Robust coexistence in ecological competitive communities

Darwin already recognized that competition would be the fiercest among conspecifics. In time, intraspecific competition has become a centerpiece of ecological theory, yielding for example the notions of niche differentiation and limiting similarity. When considering the dynamics of ecological communities, one can show that a sufficiently strong level of intraspecific competition can buffer the effects of perturbations, such that populations stably coexist at a steady state—i.e., they return to it after disturbance. Here we analyze the effect of intraspecific competition on the existence of such a steady state, in large random ecological communities where competition is the prevalent mode of interaction. We show that, in analogy with stability, when a critical level of intraspecific competition is surpassed, the existence of the steady state is guaranteed. More importantly, we derive a general expression for the probability of feasibility for these systems, and show that the transitions to stability and feasibility always occur in the same order: stability first, feasibility second. Consequently, feasible systems will necessarily be stable. This result holds generally, even when the initial pool of species lacks a feasible equilibrium. That is, when dynamics play out, species extinctions affect the stability and feasibility threshold values but their ordering is maintained. This has profound consequences for ecological dynamics: a subset of the species pool will always coexist robustly at a stable equilibrium, and out-of-equilibrium coexistence via limit cycles or chaos, will never be observed—consistently with experimental results.