Mathematical Sciences: Stochastic Models in Population Genetics and Molecular Evolution

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The principal investigator, along with Dr. Donnelley from England, will continue the research in mathematical models in molecular evolution and population biology. The particular problems are quite diverse and build on the results previously obtained by their collaboration. A more powerful statistical test for neutrality will be designed assuming that the age- ordering of the alleles in the sample is known. Asymptotic theory will show that the weak limit for the age-ordered allele frequencies of a range of exchangeable models lead to the GEM distribution. The canonical representation of the genealogical urn model will be used to provide more detailed description of the evolution of the population. Distribution of the segregating sites in a sample from a stationary population of an infinitely- many sites model will be found. New statistical methods will be developed for the analyses of substitution rates and divergence times in pairs of homologous sequences.