Abstract
Despite considerable studies on the adaptation of plant pathogens to qualitative resistance, few theoretical studies have investigated whether and how fast quantitative resistance can select for increased pathogen aggressiveness. In this paper, we formulate an integro-differential model with nonlocal mutation terms to describe the evolutionary epidemiology of fungal plant pathogens in heterogeneous agricultural environments. Parasites reproduce clonally and each strain is characterized by several phenotypic traits corresponding to the basic infection steps (infection efficiency, latent period, sporulation rate depending on the age of infection). We first derive a general expression of the basic reproduction number R0 for fungal pathogens in heterogeneous environments, typically several cultivars cultivated in the same field (cultivar mixtures) or in different fields landscape (mosaics). Next, by characterizing the evolutionary endpoints of the coupled epidemiological evolutionary dynamics, we investigate how host heterogeneity and the effect of resistance on the pathogen traits impact the evolutionary dynamics of the pathogen population both at equilibrium and during transient epidemiological dynamics. We then show that the environmental feedback loop is one-dimensional and that the model admits an optimization principle relying on an R0 maximization approach. We then highlight how one may take advantage of evolutionary dynamics leading to neutral coexistence to increase the durability of quantitative resistance, in particular for resistance genes targeting infection efficiency. Our analyses can guide experimentations by providing testable hypotheses and help plant breeders to design breeding programs.