  We describe a general Godunov type splitting for numerical simulations of the
Fisher/Kolmogorov-Petrovski-Piskunov growth and diffusion equation in two
spatial dimensions. In particular, the method is appropriate for modeling
population growth and dispersal on a terrestrial map. The procedure is
semi-implicit, hence quite stable, and approximately second order accurate,
excluding boundary condition complications. It also has low memory requirements
and shows good performance. We illustrate an application of this solver: global
human dispersal in the late Pleistocene, modeled via growth and diffusion over
geographical maps of paleovegetation and paleoclimate.
