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

Jeff S. Hatfield, Peter Chesson

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

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
Volume36
Issue number3
DOIs
StatePublished - 1989
Externally publishedYes

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coexistence
Mortality
Birth Rate
Population
birth rate
competitive exclusion
forest trees
benthos
distribution
analysis
organisms
Forests
rate
methodology
organism

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Diffusion analysis and stationary distribution of the two-species lottery competition model. / Hatfield, Jeff S.; Chesson, Peter.

In: Theoretical Population Biology, Vol. 36, No. 3, 1989, p. 251-266.

Research output: Contribution to journalArticle

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