Computational and mathematical methods for population genetics analysis of multi-locus data under selection and strong recombination

马尔可夫扩散过程被用来模拟种群中遗传信息的动态变化。中性的单基因情况已经扩展到包括选择和重组。这与描述个体祖先的联合过程相辅相成。从一个群体中抽样某一遗传构型的概率可以通过对合并历史的重要性抽样来估计。该方法的中心目标是已观察到给定遗传结构的额外抽样个体的条件抽样分布。我将应用Paul和Song(2010)介绍的条件抽样分布来推断缺失序列数据，并使用已建立的算法来推断混合群体中的局部祖先，所述算法使用条件抽样分布基于相关个体的已知数据来更新个体遗传信息。我还将开发一种方法，通过对不完整的历史进行重要性抽样来归因于缺失数据。由于有人认为选择的检测必须考虑基因座之间的上位相互作用来解释某些疾病的遗传，因此我将调查上位性和无上位性选择对基因座之间相关性的统计测量的影响，以开发一种上位性检验。为了促进这一点，我还将在Jenkins和Song(2010)给出的抽样概率的渐近扩展中引入上位选择。全基因组关联研究检测影响疾病的遗传标记依赖于遗传序列的连锁结构。连锁不平衡起着重要作用，了解其动力学是至关重要的。宿主博士后已经证明，对于大的重组概率，连锁不平衡可以用服从的扩散过程来近似。我想要推导出一个近似于大重组概率的祖先的过程，并分析它对这种扩散的二元性。

Markov diffusion processes are used to model the dynamics of genetic information in a population. The neutral one-locus case has been extended to include selection and recombination. This is complemented by coalescent processes describing the ancestry of individuals. The probability of sampling a certain genetic configuration from a population can be estimated via importance sampling on coalescent histories. A central object in this approach is the conditional sampling distribution of an additionally sampled individual, having already observed a given genetic configuration.I will apply the conditional sampling distribution introduced by Paul and Song (2010) to impute missing sequence data and to infer local ancestry in admixed populations using established algorithms that update individual genetic information based on known data for related individuals using the conditional sampling distribution. I will also develop an approach to impute missing data via importance sampling on incomplete histories.Since it has been argued that detection of selection has to account for epistatic interaction between loci to explain the inheritance of certain diseases, I will investigate the influence of epistatic and epistasis-free selection on statistical measures of correlation among loci to develop a test for epistasis. To foster this, I will also introduce epistatic selection into the asymptotic expansion of the sampling probability given by Jenkins and Song (2010).Genome-wide association studies detecting genetic markers that influence diseases rely on the linkage structure of genetic sequences. Linkage disequilibrium plays an important role and understanding its dynamics is essential. The hosts postdoc has shown that for large recombination probabilities the linkage disequilibrium can be approximated by an amenable diffusion process. I want to derive a process that approximates the ancestry for large recombination probabilities and analyse its duality to this diffusion.