Modeling parr-mark pattern formation during the early development of Amago trout

This paper studies the formation of the large dark patterns, known as parr marks, that form on the Amago trout as it grows from the early larval stages to adulthood. The Amago trout, known as Oncorhynchus masou ishikawa, exhibits stripes during the early stages of development that in turn evolve (through reorientation and peak insertion) to form zigzag spot patterns as the fish grows to adulthood. By considering a standard representation of the Turing model for biological self-organization via interacting and diffusing morphogens, we illustrate that a diffusively driven instability can generate transient patterns consistent with those experimentally observed during the process of parr-mark formation in the early development of the Amago trout. Surface evolution is modeled through an experimentally driven growth function. Our studies conclude that the surface evolution profile, the surface geometry, and the curvature are key factors that play a pivotal role in reaction-diffusion systems in a study motivated by observations of Amago trout parr-mark pattern formation.