Neither pulled nor pushed: Genetic drift and front wandering uncover a new class of reaction-diffusion waves

TL;DR

This paper uncovers a new class of reaction-diffusion waves that exhibit properties of both pulled and pushed waves, characterized by bulk-driven growth and large fluctuations, challenging the traditional dichotomy.

Contribution

The study identifies an intermediate wave class with combined edge and bulk influences, expanding the understanding of wave dynamics in reaction-diffusion systems.

Findings

Discovery of a new wave class with mixed properties

Large fluctuations despite bulk-driven growth

Properties influenced by both front edge and bulk

Abstract

Traveling waves describe diverse natural phenomena from crystal growth in physics to range expansions in biology. Two classes of waves exist with very different properties: pulled and pushed. Pulled waves are driven by high growth rates at the expansion edge, where the number of organisms is small and fluctuations are large. In contrast, fluctuations are suppressed in pushed waves because the region of maximal growth is shifted towards the population bulk. Although it is commonly believed that expansions are either pulled or pushed, we found an intermediate class of waves with bulk-driven growth, but exceedingly large fluctuations. These waves are unusual because their properties are controlled by both the leading edge and the bulk of the front.