Mathematical Sciences: Stochastic Models in Population Genetics

9505129唐纳利摘要这项拟议的研究涉及三大领域。这些问题中的第一个涉及衡量价值的人口模型。用粒子表示法研究了一类一般的“中性”过程(包括Dawson-Watanabe和Fleming-Viot)的性质及其诱导的谱系结构。该提案的一个主要目的是扩展这一结构，最显著的是纳入选择(在空间环境中相当于位置相关的分枝率)，但也(在遗传学背景下)允许重组和种群亚结构。出于对人类种群遗传数据的解释问题的驱使，研究人员和他的同事研究了一般模型的特定子类，以期了解关于种群动态的各种假设以及可能的人口相关性对系谱的影响，从而对遗传数据的影响。该提案的第二个领域涉及地理结构的人口遗传学模型的性质。这些模型中与结合时间相关的最新结果允许显式计算与分子DNA数据相关的突变结构(超越无限等位基因)的同一性度量的矩。相反，对模型的理解激发了对分子遗传数据的种群分化度量(以及相关估计值)的研究，这些数据推广了赖特的F_st系数。该提案的第三个领域涉及将现有和预期的理论结果应用于遗传数据分析中的统计问题。这些问题包括针对中立性的一大类选择性模型的精确似然比(因此也包括有效的推理程序)、在测试中立性时利用等位基因年龄顺序信息的可能性、从连锁基因样本估计进化参数的关联结构、以及从单e-座位数据对某些进化参数的(非)一致估计值的(非)存在。该项目致力于促进我们对进化过程的理解。数学模型的发展使人们能够检验特定进化机制的后果：有人可能会问，如果进化按照下面的方式进行，我们会在基因数据中期待什么样的模式？数学建模是必要的，因为许多进化力量在极长的时间尺度上运行，对此不可能进行直接观察或实验。然后，将模型预测与实际遗传数据进行比较，可以洞察假设的机制在多大程度上起作用。调查者在一般层面上研究关于感兴趣人口的结构和人口统计的特定假设的后果。该项目的具体方面涉及人类人口进化的模型。在解释遗传数据时出现的各种统计问题也包括在内。

9505129 Donnelly Abstract The proposed research falls in three broad areas. The first of these concerns measure-valued population models. A particle representation is used to study properties of a general class (including the Dawson-Watanabe and Fleming-Viot) of "neutral" processes and their induced genealogical structure. A major aim of the proposal is to extend this construction, most notably to incorporate selection (equivalently location dependent branching rates in the spatial setting), but also (in the genetics context) to allow for recombination and population substructure. Motivated by problems in the interpretation of human population genetic data, the investigator and his colleagues study particular subclasses of the general models with a view to understanding the effects on genealogy, and hence on genetic data, of various assumptions about population dynamics, and possible demographic correlations. A second area of the proposal concerns properties of geographically structured population genetics models. Recent results relating to coalescence times in these models allow explicit calculation of moments of identity measures for mutation structures (beyond infinite alleles) relevant to molecular DNA data. Conversely, an understanding of the models motivates a study of measures of population differentiation (and associated estimators) for molecular genetic data which generalize Wright's F_st coefficient. The third area of the proposal concerns the application of existing and anticipated theoretical results to statistical questions in the analysis of genetic data. These include exact likelihood ratios for a wide class of selective models against neutrality (and hence efficient inference procedures), the potential for use of information on the age order of alleles in testing neutrality, the correlation structure of estimates of evolutionary parameters from samples of linked genes, and the (non-)existence of consistent estimators of certain evolutionary parameters from singl e-locus data. The project is concerned with advancing our understanding of evolutionary processes. The development of mathematical models allows an examination of the consequences of particular evolutionary mechanisms: one may ask "if evolution acted in the following way, what sort of patterns would we expect in genetic data?". Mathematical modeling is necessary because many evolutionary forces operate over extremely long time scales for which direct observation, or experimentation, is impossible. Comparisons of model predictions with actual genetic data then provides insight into the extent to which the posited mechanisms are acting. The investigator studies, at a general level, the consequences of particular assumptions about the structure and demography of populations of interest. Particular aspects of the project relate to models for the evolution of human populations. Various statistical questions which arise in the interpretation of genetic data are also included.