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Statistical methods have proven to be fundamental in the analyses of genetic data and have been used as a means to arrive at many novel biological discoveries; for example, these methods have helped researchers better understand human history, long-term evolutionary processes between species, and increased the power of studies with linkage-based imputation. Many methods in statistical genetics model sequence data along the genome and assumes that the data is generated from a tree; while some methods do not. Here, I talk about three PhD projects that encompass many classes of methods in statistical genetics. Two projects are connected in that they model nucleotide variation along the genome and assumes the data is generated from a tree, while the third project models data at the levels of reads and utilizes a popular class of methods based on an "Admixture'' model, which assumes no underlying tree. ,Trees connect all biological organisms on earth. At the most basic level, individuals within a population are related through a genealogical tree. These trees are influenced by population level parameters and can be characterized using coalescent theory. In my first project, the underlying tree structure is utilized to infer dispersal and population density in Europe across space and different time periods. At a higher level, individuals between species are related through a phylogenetic tree, which can be studied using methods from phylogenetics. In my second PhD project, phylogenetic-based methods for inferring positive selection are studied in both simulated and empirical datasets. ,However, many methods in statistical genetics do not assume an underlying tree, such as methods based on "Admixture'' models. In my third project, an Admixture model is used to model mismatches from sequencing reads in ancient DNA. Unlike tree models, Admixture models assume that each sample is unrelated and has an estimated grade of membership in each of K unrelated clusters that are estimated from the data. Taken together, my three PHD projects span a wide class of models in statistical genetics


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