Some Stochastic Models And Methods To Infer Demographic Histories

Population genetics is a branch of genetics which quantifies biological evolutionary mechanism and provides solid theoretical foundation of evolution. The inference of demographic histories is a critical question to study the origin and evolution of human beings. Demographic histories such as migration, admixture and population expansions will have great effects on the genetic variations of the populations and leave plenty of information in the genetic data. Therefore, we can use the useful information hidden behind genetic data to infer demographic histories.With the development of sequencing technology and computational methods, we can obtain more and more public available genetic data easily. However, it is a challenging problem to characterize and apply the genetic data to infer demographic histories. In order to use the features of data, we should firstly describe the process of creation and variation of features. In this thesis, we build stochastic process to depict the biological process and then apply statistical inference methods to reconstruct the demographic history. Here we mainly focus on two types of recombination related genetic features:ancestral tracks and IBD segments.The first part of this thesis is to infer population admixture history by using ancestral tracks. Until now, the ancestral tracks based methods have the same flaw:we should firstly provide an admixture model when trying to infer population admixture history, and then estimate corresponding parameters under the given model. Nontheless, the fact is that we do not know the model ahead of time. The inference of history might be biased or even unreliable if the assumed model is far from the real situation. To address this question, we firstly deduce the theoretical distribution of ancestral tracks under general admixture model, which provides a theoretical foundation for our inference. Then we develop two new ancestral tracks based methods to infer demographic histories. First method named Admixlnfer can select optimal model and estimate corresponding parameters under three typical models. Good performances are observed in both extensive computer simulations and real datasets. Moreover, to solve the problem that select optimal model and estimate parameters under general model, we develop a second method named MultiWavelnfer. Specifically, we firstly use likelihood ratio test to determine the number of waves of admixture, then apply EM algorithm to estimate admixture parameters. Similarly, extensive computer simulations are used to validate the reliability and effectiveness of our method.The second part of this thesis is to infer population migration history based on IBD segments. Previous studies have proved that IBD segments are useful to infer recent demographic histories of populations. The key point to infer demographic histories is the calculation of distribution of coalescence time. However, under migration model, previous studies ignored the coalescent events before tMRCA and the joint effects of coalescent and migration, which could lead to inaccurate calculation of coalescence time. Here we adopt structured coalescent theory and use a continuous-time Markov process to describe the genealogical process under two-population model with migration. Then we apply Kolmogorov backward equation to calculate the distribution of coalescence time. With the distribution, we develop a new formula for estimating the IBD sharing and apply it to infer population migration histories. The simulation studies show that our method to estimate IBD sharing for this demographic model is robust and accurate.