Persistence and frequency of application of an insecticide in relation to the rate of evolution of resistance

In an earlier paper, it was demonstrated that in order to delay the evolution of resistance, it is important to ensure that heterozygous carriers of resistance genes are killed so that the R gene is made effectively recessive. How this may be achieved is considered here, with (a) a persistent insecticide declining in effectiveness with time, and (b) a non-persistent insecticide (or fumigant). The relationship between the time taken for the dosage to decline to one-tenth (NGI) and the interval between insecticide applications (N12) was investigated. The optimal value of N12 was found to depend not only on the rate of decline but also on the shape of the degradation curve. Other important factors were (a) the dosage of insecticide applied (the initial effective dominance); (b) the initial frequency of the R gene; (c) the proportion of insects per generation that escaped exposure; and (d) whether selection occurred before or after mating. When considering non-persistent insecticides, it was necessary to distinguish between the short-lived deposit and the space spray, the latter being much less likely to lead to resistance.