Spatial variation in boundary conditions can govern selection and location of eyespots in butterfly wings

Abstract

Despite being the subject of widespread study, many aspects of thedevelopment of eyespot patterns in butterfly wings remain poorly understood. Inthis work, we examine, through numerical simulations, a mathematical model foreyespot focus point formation in which a reaction-diffusion system is assumed toplay the role of the patterning mechanism. In the model, changes in the boundaryconditions at the veins at the proximal boundary alone are capable of determiningwhether or not an eyespot focus forms in a given wing cell and the eventual positionof focus points within the wing cell. Furthermore, an auxiliary surface reactiondiffusionsystem posed along the entire proximal boundary of the wing cells isproposed as the mechanism that generates the necessary changes in the proximalboundary profiles. In order to illustrate the robustness of the model, we performsimulations on a curved wing geometry that is somewhat closer to a biologicalrealistic domain than the rectangular wing cells previously considered, and we alsoillustrate the ability of the model to reproduce experimental results on artificialselection of eyespots.