Population dynamics and Burgers’ equation

A brief review of recent results [D.R. Nelson, N.M. Shnerb, Phys. Rev. E 58 (1998) 1383] connecting population dynamics in the presence of disorder and convection with a noisy Burgers’ equation is given. In the limit of high convection velocity, linearized population growth in dimensions is described by a (d−1)-dimensional Burgers’ equation with random noise. The Burgers mapping leads to universal results for the spreading and transverse profile of populations drifting downstream through a disordered medium with spatially varying growth rates.