Resistance to insecticide is considered nowadays one of the major threats to insect control, as its occurrence reduces drastically the efficiency of chemical control campaigns, and may also perturb the application of other control methods, like biological and genetic control. In order to account for the emergence and spread of such phenomenon as an effect of exposition to larvicide and/or adulticide, we develop in this paper a general time-continuous population model with two life phases, subsequently simplified through slow manifold theory. The derived models present density-dependent recruitment and mortality rates in a non-conventional way. We show that in absence of selection, they evolve in compliance with Hardy–Weinberg law; while in presence of selection and in the dominant or codominant cases, convergence to the fittest genotype occurs. The proposed mathematical models should allow for the study of several issues of importance related to the use of insecticides and other adaptive phenomena.

如今，对杀虫剂的抗性被认为是对昆虫控制的主要威胁之一，因为其发生会大大降低化学防治活动的效率，还可能干扰其他控制方法的应用，例如生物学和遗传控制。为了说明这种现象的出现和传播，例如暴露于杀幼虫剂和/或杀成虫剂的影响，我们在本文中开发了一个具有两个生命阶段的通用时间连续种群模型，随后通过慢流形理论对其进行了简化。派生模型以非常规方式显示了密度依赖的招聘和死亡率。我们表明，在没有选择的情况下，它们会按照哈迪-温伯格定律发展；而在存在选择的情况下以及在显性或显性情况下，会发生向最适基因型的融合。