Genealogical traits of spatial models in Population Genetics

在基因组数据分析中，能够处理地理参照数据的方法(即纳入关于采样地点的信息)日益重要。例如，这是病毒学的一个重要特征，在病毒学中，数据的地理来源在分析中非常重要，通常在种群的进化史受到其栖息地的地理特征严重影响的情况下。空间Lambda-Fleming-Viot过程给出了一种模拟空间种群的方法。这一过程表现出良好的概率特征，并被认为在几个方面优于包括空间成分在内的其他群体遗传学方法。然而，到目前为止，人们对在这一过程的假设下产生的样本数据的统计特性知之甚少，特别是关于样本谱系。该项目的主要目的是提供对该过程的一些关键特征的洞察。将特别关注聚并率和概率的推导。在此基础上，目标将是在给定样本成员当前位置的情况下对样本谱系的概率空间进行近似描述。这些结果将被用于执行贝叶斯统计。特别是，应提供一种软件实现，它能够通过马尔科夫链蒙特卡罗模拟从数据中估计总体遗传参数。由于这一方法的优点是利用了有关基本模型的统计特性的先验知识，因此项目第一部分的结果将大大改进现有方法。最后，计划将这些改进的方法应用于流感和水稻黄斑驳病毒的数据。

In the analysis of genomic Data, methods that allow for the treatment of geo-referenced data (i.e., the inclusion of information on sampling locations), are of increasing importance. For example, this is an important feature in virology, where the geographical origin of data is very important in the analysis, and generally in cases where the evolutionary history of a population is heavily influenced by geographical traits of its habitat. One approach to model populations in space is given by the spatial Lambda-Fleming-Viot-Process. This process exhibits favorable probabilistic traits and is considered to be in several ways superior to other approaches of Population Genetics including a spatial component. However, so far little is known about the statistical properties of sample data generated under the assumption of this process, in particular with respect to sample genealogies. The primary aim of this project is to provide insight on some key features of the process. Special focus will be placed on the derivation of coalescence rates and probabilities. Following up on that, the goal will be an approximate description of the probability space of sample genealogies, given the present locations of sample members. These results will be utilized to perform Bayesian Statistics. In particular, an implementation in software shall be provided, which is capable of estimating population-genetical parameters from data by Markov-Chain Monte-Carlo simulation. Since the advantages of this approach result from the use of prior knowledge on statistical properties of the underlying model, the results from the first part of the project will provide a substantial improvement to the existing methods. Finally, it is planned to apply these improved methods to data from Influenza and Rice Yellow-Mottle viruses.