Evolutionary dynamics and fixation probabilities in directed networks

TL;DR

This paper explores how the structure of directed and weighted networks influences the likelihood that a new mutant will take over a population, highlighting the importance of global network features.

Contribution

It introduces a comprehensive analysis of fixation probabilities in directed networks, emphasizing the role of global network properties like small-worldness and modularity.

Findings

Fixation probability depends on global network structure.

Directed networks show different fixation dynamics than undirected ones.

Network features like small-world and modularity significantly impact fixation chances.

Abstract

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 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.