Homogenization and influence of fragmentation in a biological invasion model

TL;DR

This paper investigates how habitat fragmentation and environmental homogenization affect the speed of biological invasion fronts, providing rigorous analysis and insights into the dynamics in periodic and patchy environments.

Contribution

It rigorously establishes the limit of invasion speeds under homogenization and analyzes the impact of habitat fragmentation on invasion dynamics.

Findings

Speeds approach a limit under homogenization.

Front speeds increase with larger spatial periods.

Fragmentation influences invasion speed in patch models.

Abstract

In this paper, some properties of the minimal speeds of pulsating Fisher-KPP fronts in periodic environments are established. The limit of the speeds at the homogenization limit is proved rigorously. Near this limit, generically, the fronts move faster when the spatial period is enlarged, but the speeds vary only at the second order. The dependence of the speeds on habitat fragmentation is also analyzed in the case of the patch model.