Resistance management: the stable zone strategy

The di¡erent strategies of insecticide resistance management that have been formulated so far consist of delaying the appearance and spread of resistance genes. In this paper, we propose a strategy that can be used even if resistance genes are already present. This strategy consists of applying insecticides in an area smaller than a certain critical size, so that gene £ow from the untreated area, combined with the ¢tness cost of the resistance genes, prevents its frequency reaching high equilibrium value. A two-locus model was analysed numerically to determine population densities at equilibrium as a function of selection coe¤cients (insecticide selection, ¢tness costs of resistance genes and dominances), gene £ow and size of the treated area. This model indicates that there is an optimal size for the treated area where a minimal and stable density reach equilibrium, and where resistance genes cannot invade. This resistance management strategy seems applicable to a large variety of ¢eld situations, but eventually it may encounter obstacles due to a modi¢er which reduces the ¢tness costs of resistance genes.