Plant pathogens respond to selection pressures exerted by disease management strategies. This can lead to fungicide resistance and/or the breakdown of disease-resistant cultivars, each of which significantly threaten food security. Both fungicide resistance and cultivar breakdown can be characterised as qualitative or quantitative. Qualitative (monogenic) resistance/breakdown involves a step change in the characteristics of the pathogen population with respect to disease control, often caused by a single genetic change. Quantitative (polygenic) resistance/breakdown instead involves multiple genetic changes, each causing a smaller shift in pathogen characteristics, leading to a gradual alteration in the effectiveness of disease control over time. Although resistance/breakdown to many fungicides/cultivars currently in use is quantitative, the overwhelming majority of modelling studies focus on the much simpler case of qualitative resistance. Further, those very few models of quantitative resistance/breakdown which do exist are not fitted to field data. Here we present a model of quantitative resistance/breakdown applied to Zymoseptoria tritici, which causes Septoria leaf blotch, the most prevalent disease of wheat worldwide. Our model is fitted to data from field trials in the UK and Denmark. For fungicide resistance, we show that the optimal disease management strategy depends on the timescale of interest. Greater numbers of fungicide applications per year lead to greater selection for resistant strains, although over short timescales this can be offset by the increased control offered by more sprays. However, over longer timescales higher yields are attained using fewer fungicide applications per year. Deployment of disease-resistant cultivars is not only a valuable disease management strategy, but also offers the secondary benefit of protecting fungicide effectiveness by delaying the development of fungicide resistance. However, disease-resistant cultivars themselves erode over time. We show how an integrated disease management strategy with frequent replacement of disease-resistant cultivars can give a large improvement in fungicide durability and yields.

There is a strong consensus that selection for fungicide resistant pathogen strains can be most effectively limited by using applications of mixtures of fungicides designed to balance disease control against selection. However, how to do this in practice is not entirely characterised. Previous work indicates optimal mixtures of pairs of fungicides which are both at a high risk of resistance can be constructed using pairs of doses which select equally for both single resistant strains in the first year of application. What has not been addressed thus far is the important real-world case in which the initial levels of resistance to each fungicide differ, for example because the chemicals have been available for different lengths of time. We show how recommendations based on equal selection in the first year can be sub-optimal in this case. We introduce a simple alternative approach, based on equalising the frequencies of single resistant strains in the year that achieving acceptable levels of control is predicted to become impossible. We show that this strategy is robust to changes in parameters controlling pathogen epidemiology and fungicide efficacy. We develop our recommendation using a pre-existing, parameterised model of Zymoseptoria tritici (the pathogen causing Septoria leaf blotch on wheat), which exemplifies the range of plant pathogens which predominantly spread clonally, but for which sexual reproduction forms an important component of the life cycle. We show that pathogen sexual reproduction can influence the rate at which fungicide resistance develops, but does not qualitatively affect our optimal resistance management recommendation.

We extend a spatially non-local cross-diffusion model of aggregation between multiple species with directed motion toward resource gradients to include many species and more general kinds of dispersal. We first consider diffusive instabilities, determining that for directed motion along fecundity gradients, the model permits the Turing instability leading to colony formation and persistence provided there are three or more interacting species. We also prove that such patterning is not possible in the model under the Turing mechanism for two species under directed motion along fecundity gradients, confirming earlier findings in the literature. However, when the directed motion is not along fecundity gradients, for instance if foraging or migration is sub-optimal relative to fecundity gradients, we find that very different colony structures can emerge. This generalization also permits colony formation for two interacting species. In the advection -dominated case, aggregation patterns are more broad and global in nature, due to the inherent non-local nature of the advection which permits directed motion over greater distances, whereas in the diffusion -dominated case, more highly localized pattens and colonies develop, owing to the localized nature of random diffusion. We also consider the interplay between Turing patterning and spatial heterogeneity in resources. We find that for small spatial variations, there will be a combination of Turing patterns and patterning due to spatial forcing from the resources, whereas for large resource variations, spatial or spatiotemporal patterning can be modified greatly from what is predicted on homogeneous domains. For each of these emergent behaviors, we outline the theoretical mechanism leading to colony formation, and then provide numerical simulations to illustrate the results. We also discuss implications this model has for studies of directed motion in different ecological settings.

Plant pathogens respond to selection pressures exerted by disease management strategies. This can lead to fungicide resistance and/or the breakdown of disease-resistant cultivars, each of which significantly threaten food security. Both fungicide resistance and cultivar breakdown can be characterised as qualitative or quantitative. Qualitative (monogenic) resistance/breakdown involves a step change in the characteristics of the pathogen population with respect to disease control, often caused by a single genetic change. Quantitative (polygenic) resistance/breakdown instead involves multiple genetic changes, each causing a smaller shift in pathogen characteristics, leading to a gradual alteration in the effectiveness of disease control over time. Although resistance/breakdown to many fungicides/cultivars currently in use is quantitative, the overwhelming majority of modelling studies focus on the much simpler case of qualitative resistance. Further, those very few models of quantitative resistance/breakdown which do exist are not fitted to field data. Here we present a model of quantitative resistance/breakdown applied to Zymoseptoria tritici, which causes Septoria leaf blotch, the most prevalent disease of wheat worldwide. Our model is fitted to data from field trials in the UK and Denmark. For fungicide resistance, we show that the optimal disease management strategy depends on the timescale of interest. Greater numbers of fungicide applications per year lead to greater selection for resistant strains, although over short timescales this can be oset by the increased control oered by more sprays. However, over longer timescales higher yields are attained using fewer fungicide applications per year. Deployment of disease-resistant cultivars is not only a valuable disease management strategy, but also oers the secondary benefit of protecting fungicide effectiveness by delaying the development of fungicide resistance. However, disease-resistant cultivars themselves erode over time. We show how an integrated disease management strategy with frequent replacement of disease-resistant cultivars can give a large improvement in fungicide durability and yields.

