WHEN CAN REDUCED DOSES AND PESTICIDE MIXTURES DELAY THE BUILDUP OF PESTICIDE RESISTANCE - A MATHEMATICAL-MODEL

1. Resistance against pesticides is a widespread and increasing proble m, The control of pesticide dose and the mixing of pesticides have bee n proposed as methods to reduce the rate at which pesticide resistance develops. 2. A mathematical model is developed to analyse the relatio nship 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 i n terms of its impact on a specific, sensitive pest phenotype. This me asure depends both on the amount of pesticide applied and the applicat ion regime, 4, The model separates the impact of a pesticide into a pa rt that differs between pest phenotypes with different levels of resis tance and a part that is similar for all phenotypes. Cases in which pe sticide resistance can be delayed by reducing pesticide impact are def ined algebraically. For these cases a simple relationship is presented between the rate at which pesticide resistance builds up, the varianc e of resistance in the pest population and the size of the part of the pesticide impact that differs between pest phenotypes. 5. If pesticid e 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 posit ive (i.e. causes a reduction in pest growth), the pesticide is suitabl e for use in mixtures. Mixing only reduces the build-up of pesticide r esistance by reducing the required doses of the pesticides that are mi xed. 6, Although the development of resistance against two different p esticides is delayed when resistance against one is negatively correla ted 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.