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Abstract

The Moran process is widely used for modeling stochastic dynamics of finitely large populations. It describes the invasion process of a novel mutant into a resident population. Generally, the population is assumed to be well-mixed, which is a rather strong assumption. Studying the Moran process on graphs instead of unstructured populations is a recent approach to overcome this assumption. Some graph structures increase the fixation probability of a mutant that has a fitness advantage compared to the resident population. Graphs with this property are called amplifiers of selection. However, simulations show that the time until fixation increases considerably on those graphs. The objective of this thesis is to analyze different graphs of small size with respect to the fixation time. Simulations support the results for larger population size, where analytical approaches are unfeasible. We show that depending on the initial graph structure, the removal of one link can either lead to an increase or decrease in fixation time. This result is surprising and counterintuitive. Another interesting finding is that the shortest average fixation time does not only depend on the mutant’s starting node. But instead, different starting nodes are preferable, depending on the mutant’s fitness.