Models for the evolution of resistance have been crucial for informing policy decisions on the regulation of transgenic crops around the world.  These models have ranged from relatively simple ones with basic dynamical equations for population growth and directional selection on a two-allele, one-locus trait, to quite complex models that attempt to mimic the specific crop and pest herbivore.  Most decisions based on the high-dose refuge strategy and associated models have been consistent world wide, but for low-dose crops the decisions have been diverse.  Two additional areas have resulted in substantial discrepancies or controversies around the world.  First, management of the refuge population has been restricted in some situations in the US, while it is generally allowed in Australia.  Second, for crops with multiple toxins (so-called pyramided traits), should the size of the refuge be reduced?  These problems have resulted in an intriguing mix of science and policy, to which models have been added. 

Results/Conclusions

Crucial differences among the models have in part contributed to the heterogeneous decisions around the world.  I review several of the published models, and show how the concepts of high-dose and low-dose can be confused.  By defining these concepts in terms of selection coefficients on the SS susceptible homozygotes and SR heterozygotes, the distinction between high-dose and low-dose can be clarified, and regulatory implications can be clarified.  Population suppression on the refuge has been shown to accelerate resistance evolution in some models, and to have no effect on evolutionary rates in others (expect when population suppression is severe).  The reasons for these differences are due to the way the models are structured, not to population management per se.  The details are complicated, but a close look reveals the underlying basis for how the refuge population affects resistance evolution, and helps clarify how population ecology and population genetics may interact to affect evolutionary rates.  If time is available, evolution and cross-resistance to pyramided traits will also be discussed.