Effect of the degree of an initial mutant in Moran processes in structured populations.

Abstract

We study effects of the mutant's degree on the fixation probability, extinction, and fixation times in Moran processes on Erdös-Rényi and Barabási-Albert graphs. We performed stochastic simulations and used mean-field-type approximations to obtain analytical formulas. We showed that the initial placement of a mutant has a significant impact on the fixation probability and extinction time, while it has no effect on the fixation time. In both types of graphs, an increase in the degree of an initial mutant results in a decreased fixation probability and a shorter time to extinction. Our results extend previous ones to arbitrary fitness values.