How mutation alters the evolutionary dynamics of cooperation on networks

TL;DR

This paper extends the average gradient of selection (AGoS) method to include stochastic mutation effects, revealing that mutation generally hampers cooperation evolution and significantly impacts dynamics on scale-free networks.

Contribution

The authors extend AGoS to analyze mutation effects on cooperation, demonstrating mutation's negative impact and unique dynamics on scale-free networks.

Findings

Mutation negatively affects cooperation evolution.

Scale-free networks are most vulnerable to mutation.

Cooperation dynamics shift from bistability to coexistence with mutation.

Abstract

Cooperation is ubiquitous at every level of living organisms. It is known that spatial (network) structure is a viable mechanism for cooperation to evolve. A recently proposed numerical metric, average gradient of selection (AGoS), a useful tool for interpreting and visualizing evolutionary dynamics on networks, allows simulation results to be visualized on a one-dimensional phase space. However, stochastic mutation of strategies was not considered in the analysis of AGoS. Here we extend AGoS so that it can analyze the evolution of cooperation where mutation may alter strategies of individuals on networks. We show that our extended AGoS correctly visualizes the final states of cooperation with mutation in the individual-based simulations. Our analyses revealed that mutation always has a negative effect on the evolution of cooperation regardless of the payoff functions, fraction of cooperators, and network structures. Moreover, we found that scale-free networks are the most vulnerable to mutation and thus the dynamics of cooperation are altered from bistability to coexistence on those networks, undergoing an imperfect pitchfork bifurcation.