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A class of fast–slow models for adaptive resistance evolution

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  • Pérez-Estigarribia, Pastor E.
  • Bliman, Pierre-Alexandre
  • Schaerer, Christian E.

Abstract

Resistance to insecticide is considered nowadays one of the major threats to insect control, as its occurrence reduces drastically the efficiency of chemical control campaigns, and may also perturb the application of other control methods, like biological and genetic control. In order to account for the emergence and spread of such phenomenon as an effect of exposition to larvicide and/or adulticide, we develop in this paper a general time-continuous population model with two life phases, subsequently simplified through slow manifold theory. The derived models present density-dependent recruitment and mortality rates in a non-conventional way. We show that in absence of selection, they evolve in compliance with Hardy–Weinberg law; while in presence of selection and in the dominant or codominant cases, convergence to the fittest genotype occurs. The proposed mathematical models should allow for the study of several issues of importance related to the use of insecticides and other adaptive phenomena.

Suggested Citation

  • Pérez-Estigarribia, Pastor E. & Bliman, Pierre-Alexandre & Schaerer, Christian E., 2020. "A class of fast–slow models for adaptive resistance evolution," Theoretical Population Biology, Elsevier, vol. 135(C), pages 32-48.
    • Handle: RePEc:eee:thpobi:v:135:y:2020:i:c:p:32-48
    DOI: 10.1016/j.tpb.2020.07.003
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    References listed on IDEAS

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    1. Li, Yazhi & Liu, Xianning, 2020. "Modeling and control of mosquito-borne diseases with Wolbachia and insecticides," Theoretical Population Biology, Elsevier, vol. 132(C), pages 82-91.
    2. Samir Bhatt & Peter W. Gething & Oliver J. Brady & Jane P. Messina & Andrew W. Farlow & Catherine L. Moyes & John M. Drake & John S. Brownstein & Anne G. Hoen & Osman Sankoh & Monica F. Myers & Dylan , 2013. "The global distribution and burden of dengue," Nature, Nature, vol. 496(7446), pages 504-507, April.
    3. Denis D. Bourguet & Anne Genissel & Michel Raymond, 2000. "Insecticide resistance and dominance levels," Post-Print hal-02690678, HAL.
    4. Siegfried Berninghaus & Karl-Martin Ehrhart & Marion Ott & Bodo Vogt, 2007. "Evolution of networks—an experimental analysis," Journal of Evolutionary Economics, Springer, vol. 17(3), pages 317-347, June.
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