Robust coexistence in ecological competitive communities

The notions of intraspecific competition and population self-regulation play a central role in ecological theory, leading to foundational concepts such as limiting similarity and niche differentiation[1–6]. They also are crucial for coexistence: for example, May[7] showed that ecological dynamics around a “feasible” equilibrium can be stabilized by imposing sufficiently strong self-regulation on all populations. For large random systems, the transition from instability to stability is sharp[7– 9], and achieved beyond a critical value of intraspecific competition d > d _S . Here we show that, in ecological communities where competitive interactions are prevalent, the existence of a feasible state is guaranteed whenever d > d _F . We compute the probability of feasibility for a community of n populations given the level of intraspecific competition d , and show that the transition to feasibility is smooth, contrary to what found for stability. We explore the relationship between the two critical levels, d _S and d _F , and determine that, for large random ecological communities dominated by competition, d _F > d _S , that is, the existence of a feasible equilibrium implies its stability. This means that non-equilibrium coexistence via limit cycles or chaos[10, 11] is never observed in these large ecological systems. Dynamics always converge to an equilibrium in which a set of competitors robustly coexist, such that the community can recover from perturbations, be assembled from the bottom-up, and is resistant to invasions[12, 13]