Mathematical Sciences: Problems in Population Genetics

将研究使用DNA序列数据的数学模型，以估计过去在生物物种中起作用的突变数量和达尔文选择的数量。这些方法是基于同一基因的一组个体的一组对齐的DNA序列内的位点配置分布。这项技术既可以应用于“沉默位点”（不改变基因产物），也可以应用于“替代位点”（产生不同的蛋白质或酶）。两种突变率之比可以估计蛋白质中可能发生的非致死性变化的数量，而沉默位点的选择率可以估计密码子偏倚。这些方法将扩展并应用于来自各种物种的各种基因的DNA序列，以及来自两个或多个相关物种的对齐DNA序列。后者将允许分析更多的数据，并将允许估计相关物种之间的选择差异。还将研究其他扩展和类似程序。将研究使用DNA序列数据的数学模型，以估计过去在生物物种中起作用的突变数量和达尔文选择的数量。这些方法将扩展并应用于来自各种物种的各种基因的DNA序列，以及来自两个或多个相关物种的对齐DNA序列。后者将允许分析更多的数据，并将允许估计相关物种之间的选择差异。还将研究其他扩展和类似程序。

Mathematical models will be studied that use DNA sequence data to estimate the amount of mutation and the amount of Darwinian selection that have acted in the past within a biological species. These methods are based on the distribution of site configurations within a set of aligned DNA sequences from a set of individuals at the same gene. The technique can be applied both at ``silent sites'' (which do not change the gene product) and ``replacement sites'' (which cause a different protein or enzyme). The ratio of the two mutation rates gives an estimate of the number of nonlethal changes possible in the protein, and selection rates at silent sites give an estimate of codon bias. These methods will be extended and applied to DNA sequences from a variety of genes in a variety of species, and to aligned DNA sequences from two or more related species. The latter will allow more data to be analyzed, and will allow estimation of the selective differences between related species. Other extensions and similar procedures will also be studied. Mathematical models will be studied that use DNA sequence data to estimate the amount of mutation and the amount of Darwinian selection that have acted in the past within a biological species. These methods will be extended and applied to DNA sequences from a variety of genes in a variety of species, and to aligned DNA sequences from two or more related species. The latter will allow more data to be analyzed, and will allow estimation of the selective differences between related species. Other extensions and similar procedures will also be studied.