A model of weak selection in the infinite alleles framework

Area of Science:

• Population genetics
• Theoretical biology
• Mathematical modeling

Background:

• The Ewens (1972) model describes allele frequency dynamics assuming all alleles are neutral.
• Understanding deviations from neutrality is crucial for evolutionary studies.
• Infinite allele models are fundamental in population genetics.

Purpose of the Study:

• To generalize Ewens' infinite allele model to incorporate weak selection.
• To provide a mathematical framework for analyzing allele frequency changes under weak selection.
• To extend the applicability of the infinite allele model.

Main Methods:

• Development of a generalized Ewens sampling formula.
• Utilizing continuous-time, discrete-state space Markov processes.
• Mathematical analysis of allele frequency distributions.

Main Results:

• A generalized result for the infinite allele model under weak selection is derived.
• The model accounts for the impact of weak selection on allele frequencies.
• The framework allows for the study of allele diversity with weak selection.

Conclusions:

• The generalized model provides a more realistic framework for population genetics.
• Weak selection can be incorporated into the infinite allele model using Markov processes.
• This work extends theoretical population genetics by including weak selection effects.