Robust coexistence in ecological competitive communities

Abstract

AbstractThe 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 competitiond > dS. Here we show that, in ecological communities where competitive interactions are prevalent, the existence of a feasible state is guaranteed wheneverd > dF. We compute the probability of feasibility for a community ofnpopulations given the level of intraspecific competitiond, and show that the transition to feasibility is smooth, contrary to what found for stability. We explore the relationship between the two critical levels,dSanddF, and determine that, for large random ecological communities dominated by competition,dF> dS, 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]