Globally there is growing concern about the problem of genetic pollution. This issue has gained public prominence with the creation of novel genotypes using genetic engineering, and their subsequent release into the environment. Of particular, public concern are the risks associated with genetic pollution from the release of genetically modified plants into centres of diversity. This problem is of significance in Australia, which is a centre of diversity for eucalyptus. Gene flow is managed using isolation distances, which are set using qualitative risk assessments by experts. However, we believe that quantitative risk assessments using mathematical models can augment expert opinion by better informing decision makers about the risks of gene flow. We develop a spatially explicit gene flow and invasion model using cellular automata, which we use to investigate gene introgression between plantations of genetically modified eucalypts and stands of wild eucalypts. Our results suggest that an isolation distance in excess of 100 m is likely to be the minimum distance needed to limit gene introgression.