Disease-induced natural selection in a diploid host

Area of Science:

• Population Genetics
• Epidemiology
• Mathematical Biology

Background:

• Understanding host-pathogen interactions is crucial for predicting disease dynamics.
• Genetic variation influences disease susceptibility and resistance within host populations.
• Mathematical models are essential for analyzing complex evolutionary and epidemiological processes.

Purpose of the Study:

• To develop a model describing natural selection for disease resistance in a diploid host.
• To analyze the dynamics of gene frequency changes under disease pressure.
• To derive explicit expressions for genotypic fitness based on epidemiological parameters.

Main Methods:

• Utilized an SIR-type disease transmission model for a continuously breeding diploid host.
• Transformed the system into variables representing population size, gene frequency, and deviation from Hardy-Weinberg proportions (fixation index).
• Assumed slow selection (small variation in disease response among genotypes) to simplify the model into three blocks: disease dynamics, fixation index, and gene frequency change.

Main Results:

• The model separates into blocks describing population disease dynamics, fixation index, and gene frequency change.
• Disease dynamics and fixation index reach equilibrium determined by population turnover time.
• Gene frequency dynamics are dominated by a slowly changing average gene frequency, yielding explicit genotypic fitness expressions.

Conclusions:

• The developed model provides a framework for understanding the interplay between disease dynamics and host genetic evolution.
• The findings offer epidemiologically justified fitness expressions applicable to various disease transmission patterns.
• The approach can be extended to analyze diseases with temporally varying incidence through time averaging.