Evolutionary dynamics and fixation probabilities in directed networks

In this paper, we investigate the evolutionary dynamics in directed and/or weighted networks. We study the fixation probability of a mutant in finite populations in stochastic voter-type dynamics for several update rules. The fixation probability is defined as the probability of a newly introduced mutant in a wild-type population taking over the entire population. In contrast to the case of undirected and unweighted networks, the fixation probability of a mutant in directed networks is characterized not only by the degree of the node that the mutant initially invades but also by the global structure of networks. Consequently, the gross connectivity of networks such as small-world property or modularity has a major impact on the fixation probability.