Exactly solvable model for a genetically induced geographical distribution of a population

We consider a population with biparental procreation which genetically transmits, through a specific blending-like mechanism, a combination of two characters, namely a nomadic and a sedentary one. Consequently, as time goes on, the population spreads out geographically, space distribution thus reflecting genetic distribution. The model is exactly tractable, and we calculate the relevant quantities. We finally present and calculate a generalized version of the model.