  We combine random walks, growth and decay, and convection, in a Monte Carlo
simulation to model 1D interface dynamics with fluctuations. The continuum
limit corresponds to the deterministic Fisher equation with convection. We find
qualitatively the same type of asymmetry, as well as velocity difference, for
interface profiles moving in opposite directions. However a transition apparent
in the mean-field (continuum) limit is not found in the Monte Carlo simulation.
