Stochastic model for population migration and the growth of human settlements during the Neolithic transition

We present a stochastic two-population model that describes the migration and growth of semisedentary foragers and sedentary farmers along a river valley during the Neolithic transition. The main idea is that random migration and transition from a sedentary to a foraging way of life, and backwards, is strongly coupled with the local crop production and associated degradation of land. We derive a nonlinear integral equation for the population density coupled with the equations for the density of soil nutrients and crop production. Our model provides a description of the formation of human settlements along the river valley. The numerical results show that the individual farmers have a tendency for aggregation and clustering. We show that the large-scale pattern is a transient phenomenon which eventually disappears due to land degradation.