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

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 are 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 hypothesize that (as others have) pattern formation behind a wave of competency can account for the pattern organization observed in many biological systems.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This study investigates pattern formation behind a wave of competency using Turing's diffusion-driven instability model. The results show that wave speed has an impact on pattern formation, with slower speeds leading to peak splittings and higher speeds resulting in peak insertions. In two spatial dimensions, different wave speeds lead to the formation of perpendicular or parallel stripes.