Boundaries between ancient cultures: Origins and persistence

In a recent work on the wave of advance of a beneficial technology and associated hitchhiking of cultural and biological traits, we simulated the advance of neolithic agriculture into Europe. That model embraced geographical variation of land fertility and human mobility, conversion of indigenous mesolithic hunter-gatherers to agriculture, and competition between invading farmers and indigenous converts. A key result is a sharp cultural boundary across which the agriculturalists' heritage changes from that of the invading population to that of the converts. Here we present an analytical study of the cultural boundary for some simple cases. We show that the width of the boundary is determined by human mobility and the strength of competition. Simulations for the full model give essentially the same result. The finite width facilitates irreversible gene flow between the populations, so over time genetic differences appear as gradients while e.g. linguistic barriers may remain sharp. We also examine the various assumptions of the model relating to purposeful versus. random movement of peoples and the competition between cultures, demonstrating its richness and flexibility.