Competition on the edge of an expanding population

TL;DR

This paper develops a theoretical framework combining population expansion and competition, revealing three regimes based on expansion rates and competitive abilities, to better understand spatial competition dynamics.

Contribution

It introduces a coupled model integrating Fisher and KPZ equations to analyze mutant competition during population expansion, a novel approach in spatial evolutionary theory.

Findings

Identified three distinct regimes of competition based on expansion and fitness.

Derived solutions for coupled Fisher-KPZ equations.

Provided a unified framework for spatial competition analysis.

Abstract

In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). We solved these equations and found three regimes, which are controlled solely by the expansion rates, solely by the competitive abilities, or by both. Collectively, our results provide a simple framework to study spatial competition.