Optimal resistance management for mixtures of high-risk fungicides: robustness to the initial frequency of resistance and pathogen sexual reproduction

There is a strong consensus that selection for fungicide resistant pathogen strains can be most effectively limited by using applications of mixtures of fungicides designed to balance disease control against selection. However, how to do this in practice is not entirely characterised. Previous work indicates optimal mixtures of pairs of fungicides which are both at a high risk of resistance can be constructed using pairs of doses which select equally for both single resistant strains in the first year of application. What has not been addressed thus far is the important real-world case in which the initial levels of resistance to each fungicide differ, for example because the chemicals have been available for different lengths of time. We show how recommendations based on equal selection in the first year can be sub-optimal in this case. We introduce a simple alternative approach, based on equalising the frequencies of single resistant strains in the year that achieving acceptable levels of control is predicted to become impossible. We show that this strategy is robust to changes in parameters controlling pathogen epidemiology and fungicide efficacy. We develop our recommendation using a pre-existing, parameterised model of Zymoseptoria tritici (the pathogen causing Septoria leaf blotch on wheat), which exemplifies the range of plant pathogens which predominantly spread clonally, but for which sexual reproduction forms an important component of the life cycle. We show that pathogen sexual reproduction can influence the rate at which fungicide resistance develops, but does not qualitatively affect our optimal resistance management recommendation.