resulting steady-state species abundance distribution is a Gamma law that ties the dynamical phases to the variability-based stability metrics used in empirical studies. Recasting the effective dynamics as a multivariate regression model, we infer interaction statistics, environmental variability and the characteristic timescale of the dynamics from community data, without reconstructing the interaction network. Applied to natural communities spanning a broad range of habitats and taxa, the method resolves contrasting stability regimes and yields quantitative estimates of species extinction risk.