A spatial model for selection and cooperation

TL;DR

This paper models the evolution of cooperation using an extended biased voter model, revealing a phase transition at the point where cooperation benefits outweigh defection bias, with implications for understanding cooperative behavior.

Contribution

It introduces a spatial model extending the biased voter model to include cooperation benefits, demonstrating a phase transition in one-dimensional systems.

Findings

Cooperators die out when defector bias exceeds cooperation benefit.

Cooperation prevails when benefits outweigh defector bias.

A phase transition occurs at the point where bias equals cooperation benefit.

Abstract

We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called defector) has a (positive) bias $\alpha$ with respect to the other type (called cooperator). However, a cooperator helps a neighbor (either defector or cooperator) to reproduce at rate $\gamma$. We prove that the one-dimensional nearest-neighbor interacting dynamical system exhibits a phase transition at $\alpha=\gamma$. For $\alpha>\gamma$ cooperators always die out, but if $\gamma>\alpha$, cooperation is the winning strategy.