Control of diffusion-driven pattern formation behind a wave of competency

TL;DR

This study investigates how a wave of competency influences biological pattern formation using Turing's model, revealing that wave speed affects pattern types and organization in one and two dimensions.

Contribution

It provides a novel analysis of pattern formation behind a wave of competency, linking wave speed to specific pattern outcomes in biological systems.

Findings

Slower wave speeds cause peak splittings in 1D patterns.

Faster wave speeds lead to peak insertions.

Pattern orientation in 2D depends on wave speed.

Abstract

In certain biological contexts, such as the plumage patterns of birds and stripes on certain species of fishes, pattern formation takes place behind a so-called "wave of competency". Currently, the effects of a wave of competency on the patterning outcome is not well-understood. In this study, we use Turing's diffusion-driven instability model to study pattern formation behind a wave of competency, under a range of wave speeds. Numerical simulations show that in one spatial dimension a slower wave speed drives a sequence of peak splittings in the pattern, whereas a higher wave speed leads to peak insertions. In two spatial dimensions, we observe stripes that are either perpendicular or parallel to the moving boundary under slow or fast wave speeds, respectively. We argue that there is a correspondence between the one- and two-dimensional phenomena, and that pattern formation behind a wave of competency can account for the pattern organization observed in many biological systems.