Diffusion analysis and stationary distribution of the two-species lottery competition model

Jeff S. Hatfield, Peter L. Chesson

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


The lottery model is a stochastic population model in which juveniles compete for space. Examples include sedentary organisms such as trees in a forest and members of marine benthic communities. The behavior of this model appears to be characteristic of that found in other sorts of stochastic competition models. In a community with two species, it was previously demonstrated that coexistence of the species is possible if adult death rates are small and environmental variation is large. Environmental variation is incorporated by assuming that the birth rates and death rates are random variables. Complicated conditions for coexistence and competitive exclusion have been derived elsewhere. In this paper, simple and easily interpreted conditions are found by using the technique of diffusion approximation. Formulae are given for the stationary distribution and means and variances of population fluctuations. The shape of the stationary distribution allows the stability of the coexistence to be evaluated.

Original languageEnglish (US)
Pages (from-to)251-266
Number of pages16
JournalTheoretical Population Biology
Issue number3
StatePublished - Dec 1989

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics


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