Limit Cycles in Competition Communities

A three-species Lotka-Volterra competition community may exhibit population oscillations of a neutral or undamped nature. Nontransitive interference competition, in which 1 can exclude 2, 2 can exclude 3, but 3 can exclude 1, is the underlying mechanism. If immigration, incomplete spatial overlap, or any other mechanism prevents extinction, then such a three-species system must go into true limit cycles. For higher-dimension systems, limit cycles are more likely in communities with an odd number of species. Such limit cycles are most likely to be found in the tropics. A cautionary moral is given: simple competition systems that appear to be unstable and random may be stable and deterministic.