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Measures of Durability of Resistance

Conventional models for the durability of resistant cultivars focus on the dynamics of the frequency of resistance genes. This leads to a definition of the durability of resistance as the time from introduction of the cultivar to the time when the frequency of the virulence gene reaches a preset threshold. It is questionable whether this is the most appropriate way to measure durability. Here we use a simple epidemiological model to link population dynamics and population genetics to compare three measures of durability: (i) the expected time until invasion of the virulent genotype, by mutation or immigration, and subsequent establishment of a population (T_invasion); (ii) the virulence frequency related measure of the time for the virulent genotype to take-over the pathogen population ( T_take-over); and (iii) the additional yield, measured by the additional number of uninfected host growth days (T_additional). Specifically, we show how the measures of durability are affected by deployment and epidemiological parameters. We use a combination of numerical solution and analytical approximation of a model for the population dynamics of avirulent and virulent genotypes of a pathogen growing in dynamically changing populations of resistant and susceptible cultivars. The three measures of durability are compared. Some consequences of the results for durable resistance in multilines and mixtures and the regional deployment of resistant cultivars are discussed.