Durability of resistance and cost of virulence

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A seasonal model, where a growing season is defined as the time between sowing and harvest and alternates with an inter-crop period, was derived to study the effects of the ‘cost of virulence’ and cropping ratio on durability of resistance. We assumed a single strain of virulent pathogen, a single strain of avirulent pathogen and two cultivars (one resistant and one susceptible) and studied two measures of durability of resistance (‘take-over time’ and ‘usefulness time’). Take-over time is defined as the time needed for the virulent strain of the pathogen to reach a preset threshold and predominate over the previous pathogen population. Usefulness time is the time needed before the estimated gain in green canopy area duration per plant through the use of the resistant cultivar becomes negligible. The model suggested that, although it could take several seasons before the virulent strain of the pathogen predominated over the previous pathogen population, the usefulness time of the resistant cultivar was always much shorter. Furthermore, increasing selection for the virulent strain of the pathogen (through increasing the cropping ratio of the resistant cultivar) caused the virulent strain of the pathogen to invade the system more rapidly. Cost of virulence, reflecting differences in pathogen infection rates between the four possible combinations of cultivar/pathogen strain, significantly affected durability of resistance, with the dynamics of the virulent and avirulent strains ranging from a case where the virulent strain of the pathogen died out to a case where the virulent strain of the pathogen invaded the resident pathogen population. An intermediate state, where the system reached equilibrium and the virulent strain of the pathogen neither became predominant nor died out, was defined as ‘coexistence’ of both strains of the pathogen. Occurrence of coexistence was directly related to the cost of virulence since it did not occur when virulence of the pathogen did not have a fitness cost. Two methods to include cost of virulence in the model gave similar results in relation to the two measures of durability of resistance studied.