A class of fast-slow models for adaptive resistance evolution

Area of Science:

• Mathematical modeling
• Population dynamics
• Insecticide resistance

Background:

• Insecticide resistance is a major threat to effective insect control.
• Resistance compromises chemical, biological, and genetic control methods.
• Understanding resistance emergence is crucial for sustainable pest management.

Purpose of the Study:

• To develop and simplify mathematical models for insect population dynamics under insecticide exposure.
• To analyze the evolutionary trajectories of insect populations with density-dependent rates.
• To investigate the impact of selection on genotype frequencies.

Main Methods:

• Development of a general time-continuous population model with two life phases.
• Simplification of the model using slow manifold theory.
• Analysis of population dynamics under varying selection pressures.

Main Results:

• Derived models exhibit density-dependent recruitment and mortality.
• In the absence of selection, populations adhere to Hardy-Weinberg law.
• Under selection (dominant/codominant cases), populations converge to the fittest genotype.

Conclusions:

• The developed mathematical models provide insights into insecticide resistance.
• Models can aid in studying adaptive phenomena related to insecticide use.
• Understanding evolutionary dynamics is key to optimizing insect control strategies.