Abstract
Transgenic crops expressing Bacillus thuringiensis (Bt) toxins have been widely and successfully deployed for the control of target pests, while allowing a substantial reduction of insecticide use. The evolution of resistance (a heritable decrease in susceptibility to Bt toxins) can pose a threat to sustained control of target pests, but a high-dose refuge (HDR) management strategy has been key to delaying countervailing evolution of Bt resistance. The HDR strategy relies on the mating frequency between susceptible and resistant individuals, so either partial dominance of resistant alleles or non-random mating in the pest population itself could elevate the pace of resistance evolution. Using classic Wright-Fisher genetic models, we investigated the impact of deviations from standard refuge model assumptions on resistance evolution in the pest populations. We show that when Bt selection is strong, even deviations from random mating and/or strictly recessive resistance that are below the threshold of detection can yield dramatic increases in the pace of resistance evolution. Resistance evolution is hastened whenever the order of magnitude of model violations exceeds the initial frequency of resistant alleles. We also show that existence of a fitness cost for resistant individuals on the refuge crop cannot easily overcome the effect of violated HDR assumptions. We propose a parametrically explicit framework that enables both comparison of various field situations and model inference. Using this model, we propose novel empiric estimators of the pace of resistance evolution (and time to loss of control), whose simple calculation relies on the observed change in resistance allele frequency.