Range Expansion with Mutation and Selection: Dynamical Phase Transition in a Two-Species Eden Model

TL;DR

This paper introduces a two-species Eden growth model to study how mutations and selection influence range expansion, revealing a phase transition affected by surface roughness and deviating from classical models.

Contribution

It presents a novel two-species Eden model analyzing mutation-selection dynamics and their impact on surface roughness and phase transition properties.

Findings

Beneficial mutations lead to mutant-dominated Eden-like growth.

Slower-growing mutants cause an absorbing state phase transition.

Surface roughness significantly alters critical behavior from classical models.

Abstract

The colonization of unoccupied territory by invading species, known as range expansion, is a spatially heterogeneous non-equilibrium growth process. We introduce a two-species Eden growth model to analyze the interplay between uni-directional (irreversible) mutations and selection at the expanding front. While the evolutionary dynamics leads to coalescence of both wild-type and mutant clusters, the non-homogeneous advance of the colony results in a rough front. We show that roughening and domain dynamics are strongly coupled, resulting in qualitatively altered bulk and front properties. For beneficial mutations the front is quickly taken over by mutants and growth proceeds Eden-like. In contrast, if mutants grow slower than wild-types, there is an antagonism between selection pressure against mutants and growth by merging of mutant domains with an ensuing absorbing state phase transition to an all-mutant front. We find that surface roughening has a marked effect on the critical properties of the absorbing state phase transition. While reference models, which keep the expanding front flat, exhibit directed percolation critical behavior, the exponents of the two-species Eden model strongly deviate from it. In turn, the mutation-selection process induces an increased surface roughness with exponents distinct from that of the classical Eden model.