Abstract
The large deviation principle is established for the Poisson-Dirichlet distribution when the parameterapproaches 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 �, then the large deviation rate function is the same as the neutral model; if the selection inten- sity grows at a linear or greater rate in �, then the large deviation rate function includes an additional term coming from selection. The application of these results to the heterozygote advantage model pro- vides an alternate proof of one of Gillespie's conjectures in (Theoret. Popul. Biol. 55 145-156).
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