Multispecies Lottery Competition: A Diffusion Analysis
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.
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- 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
- Chesson, P. L. 1991. A need for niches? Trends in Ecology and Evolution 6: 26–28.Google Scholar
- Chesson, P. L. 1994. Multispecies competition in variable environments. Theoretical Population Biology 45: 227–276.Google Scholar
- 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
- Gillespie, J. H. 1991. The Causes of Molecular Evolution. Oxford University Press.Google Scholar
- Hatfield, J. S. 1986. Diffusion analysis and stationary distribution of the lottery competition model. Ph.D. diss. Ohio State University, Columbus.Google Scholar
- 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
- Karlin, S., and H. M. Taylor. 1981. A Second Course in Stochastic Processes. Academic Press, New York.Google Scholar
- 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