The stabilizing effect of a random environment
 Peter L. Chesson
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It is shown that the lottery competition model permits coexistence in a stochastic environment, but not in a constant environment. Conditions for coexistence and competitive exclusion are determined. Analysis of these conditions shows that the essential requirements for coexistence are overlapping generations and fluctuating birth rates which ensure that each species has periods when it is increasing. It is found that a species may persist provided only that it is favored sufficiently by the environment during favorable periods independently of the extent to which the other species is favored during its favorable periods.
Coexistence is defined in terms of the stochastic boundedness criterion for species persistence. Using the lottery model as an example this criterion is justified and compared with other persistence criteria. Properties of the stationary distribution of population density are determined for an interesting limiting case of the lottery model and these are related to stochastic boundedness. An attempt is then made to relate stochastic boundedness for infinite population models to the behavior of finite population models.
 Title
 The stabilizing effect of a random environment
 Journal

Journal of Mathematical Biology
Volume 15, Issue 1 , pp 136
 Cover Date
 198209
 DOI
 10.1007/BF00275786
 Print ISSN
 03036812
 Online ISSN
 14321416
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Stochastic competition models
 Stochastic stability
 Stochastic boundedness
 Authors

 Peter L. Chesson ^{(1)}
 Author Affiliations

 1. Department of Biological Sciences and Marine Science Institute, University of California, 93106, Santa Barbara, CA, USA