Evolution of resistance to a single Bt toxin crop under random oviposition (magenta lines) and damage-avoiding oviposition (blue lines). Models simulated three scenarios for pest management with different forms of density dependence under fully recessive (h = 0) or partially dominant resistance (h = 0.1). In A and B pest management in refugia uses a density-dependent spray threshold of 0.25 egg masses per plant; in C and D natural enemies cause density-dependent mortality in refugia while in E and F natural enemies cause density-dependent mortality throughout the refugia and the Bt crop. The response variable is the number of generations required for the resistance gene frequency (R) to equal or exceed 0.5, up to maximum of 200. Note that a value of 200 is returned if the frequency of resistance never exceeded 0.5. Fecundity was set at 300 eggs per female and the initial resistance gene frequency was 0.001. G and H show the relationship between population density and avoidance of refugia under the two modeling scenarios with h = 0.1. Parameter values in the last two panels are calculated before the evolution of full resistance, that is, from generation 1 until the time point at which the frequency R > = 0.5. The refuge avoidance factor is 1/b and represents the multiplicative reduction in eggs laid in the refuge relative to random expectation, so that 1 indicates random oviposition and 3 indicates a three-fold reduction in egg counts relative to random expectation.