The growth of human settlements during the Neolithic, clustering and   food crisis
  We present a stochastic two-population model that describes the migration and growth of semi-sedentary foragers and sedentary farmers along a river valley during the Neolithic transition. The main idea of this paper is that random migration and transition from sedentary to foraging way of life and backward is strongly coupled with the local crop production and the associated degradation of land. We derive a non-linear integral equation for the population density coupled with the equations for the density of soil nutrients and crop production. Our model provides an explanation for the formation of human settlements along a 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. 
Sergei Fedotov, David Moss, Daniel Campos