Competition at the front of expanding populations

TL;DR

This paper models how competing species expand into new territories, integrating reproductive fitness and spatial colonization ability, revealing growth morphologies and statistical distributions of fitness variations.

Contribution

It introduces a coupled model combining Fisher and KPZ equations to analyze expansion dynamics and trait variation effects.

Findings

Expansion rate influences growth morphology.

Spatial ability can outweigh reproductive advantage.

Fitness variations follow Tracy--Widom distribution.

Abstract

When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on both the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. We present a model that integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations are distinct growth morphologies controlled by expansion rates, competitive abilities, or spatial anisotropy. In some cases the ability to expand in space may overcome reproductive advantage in colonizing new territory. When new traits appear with accumulating mutations, we find that variations in fitness in range expansion may be described by the Tracy--Widom distribution.