Durable Resistance to Crop Pathogens: An Epidemiological Framework to Predict Risk under Uncertainty

Gilligan CA (2013) Durable Resistance to Crop Pathogens: An Epidemiological Framework to Predict Risk under Uncertainty. PLoS Comput Biol 9(1): e1002870. doi:10.1371/journal.pcbi.1002870 Durable Resistance to Crop Pathogens: An Epidemiological Framework to Predict Risk under Uncertainty Giovanni Lo Iacono 0 Frank van den Bosch 0 Chris A. Gilligan 0 Ariena van Bruggen, Plant Pathology Department, IFAS University of Florida, United States of America 0 1 Department of Veterinary Medicine, Disease Dynamics Unit, University of Cambridge , Cambridge , United Kingdom , 2 Rothamsted Research, Harpenden , United Kingdom , 3 Epidemiology and Modelling Group, Department of Plant Sciences, University of Cambridge , Cambridge , United Kingdom 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. - There is increasing social pressure to integrate science, policy and regulation in order to assess and minimize the risks associated with agricultural practices. Major risks and uncertainties persist whereby pests and pathogens rapidly overcome disease control methods using resistant cultivars and fungicides. Although disease resistant genes have been successfully used for disease management, many crop geneticists and plant breeders view resistance genes as a limited and potentially non-renewable resource, whereby once a pathogen has evolved to overcome the resistance, the resistance genes have permanently lost their value. Thus 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 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. However, such definition, although conceptually simple, does not provide an objective procedure for measuring and predicting the durability of crop resistance (see e.g. the discussion in [3]). In particular, the beguilingly simple concepts of remaining effective, prolonged period and widespread use are subject to a range of interpretations. Durability of resistance is also confounded with the inherent variability exemplified by a wide range of plant pathogens. As pointed out by Leach et al. [3], although many resistance genes have been identified in plant germplasm, identifying the factors that render the resistance effective is still a challenging task. One exception is, perhaps, the polygenic vs monogenic paradigm, according to which resistance due to the additive action of many genes (also known approximately in the literature as polygenic, quantitative, horizontal resistance, see e.g. [8,9]) is expected to be more durable than resistance due to the action of a single gene (also referred to as monogenic, qualitative, vertical resistance [1,46,10]). However, even this generally accepted consensus has been challenged by several authors showing that erosion of polygenic resistance may be important and relatively rapid [2,1119] and presenting evidence of durable resistance due to the action of a single gene [2,18]. This raises the key question why resistance, especially monogenic resistance, can be so ephemeral and subjected to the well known boom-and-bust cycles [20]. The review of Leach et al. [3] We want to understand if, and how, the evolution of a pathogen can be delayed/accelerated by random fluctuations always occurring in epidemics. We studied a simple biological system relevant to agriculture: a resistant crop immune to the disease, and a plant pathogen that defeats the resistance after a single mutation. Eventually the population of these more harmful pathogens will take over and the resistance can no longer protect the crop. As the availability of such resistant genes is limited in nature, this is an important problem to ensure food security for future generations as well as reduction in pesticide usage. We used a mathematical model to show that in general large stochastic fluctuations in epidemics enhance extinction of the pathogen, especially of the emerging mutant strains. We know that periodically forced epidemics oscillate at larger amplitude at some frequencies than at others (resonance), then by adequately perturbing the system (e.g. by alternating different types of fungicides) we can cause massive fluctuations in the small pathogen population increasing the chances of extinction. If such hypotheses will be experimentally confirmed, we could alleviate the disease, reduce chemical control, and in general, mitigate the risk of developing highly harmful pathogens (e.g. superbugs insensitive to antibiotics). focuses on this issue and supports the hypothesis that the inherent quality and durability of a plant resistance gene is a direct function of the amount of fitness penalty imposed on the pathogen to overcome that resistance gene. Despite this important clarification, the mechanism regulating the durability of resistance is expected to be more complex than the simple molecular changes alone in pathogen adaptation and any associated fitness cost. 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