The evolution of resistance against pesticides is an important problem of modern agriculture. The high-dose/refuge strategy, which divides the landscape into treated and nontreated (refuge) patches, has proven effective at delaying resistance evolution. However, theoretical understanding is still incomplete, especially for combinations of limited dispersal and partially recessive resistance. We reformulate a two-patch model based on the Comins model and derive a simple quadratic approximation to analyze the effects of limited dispersal, refuge size, and dominance for high efficacy treatments on the rate of evolution. When a small but substantial number of heterozygotes can survive in the treated patch, a larger refuge always reduces the rate of resistance evolution. However, when dominance is small enough, the evolutionary dynamics in the refuge population, which is indirectly driven by migrants from the treated patch, mainly describes the resistance evolution in the landscape. In this case, for small refuges, increasing the refuge size will increase the rate of resistance evolution. Our analysis distils major driving forces from the model, and can provide a framework for understanding directional selection in source-sink environments.
Bibliographical noteFunding Information:
D.T. carried out numerical and analytical investigations. T.Y., D.A.A, and D.T designed the study. D.T. and M.S. prepared an initial manuscript. All authors prepared the manuscript. We thank Dr. Yoshito Suzuki for helpful discussions. The work was supported by a grant from the Ministry of Agriculture, Forestry, and Fisheries of Japan (Genomics-based Technology for Agricultural Improvement, PRM-4201), a grant from the Kempe Foundation SMK-1447 to D.T., and USDA Regional research project NC-205 to D.A.A. We declare no competing financial or nonfinancial interests. The code is available in the Dryad data repository doi:https://doi.org/10.5061/dryad.mb4g0.
- directional selection
- genetically modified organism
- high-dose/refuge strategy
- pesticide resistance management
- spatially implicit model