Self-loops in evolutionary graph theory: Friends or foes?
Fig 6
Average extinction and fixation time for the self-looped star graph and the standard star graph.
Here, we plot the average extinction and fixation time of a mutant for the self-looped (weighted) star graph (panel A) and the star graph (panel B) as a function of mutant’s relative fitness. Solid lines corresponds to the analytic results, Eqs 31 and 39. The circles represent Moran Bd simulations. Firstly, we observe that for both the graphs, the average fixation time of a mutant is higher than its extinction time, regardless of the mutant’s relative fitness. Secondly, the average fixation time peaks near neutrality for both of the graphs. Therefore, according to Eq 4, μth for the star graphs scales as the inverse average fixation time at neutrality. Because the fixation of a mutant takes longer on the self-looped star graph, the weak mutation rate approximation is more restrictive for the self-looped star graph than the star graph. (Parameters: N = 10, wild-type fitness, f = 1, and the number of independent realisations conditioned on mutant’s fixation or extinction are 2000).