Mathematical Sciences: Stochastic Models in Population Genetics and Molecular Evolution

首席研究员，沿着和来自 英国，将继续在数学模型的研究， 分子进化和种群生物学。 的特定 问题是相当多样化的，并建立在以前的结果 通过他们的合作。 更强大的统计 中性测试将假设年龄- 样品中等位基因的排序是已知的。 渐近 理论将表明，年龄有序等位基因的弱极限 一系列可交换模型的频率导致GEM 分布 家谱的规范表示 瓮模型将被用来提供更详细的描述 人口的演变。 偏析分布 在一个样本中的一个固定的人口无限- 将发现许多网站模型。新的统计方法将 为分析替代率和差异而开发的 在成对的同源序列中。

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.