  We investigate a class of stochastic growth models involving competition
between two phases in which one of the phases has a competitive advantage. The
equilibrium populations of the competing phases are calculated using a mean
field analysis. Regression probabilities for the extinction of the advantaged
phase are calculated in a leading order approximation. The results of the
calculations are in good agreement with simulations carried out on a square
lattice with periodic boundaries. The class of models are variants of the
Williams- Bjerknes model for the growth of tumours in the basal layer of an
epithelium. In the limit in which only one of the phases is unstable the class
of models reduces to the well known variants of the Eden model.
