Effects of insect population size on evolution of resistance to transgenic crops

Models of the evolution of insect resistance to transgenic crops have often assumed that population size is infinite or that carrying capacity is fixed. To evaluate potential effects of population size on resistance evolution, we conducted sensitivity analyses by using a stochastic, spatially explicit model based partly on the interaction between pink bollworm and Bacillus thuringiensis (Bt) cotton. We examined interactions of carrying capacity, region size, dispersal, and percentage of fields planted with Bt cotton. The median and variance in the time to resistance decreased as region size increased, regardless of carrying capacity. This occurred because larger regions were more likely to have at least one field in which resistance evolved rapidly and served as a source from which resistance spread throughout the region. Carrying capacity significantly affected the median time to resistance with 75% of fields planted with Bt cotton, but not with 50% Bt cotton. In contrast, carrying capacity significantly influenced the variance in the time to resistance with 50% Bt cotton, but not with 75% Bt cotton. We also found resistance evolution was affected by interactions between carrying capacity, dispersal, and the percentage of fields planted with Bt cotton. The high variability observed in our simulations indicates that factors affecting stochastic events can play an important role in the evolution of resistance. Because population size determines the extent to which stochastic events are important, reasonable estimates of population size are essential for devising robust models of resistance evolution.