Modelling spatial strategies for the durable deployment of crop disease resistance

Maximising the durability of crop disease resistance genes in the face of pathogen evolution is a major challenge in modern agricultural epidemiology. Spatial diversification in the deployment of resistance genes, where susceptible and resistant fields are more closely intermixed, is predicted to drive lower epidemic intensities over evolutionary timescales. This is due to an increase in the strength of dilution effects, caused by pathogen inoculum challenging host tissue to which it is not well-specialised. The factors that interact with and determine the magnitude of this spatial effect are not currently well understood however, leading to uncertainty over the pathosystems where such a strategy is most likely to be cost-effective. We initially use a spatially explicit model, incorporating seasonality and localised reservoirs of inoculum, to explore disease dynamics within landscapes containing a mixture of fields planted with either susceptible or resistant cultivars. When the spatial diversification of these fields is maximised, with lower aggregation of similar fields, the overall intensity of the landscape scale epidemic is reduced. The strength of this spatial effect however depends strongly on the pathogen dispersal characteristics, any fitness cost(s) of the resistance breaking trait, the efficacy of host resistance, and the length of the timeframe of interest. The conclusions drawn from this initial work, about how multi-strain disease dynamics respond to the scale of spatial diversification in a multi-host landscape, allow us to construct a general spatially implicit model that captures these fundamental dynamics. This new model features a novel method for incorporating spatial structure using an intuitive spatial aggregation metric that can be easily estimated from spatially explicit landscape data. The model is simple enough to be amenable to mathematical invasion analysis, while being flexible enough that questions of resistance durability can be thoroughly explored. In particular, results demonstrating interaction between spatial heterogeneity and cultivar cropping ratio are presented, an investigation that was not easily possible in our earlier more complex model. These results indicate that optimal spatial deployment strategies depend on a variety of factors, and may not necessarily be constant over time. Overall, these models allow us to make general predictions of the types of system for which spatial diversification is most likely to be cost-effective, paving the way for potential economic modelling and pathosystem specific evaluation. In addition, this approach for capturing detailed spatial structure and multi-species interactions within simple mathematical models could be applied to a wide variety of ecological and evolutionary systems. This study highlights the importance of studying the effect of genetics on landscape scale spatial dynamics within host-pathogen disease systems, as well as providing new mathematical tools to do so.