title: Type of fitness cost influences the rate of evolution of resistance to transgenic Bt crops.
abstract: The evolution of resistance to pesticides by insect pests is a significant challenge for sustainable agriculture. For transgenic crops expressingBacillus thuringiensis(Bt), crystalline (Cry) toxins resistance evolution may be delayed by the high-dose/refuge strategy in which a non-toxic refuge is planted to promote the survival of susceptible insects. The high-dose/refuge strategy may interact with fitness costs associated with resistance alleles to further delay resistance. However, while a diverse range of fitness costs are reported in the field, they are typically represented as a fixed reduction in survival or viability which is insensitive to ecological conditions such as competition. Furthermore, the potential dynamic consequences of restricting susceptible insects to a refuge which represents only a fraction of the available space have rarely been considered.We present a generalized discrete time model which utilizes dynamic programming methods to derive the optimal management decisions for the control of a theoretical insect pest population exposed to Bt crops. We consider three genotypes (susceptible homozygotes, resistant homozygotes and heterozygotes) and implement fitness costs of resistance to Bt toxins as either a decrease in the relative competitive ability of resistant insects or as a penalty on fecundity. Model analysis is repeated and contrasted for two types of density dependence: uniform density dependence which operates equally across the landscape and heterogeneous density dependence where the intensity of competition scales inversely with patch size and is determined separately for the refuge and Bt crop.When the planting of Bt is decided optimally, fitness costs to fecundity allow for the planting of larger areas of Bt crops than equivalent fitness costs that reduce the competitive ability of resistant insects.Heterogeneous competition only influenced model predictions when the proportional area of Bt planted in each season was decided optimally and resistance was not recessive.Synthesis and applications. The high-dose/refuge strategy alone is insufficient to preserve susceptibility to transgenicBacillus thuringiensis(Bt) crops in the long term when constraints upon the evolution of resistance are not insurmountable. Fitness costs may enhance the delaying effect of the refuge, but the extent to which they do so depends upon how the cost is realized biologically. Fitness costs which apply independently of other variables may be more beneficial to resistance management than costs which are only visible to selection under a limited range of ecological conditions.
authors.affiliation: Department of Zoology Mathematical Ecology Research Group University of Oxford South Parks Road Oxford OX1 3PS UK.
authors.forename: Sean C
authors.initials: SC
authors.lastname: Hackett
authors.affiliation: Department of Zoology Mathematical Ecology Research Group University of Oxford South Parks Road Oxford OX1 3PS UK; St. Peter's College New Inn Hall Street Oxford OX1 2DL UK.
authors.forename: Michael B
authors.initials: MB
authors.lastname: Bonsall
keywords: Bacillus thuringiensis; density dependence; dynamic programming; evolution; high‐dose/refuge strategy; population dynamics; population genetics; resistance management; selection; transgenic crops