Article ID Journal Published Year Pages File Type
1156198 Stochastic Processes and their Applications 2009 13 Pages PDF
Abstract

A large deviation principle is established for the Poisson–Dirichlet distribution when the mutation rate θθ converges to zero. The rate function is identified explicitly, and takes on finite values only on states that have finite number of alleles. This result is then applied to the study of the asymptotic behavior of the homozygosity, and the Poisson–Dirichlet distribution with selection. The latter shows that several alleles can coexist when selection intensity goes to infinity in a particular way as θθ approaches zero.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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