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 very existence of a steady state (feasibility) in large random ecological communities where competition is the predominant mode of interaction. We show that, in analogy to stability, when a critical level of intraspecific competition is surpassed, the existence of a steady state is guaranteed. More importantly, we derive a general expression for the probability of feasibility and demonstrate that, asymptotically (for large systems), the transition to stability occurs before the transition to feasibility with probability 1. Consequently, in large random competitive communities feasible equilibria are stable. This result holds even when the initial pool of species cannot coexist, and therefore extinctions ensue. That is, as the dynamics unfold, 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 coexist at a globally stable equilibrium, and out-of-equilibrium coexistence via limit cycles or chaos will not be observed---consistently with experimental results.