A fast-slow model for adaptive resistance evolution

TL;DR

This paper introduces a novel mathematical model for understanding how insecticide resistance evolves in insect populations, accounting for different life stages and adaptive dynamics, aiding in better control strategies.

Contribution

It develops a general time-continuous population model with two life phases, simplified via slow manifold theory, to study resistance evolution under insecticide exposure.

Findings

Models comply with Hardy-Weinberg law without selection

Convergence to the fittest genotype occurs with selection

Density-dependent recruitment and mortality are modeled non-conventionally

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.