Journal of Mathematical Biology

, Volume 27, Issue 2, pp 117–138 | Cite as

Invasibility and stochastic boundedness in monotonic competition models

  • P. L. Chesson
  • S. Ellner
Article
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Revised:

Abstract

We give necessary and sufficient conditions for stochastically bounded coexistence in a class of models for two species competing in a randomly varying environment. Coexistence is implied by mutual invasibility, as conjectured by Turelli. In the absence of invasibility, a species converges to extinction with large probability if its initial population is small, and extinction of one species must occur with probability one regardless of the initial population sizes. These results are applied to a general symmetric competition model to find conditions under which environmental fluctuations imply coexistence or competitive exclusion.

Key words

Invasibility Stochastic boundedness Competition Coexistence Competitive exclusion 
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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • P. L. Chesson
    • 1
  • S. Ellner
    • 2
  1. 1.Department of ZoologyOhio State UniversityColumbusUSA
  2. 2.Biomathematics Graduate Program, Department of StatisticsNorth Carolina State UniversityRaleighUSA

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