When can reduced doses and pesticide mixtures delay the build-up of pesticide resistance? A mathematical model

1. Resistance against pesticides is a widespread and increasing problem, The control of pesticide dose and the mixing of pesticides have been proposed as methods to reduce the rate at which pesticide resistance develops. 2. A mathematical model is developed to analyse the relationship between pesticide dose and the rate of development of pesticide resistance. The model is applicable to pesticides generally, including fungicides, herbicides and insecticides. 3, The model measures dose in terms of its impact on a specific, sensitive pest phenotype. This measure depends both on the amount of pesticide applied and the application regime, 4, The model separates the impact of a pesticide into a part that differs between pest phenotypes with different levels of resistance and a part that is similar for all phenotypes. Cases in which pesticide resistance can be delayed by reducing pesticide impact are defined algebraically. For these cases a simple relationship is presented between the rate at which pesticide resistance builds up, the variance of resistance in the pest population and the size of the part of the pesticide impact that differs between pest phenotypes. 5. If pesticide resistance can be delayed by reducing pesticide impact. the part of the impact of a pesticide that does not differ between pest phenotypes determines whether it is suitable for use in mixtures, If it is positive (i.e. causes a reduction in pest growth), the pesticide is suitable for use in mixtures. Mixing only reduces the build-up of pesticide resistance by reducing the required doses of the pesticides that are mixed. 6, Although the development of resistance against two different pesticides is delayed when resistance against one is negatively correlated with resistance against the other, mixing them is not necessarily preferable to using them In rotation. The decision whether to mix the two pesticides should still be based on their individual suitabilities for mixing, as defined above.