Many plant viruses are transmitted by insect vectors. Transmission can be described as persistent or non-persistent depending on rates of acquisition, retention, and inoculation of virus. Much experimental evidence has accumulated indicating vectors can prefer to settle and/or feed on infected versus noninfected host plants. For persistent transmission, vector preference can also be conditional, depending on the vector’s own infection status. Since viruses can alter host plant quality as a resource for feeding, infection potentially also affects vector population dynamics. Here we use mathematical modelling to develop a theoretical framework addressing the effects of vector preferences for landing, settling and feeding–as well as potential effects of infection on vector population density–on plant virus epidemics. We explore the consequences of preferences that depend on the host (infected or healthy) and vector (viruliferous or nonviruliferous) phenotypes, and how this is affected by the form of transmission, persistent or non-persistent. We show how different components of vector preference have characteristic effects on both the basic reproduction number and the final incidence of disease. We also show how vector preference can induce bistability, in which the virus is able to persist even when it cannot invade from very low densities. Feedbacks between plant infection status, vector population dynamics and virus transmission potentially lead to very complex dynamics, including sustained oscillations. Our work is supported by an interactive interface https://plantdiseasevectorpreference.herokuapp.com/. Our model reiterates the importance of coupling virus infection to vector behaviour, life history and population dynamics to fully understand plant virus epidemics.

Many plant viruses are transmitted by insect vectors. Transmission can be described as persistent or non-persistent depending on rates of acquisition, retention, and inoculation of virus. Much experimental evidence has accumulated indicating vectors can prefer to settle and/or feed on infected versus noninfected host plants. For persistent transmission, vector preference can also be conditional, depending on the vector's own infection status. Since viruses can alter host plant quality as a resource for feeding, infection potentially also affects vector population dynamics. Here we use mathematical modelling to develop a theoretical framework addressing the effects of vector preferences for landing, settling and feeding, as well as potential effects of infection on vector population density, on plant virus epidemics. We explore the consequences of preferences that depend on the host (infected or healthy) and vector (viruliferous or nonviruliferous) phenotypes, and how this is affected by the form of transmission, persistent or non-persistent. We show how different components of vector preference have characteristic effects on both the basic reproduction number and the final incidence of disease. We also show how vector preference can induce bistability, in which the virus is able to persist even when it cannot invade from very low densities. Feedbacks between plant infection status, vector population dynamics and virus transmission potentially lead to very complex dynamics, including sustained oscillations. Our work is supported by an interactive interface https://plantdiseasevectorpreference.herokuapp.com/. Our model reiterates the importance of coupling virus infection to vector behaviour, life history and population dynamics to fully understand plant virus epidemics.

Increasing fungicide dose tends to lead to better short-term control of plant diseases. However, high doses select more rapidly for fungicide resistant strains, reducing long-term disease control. When resistance is qualitative and complete—i.e. resistant strains are unaffected by the chemical and resistance requires only a single genetic change—using the lowest possible dose ensuring sufficient control is well known as the optimal resistance management strategy. However, partial resistance (where resistant strains are still partially suppressed by the fungicide) and quantitative resistance (where a range of resistant strains are present) remain ill-understood. Here, we use a model of quantitative fungicide resistance (parametrized for the economically important fungal pathogen Zymoseptoria tritici ) which handles qualitative partial resistance as a special case. Although low doses are optimal for resistance management, we show that for some model parametrizations the resistance management benefit does not outweigh the improvement in control from increasing doses. This holds for both qualitative partial resistance and quantitative resistance. Via a machine learning approach (a gradient-boosted trees model combined with Shapley values to facilitate interpretability), we interpret the effect of parameters controlling pathogen mutation and characterising the fungicide, in addition to the time scale of interest.

There is a strong consensus that selection for fungicide resistant pathogen strains can be most effectively limited by using applications of mixtures of fungicides designed to balance disease control against selection. However, how to do this in practice is not entirely characterised. Previous work indicates optimal mixtures of pairs of fungicides which are both at a high risk of resistance can be constructed using pairs of doses which select equally for both single resistant strains in the first year of application. What has not been addressed thus far is the important real-world case in which the initial levels of resistance to each fungicide differ, for example because the chemicals have been available for different lengths of time. We show how recommendations based on equal selection in the first year can be sub-optimal in this case. We introduce a simple alternative approach, based on equalising the frequencies of single resistant strains in the year that achieving acceptable levels of control is predicted to become impossible. We show that this strategy is robust to changes in parameters controlling pathogen epidemiology and fungicide efficacy. We develop our recommendation using a pre-existing, parameterised model of Zymoseptoria tritici (the pathogen causing Septoria leaf blotch on wheat), which exemplifies the range of plant pathogens which predominantly spread clonally, but for which sexual reproduction forms an important component of the life cycle. We show that pathogen sexual reproduction can influence the rate at which fungicide resistance develops, but does not qualitatively affect our optimal resistance management recommendation.