Translator Disclaimer
May 2006 Asymptotic behavior of the Poisson–Dirichlet distribution for large mutation rate
Donald A. Dawson, Shui Feng
Ann. Appl. Probab. 16(2): 562-582 (May 2006). DOI: 10.1214/105051605000000818

Abstract

The large deviation principle is established for the Poisson–Dirichlet distribution when the parameter θ 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 θ, 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 θ, 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. 55 145–156].

Citation

Download Citation

Donald A. Dawson. Shui Feng. "Asymptotic behavior of the Poisson–Dirichlet distribution for large mutation rate." Ann. Appl. Probab. 16 (2) 562 - 582, May 2006. https://doi.org/10.1214/105051605000000818

Information

Published: May 2006
First available in Project Euclid: 29 June 2006

zbMATH: 1119.92046
MathSciNet: MR2244425
Digital Object Identifier: 10.1214/105051605000000818

Subjects:
Primary: 60F10
Secondary: 92D10

Rights: Copyright © 2006 Institute of Mathematical Statistics

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.16 • No. 2 • May 2006
Back to Top