Pinned, locked, pushed, and pulled traveling waves in structured environments

TL;DR

This paper investigates how structured environments like tissues and landscapes affect traveling wave fronts, revealing phenomena such as pinning, locking, and pulsating propagation, with implications for biological invasions and chemical reactions.

Contribution

It introduces the concept of velocity locking in structured environments and characterizes the transition from continuous to locked invasions, highlighting robustness to fluctuations.

Findings

Velocity locking occurs due to environmental periodicity.

Locked velocities are insensitive to moderate dispersal or growth changes.

The transition is controlled by positive density-dependence.

Abstract

Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In homogeneous environments, the alternative states are separated by a smooth front moving at a constant velocity. This simple picture can break down in structured environments such as tissues, patchy landscapes, and microfluidic devices. Habitat fragmentation can pin the front at a particular location or lock invasion velocities into specific values. Locked velocities are not sensitive to moderate changes in dispersal or growth and are determined by the spatial and temporal periodicity of the environment. The synchronization with the environment results in discontinuous fronts that propagate as periodic pulses. We characterize the transition from continuous to locked invasions and show that it is controlled by positive density-dependence in dispersal or growth. We also demonstrate that velocity locking is robust to demographic and environmental fluctuations and examine stochastic dynamics and evolution in locked invasions.