Frequency-Dependent Selection at Rough Expanding Fronts

TL;DR

This paper investigates how frequency-dependent social interactions influence the surface roughness and phase transitions in microbial colonies expanding on surfaces, revealing new universality classes and scaling behaviors.

Contribution

It introduces a generalized Eden model with frequency-dependent selection, analyzing its critical behavior and identifying a novel universality class of phase transitions.

Findings

Boundary separation decays with a new power law.

Superdiffusive boundary motion transitions from Eden to ballistic scaling.

Front roughening shifts from Eden to selective roughening regimes.

Abstract

Microbial colonies are experimental model systems for studying the colonization of new territory by biological species through range expansion. We study a generalization of the two-species Eden model, which incorporates local frequency-dependent selection, in order to analyze how social interactions between two species influence surface roughness of growing microbial colonies. The model includes several classical scenarios from game theory. We then concentrate on an expanding public goods game, where either cooperators or defectors take over the front depending on the system parameters. We analyze in detail the critical behavior of the nonequilibrium phase transition between global cooperation and defection and thereby identify a new universality class of phase transitions dealing with absorbing states. At the transition, the number of boundaries separating sectors decays with a novel power law in time and their superdiffusive motion crosses over from Eden scaling to a nearly ballistic regime. In parallel, the width of the front initially obeys Eden roughening and, at later times, passes over to selective roughening.