MEAN-FIELD ANALYSIS OF WILLIAMS-BJERKNES-TYPE GROWTH

We investigate a class of stochastic growth models involving competiti on between two phases in which one of the phases has a competitive adv antage. The equilibrium populations of the competing phases are calcul ated using a mean-field analysis. Regression probabilities for the ext inction of the advantaged phase are calculated in a leading-order appr oximation. 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 th e 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 reduce s to the well-known variants of the Eden model. (C) 1998 Elsevier Scie nce B.V. All rights reserved.