Allele frequencies in a multidimensional Wright-Fisher model with general mutation

Area of Science:

• Population genetics
• Mathematical biology
• Evolutionary genetics

Background:

• Understanding genetic variation is crucial in evolutionary studies.
• Neutral models like the Wright-Fisher model are foundational for population genetics.
• General mutation rates and asymmetry impact genetic diversity.

Purpose of the Study:

• To derive a formula for the probability of sampling two genes of specific types at a single locus.
• To analyze genetic variation under a neutral Wright-Fisher diffusion approximation with general mutation.
• To provide formulas for allele sampling probabilities and segregating sites in finite sequences.

Main Methods:

• Utilizing a diffusion approximation to the neutral Wright-Fisher model.
• Developing exact and approximate calculations for the probability matrix Q.
• Deriving a formula for the distribution of segregating sites in linked sequences.

Main Results:

• A formula for the probability of two randomly sampled genes being of particular types was obtained.
• The probability matrix Q was calculated exactly and approximately for a specific mutation rate scenario.
• A formula for the distribution of segregating sites in finite, completely linked sequences was derived.

Conclusions:

• The derived formulas offer insights into genetic variation dynamics with general mutation.
• The study provides tools for analyzing allele frequencies and site patterns in finite populations.
• This work contributes to the theoretical framework of population genetics and molecular evolution.