Novel pests and diseases are becoming increasingly common, and often cause additional mortality to host species in the newly contacted communities. This can alter the structure of the community up to, and including, the extinction of host species. In the last twenty years, ash dieback disease (ADB) has spread into Europe from East Asia. It has caused substantial mortality in ash tree (Fraxinus excelsior L.) populations. However, a proportion of the individuals in most populations appears to be less susceptible to ADB and resistance seems to have high heritability. These observations have led to suggestions that ash populations may be sustainable after the disease. In order to test this hypothesis, I modified an existing model of UK woodland (parameterised for Wytham Woods, Oxfordshire) to take into account the impact of ADB, and allowed offspring to inherit resistance traits from their parent. The results suggest that ash populations would still exist in 100 years but at lower levels than they are currently. For example, when the initial proportion of resistant individuals is about 10% and heritability of resistance is 0.5, then the population of ash falls to about one third of present levels. The proportion of individuals initially resistant to ADB had a larger effect on population size after 100 years than the heritability of resistance. The fact that the initial size of the resistant population is important to achieving a high population size in the presence of ADB suggests that a selective breeding programme with the intention of augmenting the natural ash populations would be beneficial.