Spreading speed in a farmers and hunter-gatherers model arising from Neolithic transition in Europe

We study spreading phenomena in a two-component reaction-diffusion system, modeling the Neolithic transition from hunter-gatherer societies to agricultural societies in Europe. When farmer populations were introduced into the region inhabited by hunter-gatherer populations, farmer populations spread as an expanding wave through Europe. The speed of the wave is observed to tend to be a constant. We analytically compute the spreading velocity of the model, and characterize the longtime behavior of solutions of the model. Without comparison principle, we introduce a new technique that can locate the spreading front in reaction-diffusion systems.