Abstract
Disease resistance genes are valuable natural resources which should be deployed in a way which maximises the gain to crop productivity before they lose efficacy. Here we present a general epidemiological model for plant diseases, formulated to study the evolution of phenotypic traits of plant pathogens in response to host resistance. The model was used to analyse how the characteristics of the disease resistance, and the method of deployment, affect the size and duration of the gain. The gain obtained from growing a resistant cultivar, compared to a susceptible cultivar, was quantified as the increase in green canopy area resulting from control of foliar disease, integrated over many years—termed ‘Healthy Area Duration (HAD) Gain’. Previous work has suggested that the effect of crop ratio (the proportion of land area occupied by the resistant crop) on the gain from qualitative (gene-for-gene) resistance is negligible. Increasing the crop ratio increases the area of uninfected host, but the resistance is more rapidly broken; these two effects counteract each other. We tested the hypothesis that similar counteracting effects would occur for quantitative, multi-genic resistance, but found that the HAD Gain increased at higher crop ratios. Then we tested the hypothesis that the gain from quantitative host resistance could differ depending on the life-cycle component (sporulation rate or infection efficiency) constrained by the resistance. For the patho-system considered, a quantitative resistant cultivar that reduced the infection efficiency gave a greater HAD Gain than a cultivar that reduced sporulation rate, despite having equivalent transmission rates.