The dynamics of pest resistance management: the case of refuge fields for Bt crops

We examine the optimal time-variant refuge policy to manage pest resistance to Bacillus thuringiensis (Bt) crops in a finite, discrete-time horizon model. We identify analytically the intertemporal effects of refuge fields on the pest population and its susceptibility. The shape of the optimal refuge policy and whether or not pest susceptibility should be exhausted completely at the end of the time horizon depend crucially on the values of a cost premium of Bt seeds and the fitness cost of resistance (over mortality of resistant pests) and are addressed via numerical simulations. We demonstrate the importance of modeling the dynamics of the biological system accurately, of defining a diploid (and not haploid) biological model, and of using a discrete-time (rather than continuous-time) framework