Simulation algorithms for integrals of a class of sampling distributions arising in population genetics

摘要

Efficient stochastic algorithms are presented in order to simulate allele configurations distributed according to a family π_A, 0 < A < ∞, of exchangeable sampling distributions arising in population genetics. Each distribution π_A has two parameters n and k, the sample size and the number of alleles, respectively. For A → 0, the distribution π_A is induced from neutral sampling, whereas for A → ∞, it is induced from Maxwell-Boltzmann sampling. Three different Monte Carlo methods (independent sampling procedures) are provided, based on conditioning, sequential methods and a generalization of Pitmans 'Chinese restaurant process". Moreover, an efficient Markov chain Monte Carlo method is provided. The algorithms are applied to the homozygosity test and to the Ewens-Watterson-Slatkin test in order to test the hypothesis of selective neutrality.