The speed of invasion in an advancing population

TL;DR

This paper rigorously estimates the invasion speed of advantageous traits in a spatially expanding population modeled by F-KPP equations, confirming previous heuristic and numerical predictions about faster invasion speeds during population expansion.

Contribution

It provides the first rigorous mathematical estimates for invasion speeds in a spatially advancing population, validating prior heuristic and numerical findings.

Findings

Invasion speed is faster during population expansion.

Rigorous estimates confirm previous heuristic predictions.

Feynman-Kac representation is used for analysis.

Abstract

We derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by Venegas-Ortiz et al. In that paper, it was noted that the speed of invasion by the mutant trait is faster faster when the resident population ist expanding in space compared to the speed when the resident population is already present everywhere. We use the Feynman-Kac representation to provide rigorous estimates that confirm these predictions.