Reaction Diffusion patterns in Pseudoplatystoma fishes

TL;DR

This study investigates how reaction-diffusion models can produce diverse skin patterns in Pseudoplatystoma fishes, emphasizing the influence of boundary conditions, parameter variability, and spatial dependence on pattern formation.

Contribution

It demonstrates that reaction-diffusion pattern geometry is highly sensitive to initial and boundary conditions, and explores how advection and spatially dependent parameters affect pattern outcomes.

Findings

Pattern variability can be explained by model sensitivity to initial/boundary conditions.

Inclusion of advection and spatial dependence alters pattern forms.

Model results resemble real fish skin patterns.

Abstract

This paper studies how patterns derived from a system of reaction-diffusion equations may vary significantly depending upon boundary and initial conditions, as well as in the spatial dependence of the coefficients involved. From an extensive numerical study of the BVAM model, we demonstrate that the geometric pattern of a reaction-diffusion system is not uniquely determined by the value of the parameters in the equation. From this result, we suggest that the variability of patterns among individuals of the same species may have its roots in this sensitivity. Furthermore, this study analyzes briefly how the inclusion of the advection and the space dependency in the parameters of the model influences the forms of a specific pattern. The results of this study are compared to the skin patterns that appear in Pseudoplatystom} fishes.