Multispecies Lottery Competition: A Diffusion Analysis

  • Jeff S. Hatfield
  • Peter L. Chesson

Abstract

The lottery model is a stochastic competition model designed for space-limited communities of sedentary organisms. Examples of such communities may include coral reef fishes (Chesson & Warner 1981), aquatic sessile organisms (Fagerstrom 1988), and plant communities such as trees in a tropical forest (Leigh 1982; Hatfield et al., in press). The lottery model, and its properties and behavior, has been discussed previously (Chesson & Warner 1981; Chesson 1982, 1984, 1991, 1994; Warner & Chesson 1985; Chesson & Huntly 1988). Furthermore, explicit conditions for the coexistence of two species and the stationary distribution of the two-species model were determined (in Hatfield & Chesson 1989) using an approximation with a diffusion process (Karlin & Taylor 1981). However, a diffusion approximation for the multispecies model (for more than two species) has not been reported previously, and a stagestructured version has not been investigated. The stage-structured lottery model would be more reasonable for communities of long-lived species in which recruitment or death rates depend on the age or stage of the individuals (e.g., trees in a forest). In this chapter, we present a diffusion approximation for the multispecies lottery model and also discuss a stage-structured version of this model.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. Chesson, P. L. 1982. The stabilizing effect of a random environment. Journal of Mathematical Biology 15: 1–36.CrossRefGoogle Scholar
  2. Chesson, P. L. 1984. The storage effect in stochastic population models. Pp. 76–89 in S. A. Levin and T. Hallam, eds., Mathematical Ecology. Lecture Notes in Biomathematics 54. Springer-Verlag, New York.Google Scholar
  3. Chesson, P. L. 1991. A need for niches? Trends in Ecology and Evolution 6: 26–28.Google Scholar
  4. Chesson, P. L. 1994. Multispecies competition in variable environments. Theoretical Population Biology 45: 227–276.Google Scholar
  5. Chesson, P. L., and N. Huntly. 1988. Community consequences of life-history traits in a variable environment. Annales Zoologici Fennici 25: 5–16.Google Scholar
  6. Chesson, P. L., and R. R. Warner. 1981. Environmental variability promotes coexistence in lottery competitive systems. American Naturalist 117: 923–943.CrossRefGoogle Scholar
  7. Fagerstrom, T. 1988. Lotteries in communities of sessile organisms. Trends in Ecology and Evolution 3: 303–306.PubMedCrossRefGoogle Scholar
  8. Gillespie, J. H. 1980. The stationary distribution of an asymmetrical model of selection in a random environment. Theoretical Population Biology 17: 129–140.PubMedCrossRefGoogle Scholar
  9. Gillespie, J. H. 1991. The Causes of Molecular Evolution. Oxford University Press.Google Scholar
  10. Hatfield, J. S. 1986. Diffusion analysis and stationary distribution of the lottery competition model. Ph.D. diss. Ohio State University, Columbus.Google Scholar
  11. Hatfield, J. S., and P. L. Chesson. 1989. Diffusion analysis and stationary distribution of the two-species lottery competition model. Theoretical Population Biology 36: 251–266.CrossRefGoogle Scholar
  12. Hatfield, J. S., W. A. Link, D. K. Dawson, and E. L. Lindquist. In press. Coexistence and community structure of tropical trees in a Hawaiian montane rain forest. Biotropica.Google Scholar
  13. Karlin, S., and H. M. Taylor. 1981. A Second Course in Stochastic Processes. Academic Press, New York.Google Scholar
  14. Keilson, J. 1965. A review of transient behavior in regular diffusion and birth-death processes. Part II. Journal of Applied Probability 2: 405–428.CrossRefGoogle Scholar
  15. Leigh, E. G., Jr. 1982. Introduction: Why are there so many kinds of tropical trees? Pp. 63–66 in E. G. Leigh, A. S. Rand, and D. W. Windsor, eds., The Ecology of a Tropical Forest:Seasonal Rhythms and Long-Term Changes. Smithsonian Institution Press, Washington, D.C.Google Scholar
  16. Seno, S., and T. Shiga. 1984. Diffusion models of temporally varying selection in population genetics. Advances in Applied Probability 16: 260–280.CrossRefGoogle Scholar
  17. Warner, R. R., and P. L. Chesson. 1985. Coexistence mediated by recruitment fluctuations: A field guide to the storage effect. American Naturalist 125: 769–787.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Jeff S. Hatfield
  • Peter L. Chesson

There are no affiliations available

Personalised recommendations