Background: In some populations, complete shifts in the genotype of the strain of measles circulating in the population have been observed, with given genotypes being replaced by new genotypes. Studies have postulated that such shifts may be attributable to differences between the fitness of the new and the old genotypes. Methods: We developed a stochastic model of the transmission dynamics of measles, simulating the effects of different levels of migration, vaccination coverage and importation of new genotypes on patterns in the persistence and replacement of indigenous genotypes. Results: The analyses illustrate that complete replacement in the genotype of the strain circulating in populations may occur because of chance. This occurred in >50% of model simulations, for levels of vaccination coverage and numbers of imported cases per year which are compatible with those observed in several Western European populations (>80% and >3 per million per year respectively) and for the given assumptions in the model. Conclusion: The interpretation of genotypic data, which are increasingly being collected in surveillance programmes, needs to take account of the underlying vaccination coverage and the level of the importation rate of measles cases into the population.