Abstract
We constructed a reaction-diffusion model of the development of resistance to transgenic insecticidal Bt crops in pest populations. Kostitzin's demo-genetic model describes local interactions between three competing pest genotypes with alleles conferring resistance or susceptibility to transgenic plants, the spatial spread of insects being modelled by diffusion. This new approach makes it possible to combine a spatial demographic model of population dynamics with classical genetic theory. We used this model to examine the effects of pest dispersal and of the size and shape of the refuge on the efficiency of the "high-dose/refuge" strategy, which was designed to prevent the development of resistance in populations of insect pests, such as the European corn borer, Ostrinia nubilalis Hubner (Lepidoptera, Crambidae). We found that, with realistic combinations of refuge size and pest dispersal, the development of resistance could be considerably delayed. With a small to medium-sized farming area, contiguous refuge plots are more efficient than a larger number of smaller refuge patches. We also show that the formal coupling of classical Fisher-Haldane-Wright population genetics equations with diffusion terms inaccurately describes the development of resistance in a spatially heterogeneous pest population, notably overestimating the speed with which Bt resistance is selected in populations of pests targeted by Bt crops.