Ecological Communities with Fluctuating Interactions Lead to Universal Power Law

An ecological community's fixed point is called feasible if all species' abundances are positive. Here, we study how the feasibility of an ecosystem is affected by fluctuations in the species interaction strengths. We analytically derive the complete probability distribution for the equilibrium species abundances for an arbitrary interaction matrix, and find a heavy-tailed power law. Remarkably, the power law is universal, i.e. independent of the details of the interaction structure and the size of the perturbing noise. The power law suggests that the primary threat to community persistence may not be a loss of local stability, but a sudden, fluctuation-driven loss of feasibility as the equilibrium point is pushed into a negative orthant. To quantify this risk, we calculate a species specific escape rate that identifies the most vulnerable species in the community, and the mean time to feasibility loss for the entire ecosystem. Our analysis reveals that species with long, indirect, and reinforcing interaction chains are the most prone to feasibility loss. We show that as species richness increases, ecosystems become more sensitive to interaction noise, linking complexity to this structural fragility. Lastly, we validate our analytical predictions against stochastic simulations on 98 empirical ecological networks, finding strong agreement with analytical theory. As such, our framework can be used to assess ecosystem robustness beyond traditional stability analysis.