Asymptotic behavior of the Poisson-Dirichlet distribution for large mutation rate

• 成果类型: Article
• 署名作者: Dawson, Donald A.; Feng, Shui
• 署名单位: Carleton University; McMaster University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000818
• 发表日期: 2006
• 页码: 562-582
• 关键词: FLEMING-VIOT PROCESS; random discrete-distributions; NEUTRAL MUTATION; large deviations; diffusion-model; selection; size

摘要

The large deviation principle is established for the Poisson-Dirichlet distribution when the parameter theta approaches infinity. The result is then used to study the asymptotic behavior of the homozygosity and the Poisson-Dirichlet distribution with selection. A phase transition occurs depending on the growth rate of the selection intensity. If the selection intensity grows sublinearly in theta, then the large deviation rate function is the same as the neutral model; if the selection intensity grows at a linear or greater rate in theta, then the large deviation rate function includes an additional term coming from selection. The application of these results to the heterozygote advantage model provides an alternate proof of one of Gillespie's conjectures in [Theoret. Popul. Biol. 55 145-1561.