Feasibility and stability in 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. 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. Here we analyze the effect of intraspecific competition on the existence of a steady state (feasibility) in large random ecological communities where competition is the predominant mode of interaction. We show that 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 for large systems the transition to stability occurs before the transition to feasibility. Consequently, in large random competitive communities feasible equilibria are stable. This result holds even when the initial pool of species cannot coexist. That is 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.
This IFISC Seminar will be broadcasted in the following zoom link: https://us06web.zoom.us/j/89027654460?pwd=Wg9TYMPqqP2ipfj2JVvEagmzaTw29c.1
Coffee and cookies will be served 15 minutes before the start of the seminar
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