Mathematical Modelling of Angelfish and Zebrafish Pigmentation Patterns

Fish demonstrate a remarkable diversity in coloration and patterning. These patterns result from the spatial organisation of specific pigment cells within the skin. The development of these patterns is a particularly elegant example of morphogenesis: the emergence of form in the growing embryo. In certain species, including members of the marine angelfish Pomacanthus the pattern evolves as the fish matures through larval, juvenile and adult stages. In the first part of this talk, I will introduce a continuous mathematical model based on cell chemotaxis that replicates the growing patterns in these species.

In the second part of the talk I will explore the formation of the larval pigment pattern in the Zebrafish, Danio rerio. Here, we will use a discrete-continuous model to understand how the pattern is set-up, from the emergence of pigment cells from the neural crest to their establishment in the skin. The modelling of cells as discrete objects allows the incorporation of specific biological mechanisms. We shall use the model to make a number of hypotheses on the mechanistic basis of patterning.