Markov chain Monte Carlo methods in population genetics

The properties of genealogical trees for samples of DNA sequences are studied using the methods of coalescent theory. The sample is assumed to be taken from a large non-structured population. The evolution of the DNA region is considered neutral, and the finite-sites model of mutation is adopted.; A version of a Markov chain Monte Carlo [MCMC] method for estimation of the mutation rate and properties of the genealogical tree of a sample of individuals from the same population is described. A new proposal kernel as well as some tests for stationarity of the process are also presented. A version of the algorithm modified for the case of the infinite-sites mutation model is compared to the existing algorithms. Several practical applications of the method are considered. Two major results concern the effects of rate variation on ancestral inference, and estimation of the age of a unique event polymorphism. The method is used for analysis of Nuu Chah Nulth and Yakima data sets. A modification of the general scheme which allows inference about the parameters of interest from the different types of data, i.e. from restriction fragment length polymorphism data, is presented. The method is illustrated with an analysis of Drosophila recens data set. Difficulties of the problem and some possible approaches are also considered. The neutrality test of Depaulis and Veuille is discussed. With the use of simulation studies it is shown that the power of this test depends on the unknown mutation parameter, and may be inaccurate when the true value of the mutation rate is not well-supported by the data. The problem of reconstructing haplotypes from the genotypes of a sample of individuals from a diploid population is considered. A modified version of the general algorithm which uses genotypic data from the sample of unrelated individuals is presented. As a conclusion, directions of ongoing and future work are briefly discussed. A MCMC approach to fine-scale mapping using population data is introduced and illustrated on the data set from Genetic Analysis Workshop 12.