Fig 1. A numerically-simulated traveling wave solution in which farming spreads at a constant speed and an ancestry gradient is formed in its wake.

Parameter values are a = 1, b = 1, s = 0.1, g = 2.1, w = p = q = 0. Solid grey, broken black, and solid black curves give the normalized densities of initial farmers F, converted farmers C, and hunter-gatherers H, respectively, on the interval 0≤x≤800. The black arrow marks the wave front.