COALESCENT THEORY AND ANALYSIS OF DNA POLYMORPHISM

本研究项目的目标是将联合理论发展到 DNA多态信息力量的水平， 最终解决遗传变异，才能完全实现。这个 理论有着广泛的应用范围，从研究突变率到 对我们人类共同祖先的时间估计。 具体目标包括： A.发展关于频率的合并理论 隔离类型。我们建议解析地推导出平均值，， 分离类型出现频率的方差和协方差 模型，来自经典模型，假设没有重组和相等的速率 所有站点的突变转变为更现实的模式，既允许 不同位点的重组率和突变率不均 序列。这一理论将使这一理论的应用。 聚结效率高。 B.开发高效的统计方法来估计theta。 我们提出了一个框架，它将利用系统发育 信息和分离类型的频率，以估计 关键参数theta=4Nemu。 C.开发强大的统计方法来检验假设 对西塔的担忧。我们建议开发统计测试，用于 联合理论背后的假设，包括假设 突变的中立性，通过利用 分离类型的出现频率。 D.开发一种直观的方法来识别遗传疾病的主要原因 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 不同假设下隔离类型的频率，包括 选择，种群细分。 即估计到达共同祖先的时间并确定模式和 人口增长的速度。我们提出了一种极大似然方法 估计到个体最近共同祖先的时间 在样本中。这种似然方法还允许人们分析 有效种群数量变化的模式和速度。

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.