A spatial model of the development of pest resistance to a transgenic insecticidal crop: European corn borer on Bt maize

Abstract

A mathematical model was constructed to describe the evolution of resistance to the Bacillus thuringiensis toxin (Bt) in an insect pest (European corn borer) population on a transgenic crop (Bt corn). The model comprises a set of partial differential equations of the reaction-diffusion type; local interactions of three competing pest genotypes formed by alleles of Bt resistance and susceptibility are described as in the Kostitzin model, and the spread of insects is modeled as diffusion. The model was used to evaluate the influence of pest characteristics on the efficacy of the high-dose/refuge strategy aiming to prevent or delay the spread of Bt resistance in pest populations. It was shown, by contrast, that a model based on Fisher-Haldane-Wright equations and formally incorporating a diffusion term cannot adequately describe the evolution of Bt resistance in a spatially inhomogeneous pest population. Further development of the proposed demo-genetic model is discussed.