The Neolithic transition, involving the change of subsistence from foraging to agriculture, can fruitfully be modelled mathematically, as, e.g., in the three-population model of Aoki et al. (1996). Here that model is modified to include some features of population dynamics in a realistic, two-dimensional environment, and including population pressure, competition for resources between farmers and foragers, and the dependence of the population carrying capacities and diffusivities on the environmental conditions. This modified model allows for the survival of foragers in regions where environmental conditions do not favour farming. The model is tentatively applied to the Indian subcontinent, which is a complicated example of this transition involving multiple domestication centres. The results are briefly compared with published archaeological data.