OPTIMAL CONTROL OF PEST RESISTANCE TO TRANSGENIC CROP VARIETIES

Transgenic corn varieties entered the market in 1996. These plant varieties carry a gene from the soil bacterium Bacillus thuringiensis kurstaki, Bt, that makes the plant produce a toxin deadly to the pest insect European Corn Borer (ECB) Ostrinia nubilalis (Hübner). Since ECB may build up genetic resistance to this toxin, the growers of transgenic corn varieties are required to plant a portion of their field (refuge) with regular corn. This requirement is expected to prolong the efficiency of Bt corn in combating the ECB because some non-resistant pests can survive in the refuge, and thereby dilute the build-up of resistance in the overall pest population. A fixed refuge size of 20 percent is the currently recommended "rule-of-thumb" by the Environmental Protection Agency (EPA). Past work has searched for an economically-optimal refuge size utilizing discrete-time simulation approaches in which refuge size is treated as an exogenous parameter whose optimal value is found through numerical iteration. The objective of this work is to fine-tune parametric refuge specifications by formulating a bioeconomic model capable of endogenously determining the optimal trajectory of refuge sizes over time via an analytical optimal-control rule. The model will provide novel comparative statics/dynamics results demonstrating the sensitivity of the optimal trajectory to important economic and biological parameters