Mathematical Sciences: Stochastic Models in Population Genetics and Molecular Evolution

首席研究员和来自英国的Donnelley博士将继续研究分子进化和种群生物学的数学模型。具体的问题是相当多样化的，并且建立在他们以前合作获得的结果之上。假设样本中等位基因的年龄顺序已知，将设计一个更有效的中性统计检验。渐近理论将表明，一系列可交换模型的年龄顺序等位基因频率的弱极限导致GEM分布。系谱瓮模型的规范表示将用于对种群的进化提供更详细的描述。从一个无限多位点模型的平稳种群中，将发现样本中分离位点的分布。新的统计方法将被开发用于分析同源序列对的取代率和发散时间。

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.