  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.
