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

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 …