Stochastic simulation of the spread of race‐specific and race‐nonspecific aerial fungal pathogens in cultivar mixtures

The spread of race‐specific and ‐nonspecific fungal pathogens in cultivar mixtures over space and time was simulated using an individual‐based, spatially explicit stochastic model. The spatial spread of disease was simulated using a half‐Cauchy distribution. The effects of five simulation variables on the effectiveness of cultivar mixtures in reducing disease development were investigated. These simulation variables were the sporulation rate, the median spore dispersal distance, the probabilities of cross‐infection among hosts and pathogen races, the proportion of host plants that were completely susceptible (or, in the case of race‐specific pathogens, the numbers of mixture components) and the spatial arrangement of the mixture components. Disease dynamics were summarized by the rate parameters of logistic equations and by the area under the disease progress curve (AUDPC) of incidence and severity. The potential reduction in disease development in cultivar mixtures, compared with pure cultures, was considerable. Mixtures were more effective in reducing race‐specific pathogens than race‐nonspecific pathogens. For both types of pathogen, most variation in logit‐transformed mixture efficacy was due to the main effects of the simulation variables. For race‐nonspecific pathogens, the performance of mixtures was influenced mainly by the proportion of plants that were susceptible and by the spatial arrangement of the two mixture components. For race‐specific pathogens, the performance of mixtures was determined mainly by the number and the spatial arrangement of mixture components. The smaller the homogeneous genotype area, the greater the mixture efficacy. Higher sporulation rate decreased mixture efficacy. Planting the mixture components in square blocks was more effective in reducing disease than planting in strips. For race‐nonspecific pathogens, increasing the proportion of susceptible plants decreased the mixture efficacy. For race‐specific pathogens, disease in mixtures decreased with increasing numbers of mixture components. The effect on the mixture efficacy of increasing cross‐infection probability from 0 to 0.25 was generally small. For the AUDPC‐based efficacy of disease severity, the effects of median spore dispersal distance were also very large: the shorter the median spore dispersal distance, the less effective the mixture.