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[14]Limit cycles in competition communities

   ME Gilpin - The American Naturalist, 1975 - journals.uchicago.edu
   ME Gilpin
   The American Naturalist, 1975 o journals.uchicago.edu
   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 ...
   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.
   [journals.uchicago.edu.png] The University of Chicago Press
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