Journal of Mathematical Biology

, Volume 15, Issue 1, pp 1–36

The stabilizing effect of a random environment

  • Peter L. Chesson

DOI: 10.1007/BF00275786

Cite this article as:
Chesson, P.L. J. Math. Biology (1982) 15: 1. doi:10.1007/BF00275786


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.

Key words

Stochastic competition modelsStochastic stabilityStochastic boundedness

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Peter L. Chesson
    • 1
  1. 1.Department of Biological Sciences and Marine Science InstituteUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of ZoologyThe Ohio State UniversityColumbusUSA