This result was consistent for a range of fitness costs of resistance and for different degrees of partial resistance. For solo use of a high-risk fungicide, the model output thus suggests that both the part of the effective life spent in the emergence phase and the part of the effective life spent in the selection phase can be maximised. For mixtures of a high-risk and a low-risk fungicide, the median emergence time of resistance to the high-risk fungicide was highest when high dose rates of the low-risk fungicide were combined with the lowest possible dose rate of the high-risk fungicide necessary to provide sufficient disease control of an average epidemic of M. graminicola on winter wheat. Hobbelen et al. determined the number of years that mixtures of a low-risk and a high-risk fungicide can JPH203 provide sufficient disease control in the selection phase for the same host-pathogen system. Similar to the emergence phase, their analysis shows that this number of years is highest when high dose rates of the low-risk fungicide are combined with the lowest possible dose rate of the high-risk fungicide necessary to provide sufficient disease control. It can be concluded that the dose and mixture treatment strategies which are most effective at delaying the evolution of fungicide resistance, do not differ between the emergence phase and the selection phase. The specific model in this paper describes the emergence of resistance to a high-risk fungicide in M. graminicola populations on winter wheat. However, the structure and assumptions underlying the model apply to many foliar fungal pathogens of cereal crops. For example, only parameter values would need to be changed to describe the development of the canopy of cereal crops other than winter wheat. Similarly, the division of the life cycle of fungal pathogens into latent and infectious stages is representative of BTSA1 all fungal pathogens. The division of our model into deterministic and stochastic submodels is to some extent artificial, because stochastic processes will not only influence the dynamics of the resistant strain, but also the dynamics of the host and the sensitive pathogen population. However, such a division is justified when the density of the host and the sensitive pathogen population are so high during most of the growing season that extinction due to stochastic processes is highly unlikely. The advantage of using a deterministic instead of a stochastic model to describe large populations is the much shorter simulation time. There are also a number of limitations to the generality of the model. Firstly, the sensitivity of pathogen strains is assumed to be constant in time. As a result, the model cannot be used to describe a quantitative type of resistance development, characterised by a gradual decrease in sensitivity of the pathogen population due to the accumulation of mutations over time. The best strategy for delaying the emergence of strains with sharply decreased sensitivity due to a single mutation may not be the best strategy for delaying the emergence of strains in which the reduction in sensitivity due to each mutation is relatively small. A second limitation is that the model does not account for the spatial variation in the treatment programs for fungicides.