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Stabilization of macroscopic dynamics by fine-grained disorder in many-species ecosystems

A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of organisms, or of individual species and their relations. Low-dimensional heuristic 'macroscopic' models that are widely used to capture ecological relationships -- and commonly evidence out-of equilibrium regimes -- implicitly assume that species-level 'microscopic' heterogeneity can be neglected. Here, we address the stability of such macroscopic descriptions to the addition of disordered microscopic interactions. We find that increased heterogeneity can stabilize collective as well as species fluctuations -- contrary to the well-known destabilizing effect of disorder on fixed points. We analytically find the conditions for the existence of heterogeneity-driven equilibria, and relate their stability to a mismatch in microscopic time scales. This may shed light onto the empirical observation that many-species ecosystems often appear stable at aggregated levels despite highly diverse interactions and large fluctuations at the species level.

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