# Stochastic Models in Population Genetics: The Impact of Selection and Recombination

by Rebekka Brink-Spalink

Date of Examination:2015-01-23

Date of issue:2015-03-27

Advisor:Prof. Dr. Anja Sturm

Referee:Prof. Dr. Anja Sturm

Referee:Prof. Dr. Dominic Schuhmacher

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## Abstract

### English

We consider gene genealogies from populations under selective pressure and take into account that genes can be reassembled during the reproduction process due to recombination. The main result is the derivation of an approximate distribution of the ancestral relationships of neutral genes in a sample taken out of a population after a so-called selective sweep. Such a sweep occurs if an advantageous mutation appears in one individual and then spreads in the population such that after some number of generations every individual in the population has this advantageous gene expression at the locus under selection. In this thesis, we investigate two different ways of modeling the evolution of a population which experiences such a selective sweep. The first model is a Moran model with selection and recombination and in particular constant population size N over time. Here, the resulting approximation holds true up to terms of order 1/log(N). The second approximation is based on a so-called Darwinian model with varying population size and birth and death rates depending on the current state of the population and the genetic type of an individual at the locus under selection. In this case, the approximate distribution is given in the limit of K to infinity, where K is the carrying capacity reflecting the ability of the environment to provide resources for a population. In the final chapter of the thesis, we briefly consider Lambda-coalescent processes which can be used to model genealogies of populations with skewed offspring distributions. In particular, we here describe a spatial algorithm on how to generate an ancestral recombination graph starting from such a general coalescent process.**Keywords:**stochastic population models; recombination; selection; selective sweep; stochastic processes