Evolutionary Pattern Formation

The problem of explaining the rich spectrum of the different patterns exhibited by mammals has a long history. Already in 1952 Turing proposed a Reaction-Diffusion model to explain at a mesoscopic scale the process of pattern formation. A typical Turing system consists of at least two chemical species (or morphogens), usually referred to as activator and inhibitor, reacting in such a way that their steady state is stable to small perturbations in the absence of diffusion, but becomes unstable when diffusion is present. This simple mechanism was indicated by Turing as being responsible for the creation of spatial patterns in mammals. We propose to take up this issue, and develop a stochastic mathematical model able to account for phylogenetically related Turing patterns.