Fixation probability on clique-based graphs

TL;DR

This paper investigates how the structure of clique-based graphs influences the fixation probability of mutants in the Moran process, revealing conditions for suppression and amplification effects.

Contribution

It introduces new clique-based graph families and analyzes their effects on fixation probability, highlighting the importance of overall structure over degree or heterogeneity.

Findings

Complete suppression of fixation with generalized clique-wheel graphs.

Clique-star graphs act as amplifiers.

Graph structure impacts fixation probability more than degree or heterogeneity.

Abstract

The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with the generalized clique-wheel graph in the limit of small wheel-clique ratio and infinite size. The family of clique-star is an amplifier, and clique-arms graph changes from amplifier to suppressor as the fitness of the mutant increases. We demonstrate that the overall structure of a graph can be more important to determine the fixation probability than the degree or the heat heterogeneity. The dependence of the fixation probability on the position of the first mutant is discussed.