Proportions of different habitat types are critical to the fate of a resistance allele

We describe a simple deterministic theoretical framework for analysing the gene frequency evolution of two alternative alleles at a single genetic locus in a habitat comprising two environments in which the genotypes have different relative fitnesses. We illustrate this for adaptation of pest insects, where one allele (resistance to toxins expressed in transgenic crops) is favoured in one environment (transgenic plants) and the other allele (susceptibility to toxins) is favoured in the other environment ('refuges' of non-transgenic plants). The evolution of allele frequencies depends on selection pressure because of relative sizes of the environments and relative fitnesses of the genotypes in each environment. We demonstrate that there are critical threshold proportions for habitat division that determine equilibrium allele frequencies. The stability of the system depends on relationships between the relative genotype fitnesses. In some cases, the division of the habitat in exactly the threshold proportions removes selection pressure and maintains polymorphism at all allele frequencies.