Analytical calculation of average fixation time in evolutionary graphs

The ability of a mutant individual to overtake the whole of a population is one of the fundamental problems in evolutionary dynamics. Fixation probability and Average Fixation Time (AFT) are two important parameters to quantify this ability. In this paper we introduce an analytical approach for exact calculation of AFT. Using this method we obtain AFT for two types of evolutionary graphs: cycle graph, as a highly homogeneous graph and star graph, as a highly heterogeneous graph. We use symmetries of these graphs to calculate AFT. Analytical results are confirmed with simulation. We also examine the effect of adding some random edges to each of these structures.