人口历史推断的随机模型与方法研究

发布时间：2018-04-27 01:07

本文选题：群体遗传学 + 人口历史　；参考：《北京交通大学》2016年博士论文

【摘要】：群体遗传学是一门定量地研究生物进化机制的遗传学科,它为揭示进化原理和进化过程提供坚实的理论依据。人口历史推断是群体遗传学中至关重要的问题,有利于我们更好地了解人类的起源与发展。群体迁移,群体混合以及群体扩张等人口历史事件会对基因的遗传变异产生巨大影响,在遗传数据中留下很多有用的信息,因此我们可以利用这些信息推断人口历史。随着测序技术和计算方法的不断发展,我们可以获得越来越多的遗传特征,如何更有效地利用遗传特征推断人口历史是一个非常有挑战性的问题。在本文中,我们通过构建随机模型刻画遗传特征的产生和变化过程,利用统计推断的方法实现人口历史的重构。本文主要考虑两种与基因重组密切相关的遗传特征——祖先片段和IBD片段,研究基于这两种特征推断人口历史的随机模型与方法。本文的第一项工作是研究基于祖先片段推断人口混合历史的随机模型与方法。现在已有的推断人口混合历史的方法都有一个缺陷：在推断混合历史时,需事先设定一个混合模型,然后在设定的模型下进行推断。但在实际应用中,真实的混合模型是未知的,如果设定的混合模型与真实模型相差很大,则推断出的混合历史往往不准确。为了解决这个问题,本文给出一般混合模型的刻画,并首次推导一般混合模型下祖先片段长度的理论分布,为人口混合历史的推断提供理论基础。基于祖先片段长度的分布,我们开发了两种推断人口混合历史的方法,第一种方法——AdmixInfer方法,实现三个经典混合模型下最优模型的选择以及混合历史中参数的估计。我们通过大量的模拟数据验证了AdmixInfer方法的有效性和稳定性,同时在真实数据的应用中,AdmixInfer方法也有很好的表现。更进一步,为了解决一般混合模型下人口混合历史的推断问题,我们开发了第二种方法——MultiWaveInfer方法,采用似然比检验和EM算法估计混合波数以及混合历史中的参数。同样的,大量的模拟数据验证了Multi WaveInfer方法的有效性和稳定性。本文的另一项工作是研究基于IBD片段推断人口迁移历史的随机模型与方法。IBD片段已被证实非常适合重构近代的人口历史。利用IBD片段推断人口历史,关键在于构建人口模型并计算溯祖时间的分布。前人利用IBD片段推断人口迁移历史时,忽略了溯祖时间之前溯祖事件的信息以及溯祖事件与迁移事件的相互影响,使得溯祖时间的分布不准确。为弥补这个缺陷,本文提出了一种新的推断人口迁移历史的方法-——MIBD方法,采用带结构的溯祖理论,用一个连续时间的马氏过程描述两个群体迁移模型下的溯祖过程,并利用Kolmogorov向后方程计算溯祖时间的分布。在此分布下,我们可以估计IBD共享率,进而推断人口的迁移历史。模拟结果显示,在两个群体的迁移模型下,MIBD方法估计的IBD共享率是非常稳定和准确的。
[Abstract]:Population genetics is a genetic discipline that quantitatively studies the mechanism of biological evolution, which provides a solid theoretical basis for revealing the principles and processes of evolution. Population history inference is a very important problem in population genetics, which is helpful for us to better understand the origin and development of human beings. Population historical events, such as population migration, population mixing and population expansion, will have a great impact on genetic variation, leaving a lot of useful information in genetic data, so we can use these information to infer population history. With the development of sequencing technology and computational methods, we can obtain more and more genetic characteristics. How to use genetic characteristics more effectively to infer population history is a very challenging problem. In this paper, we use the statistical inference method to reconstruct the population history by constructing a stochastic model to describe the process of generation and change of genetic characteristics. In this paper, two genetic characteristics closely related to gene recombination, ancestral fragments and IBD fragments, are considered, and the stochastic models and methods for inferring population history based on these two characteristics are studied. The first work of this paper is to study stochastic models and methods for inferring population mixed history based on ancestral fragments. There is one drawback in the existing methods for inferring the mixed history of population: in order to infer the mixed history, a mixed model should be set up in advance and then inferred under the set model. But in practical application, the real mixed model is unknown. If the set mixing model is very different from the real model, the inferred mixing history is often inaccurate. In order to solve this problem, this paper gives a description of the general mixed model, and deduces the theoretical distribution of the length of ancestral fragments under the general mixed model for the first time, which provides a theoretical basis for the inference of population mixing history. Based on the distribution of ancestral fragment length, we develop two methods to infer population mixing history. The first method, AdmixInfer method, realizes the selection of optimal models under three classical mixed models and the estimation of parameters in mixed history. The validity and stability of the AdmixInfer method are verified by a large number of simulation data. At the same time, the AdmixInfer method also has a good performance in the application of real data. Furthermore, in order to solve the problem of inferring population mixing history in general mixed model, we develop a second method, Multiwave Infer method, which uses likelihood ratio test and EM algorithm to estimate the mixed wavenumber and the parameters in the mixed history. Similarly, a large number of simulation data verify the effectiveness and stability of the Multi WaveInfer method. Another work of this paper is to study the stochastic models and methods for inferring the history of population migration based on IBD fragments. IBDfragments have been proved to be very suitable for reconstructing modern population history. The key to infer population history by using IBD fragment is to build population model and calculate the distribution of traceability time. When people used IBD fragments to infer the history of population migration, they ignored the information of the anatomic events before the date of tracing and the interaction between the events and the events of migration, which made the distribution of the time of traceback inaccurate. In order to remedy this defect, a new method of inferring the history of population migration, the MIBD method, is proposed in this paper. Using the theory of traceback with structure, a continuous time Markov process is used to describe the traceback process in two population migration models. The Kolmogorov backward equation is used to calculate the distribution of traceback time. Under this distribution, we can estimate the IBD sharing rate and infer the migration history of the population. The simulation results show that the IBD sharing rate estimated by the MIBD method is very stable and accurate under the migration model of two populations.
【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：Q347

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