Abstract

Theoretical studies on quantitative resistance are rather scarce. A general epidemiological model for plant diseases is formulated and applied to study the evolution of phenotypic traits of plant pathogens in response to both quantitative and qualitative host resistance. The model is built over fundamental biological processes occurring and measurable at the individual level (e.g. infection, spore production, genetic changes due to mutations in the offspring of the pathogen). The effects of such processes on the higher epidemiological and evolutionary scales are elucidated leading to a coherent, unified framework. The evolution of the phenotypic trait of the pathogen showing erosion of quantitative crop resistance naturally arises from the model. The model can be adapted to different patho-systems such as the effect of antibiotics on humans and animals. In particular:

• We highlight the differences between qualitative and quantitative resistance in the effect of key epidemiological and agronomic parameters on the durability of resistance.

• 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

• The model for qualitative resistance is extended to include the effect of demographic and environmental stochasticity. We show that that, in the patho-system considered here, large stochastic fluctuations in the epidemics enhance extinction of the pathogen. We discuss the effects of stochasticity on the durability of resistance and possible disease control practises by exploiting the natural sources of stochasticity.