Abstract
Increasing the durability of crop resistance to plant pathogens is one of the key goals of virulence management. Despite the recognition of the importance of demographic and environmental stochasticity on the dynamics of an epidemic, their effects on the evolution of the pathogen and durability of resistance has not received attention. We formulated a stochastic epidemiological model, based on the Kramer-Moyal expansion of the Master Equation, to investigate how random fluctuations affect the dynamics of an epidemic and how these effects feed through to the evolution of the pathogen and durability of resistance. We focused on two hypotheses: firstly, a previous deterministic model has suggested that the effect of cropping ratio (the proportion of land area occupied by the resistant crop) on the durability of crop resistance is negligible. Increasing the cropping ratio increases the area of uninfected host, but the resistance is more rapidly broken; these two effects counteract each other. We tested the hypothesis that similar counteracting effects would occur when we take account of demographic stochasticity, but found that the durability does depend on the cropping ratio. Secondly, we tested whether a superimposed external source of stochasticity (for example due to environmental variation or to intermittent fungicide application) interacts with the intrinsic demographic fluctuations and how such interaction affects the durability of resistance. We show that in the pathosystem considered here, in general large stochastic fluctuations in epidemics enhance extinction of the pathogen. This is more likely to occur at large cropping ratios and for particular frequencies of the periodic external perturbation (stochastic resonance). The results suggest possible disease control practises by exploiting the natural sources of stochasticity.
Highlights
There is increasing social pressure to integrate science, policy and regulation in order to assess and minimize the risks associated with agricultural practices
One of the key goals of virulence management is to increase the durability of crop resistance, a concept that has been extensively discussed in the literature, but which is still difficult to measure and predict [1,2,3,4,5,6,7]
We want to understand if, and how, the evolution of a pathogen can be delayed/accelerated by random fluctuations always occurring in epidemics
Summary
There is increasing social pressure to integrate science, policy and regulation in order to assess and minimize the risks associated with agricultural practices. One of the key goals of virulence management is to increase the durability of crop resistance, a concept that has been extensively discussed in the literature, but which is still difficult to measure and predict [1,2,3,4,5,6,7]. Johnson [2] was perhaps the first to provide a definition of durable resistance, i.e. a resistance that remains effective over a prolonged period of widespread use under conditions conducive to the disease. Such definition, conceptually simple, does not provide an objective procedure for measuring and predicting the durability of crop resistance (see e.g. the discussion in [3]). Even this generally accepted consensus has been challenged by several authors showing that erosion of polygenic resistance may be important and relatively rapid [2,11,12,13,14,15,16,17,18,19] and presenting evidence of durable resistance due to the action of a single gene [2,18]
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