Stochastic epidemiological model for the analysis of plant resistance break- down to pathogens subjected to genetic drift

The deployment of pathogen-resistant crops often leads to the emergence of resistance-breaking pathogens that suppress the yield bene t provided by the resistance. In this work, we analyze if and how a modulation of the genetic drift experienced by the pathogens can slow this emergence down. For that purpose, we consider a crop patch in which a given proportion of the plants carry the qualitative resistance and suppose that genetic drift, which is genetically based, can either be added to the initial infection phases of the resistant or of the susceptible plants in the crop. We develop a stochastic SI model of the crop patch, in which only the number of susceptible and resistant infected plants need to be represented. In that model, the infection events follow a Poisson process and undergo bottleneck induced drift, limiting the probability of infection of a plant by a pathogen.Through intensive simulations of this model with the Gillespie algorithm, we show which model parameters most influence the effciency of the genetic drift for improving crop yield. Also, we analyze which combination of genetic drift level and proportion of resistant plants in the crop most improves crop yield.