Population genetic models with selection fluctuating environments and population structure$nvorgelegt von Elisabeth Sester Huss Abstract: This thesis consists of three parts each dealing with different questions related to population genetics. We start with the study of the effect of natural selection on genealogies. We make use of the theory on tree valued Fleming Viot processes that describe the evolution of genealogical trees to compute the Laplace transform of the tree length both in the neutral and in the selective setting. We show that trees are shorter in the selective case (under the so called Laplace transform order) than trees under neutrality an assumption already widely believed to be true in the field of biology.<br>In the second part we work with a mutation selection model in a fluctuating environment by introducing a modifier locus determining the mutation rate at a second locus. Fitness acts on the second locus and changes as the environment fluctuates. For a fast fluctutating environment we obtain limit results for the evolution of allele frequencies and apply them to a two type setting in which we compute the fixation probability for the higher mutation rate.<br>The last part focuses on analysing human DNA samples and estimating their heritage. The aim is to extend the already existing models for inferring individual admixture proportions a vector of which each entry corresponds to the fraction of ones genome originating from a certain population. We develop a method that delivers individual admixture proportions of an individuals parents. This enables us to test whether the admixture of two populations has occured only recently or several generations ago. We apply both the already existing method and our new method to the 1000 genomes dataset and test the accuracy of their outputs by computing the distance to their true admixture proportions