COALESCENT THEORY AND ANALYSIS OF DNA POLYMORPHISM

本研究的目的是发展聚结理论， DNA多态性信息能力， 最终解决遗传变异，可以完全实现。 的 理论有着广泛的应用，从研究突变率到 我们人类的共同祖先的时间估计。 具体目标包括： a. 发展了聚结理论， 分离类型。 我们建议通过分析得出平均值， 下分离类型频率的方差和协方差 模型，从经典的假设没有重组和平等的比率 所有位点的突变，以更现实的模型， 不同位点的重组和突变率不等， 序列的 该理论将使理论的应用， 聚结高效。 B. 开发出高效的统计方法来估计θ。 我们提出了一个框架，这将利用系统发育 信息和分离类型的频率，以估计 关键参数theta=4Nemu。 C. 发展强有力的统计方法来检验假设 关注theta 我们建议开发统计测试， 结合理论的基本假设，包括假设 突变的中立性，通过利用 分离类型的频率。 D. 开发一种直观的方法来识别遗传病的主要原因， DNA序列的变异 我们建议使用图形比较 观察到的分离类型的频率与预期的 不同假设下的分离类型频率，包括 选择，人口细分。 e. 估计共同祖先的时间并确定模式， 人口增长速度。 我们提出了一个最大似然方法， 估计个体最近共同祖先的时间 在一个样本中。 这种可能性方法还允许人们分析 有效人口规模变化的模式和速度。

The goal of this research project is to develop the coalescent theory to the level so that power of the information of DNA polymorphism, the ultimate resolution of genetic variation, can be fully realized. The theory has wide applications ranging from studying mutation rate to the estimation of the time to the common ancestor of our human beings. Specific aims include: a. to develop the theory of coalescent for the frequencies of segregating types. We propose to derive analytically the mean,, variances and covariances of the frequencies of segregating types under models, from the classic which assumes no recombination and equal rates of mutations for all sites to more realistic model that allows both recombination and unequal rates of mutations at different sites of sequences. The theory will make the application of the theory of coalescent highly efficient. b. to develop highly efficient statistical methods for estimating theta. We propose a framework, which will utilize both the phylogenetic information and the frequencies of segregating types, to estimate the crucial parameter theta=4Nemu. c. to develop powerful statistical method for testing the hypotheses concerned about theta. We propose to develop statistical tests for the assumptions underlying the coalescent theory, including the assumption of neutrality of mutations, by utilizing the information contained in frequencies of segregating types. d. to develop a visual method for identifying the main causes of genetic variations at DNA sequences. We propose to use graphical comparison of the observed frequencies of segregating types with the expected frequencies of segregating types under different assumptions, including selection, population subdivision. e. to estimate the time to common ancestor and determine the pattern and speed of population growth. We propose a maximum likelihood method for estimating the time to the most recent common ancestor of the individuals in a sample. This likelihood method also allows one to analyze the pattern and speed of changes in the effective population size.