Warning signs for wave speed transitions of noisy Fisher-KPP invasion fronts

TL;DR

This paper investigates warning signs for critical transitions in wave speed of noisy Fisher-KPP invasion fronts, linking statistical indicators to bifurcations and propagation failure through detailed numerical analysis.

Contribution

It introduces statistical warning signs based on local capacity, moments, and transients to predict wave speed transitions in stochastic Fisher-KPP models.

Findings

Warning signs can indicate proximity to bifurcations.

Closeness to carrying capacity correlates with wave speed changes.

Transient dynamics provide early indicators of invasion speed shifts.

Abstract

Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The approach is based upon a detailed numerical study of various versions of the Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation. The main motivation of this work is to contribute to the following question: how much information do statistics, collected by a stationary observer, contain about the speed and bifurcations of traveling waves? We suggest warning signs based upon closeness to carrying capacity, second-order moments and transients of localized initial invasions.