Approximating genealogies for partially linked neutral loci under a selective sweep

Area of Science:

• Population Genetics
• Evolutionary Biology
• Theoretical Biology

Background:

• Selective sweeps, driven by beneficial alleles, rapidly reduce genetic diversity at linked neutral loci.
• The impact of selective sweeps extends to the joint allele distribution across multiple linked neutral loci.
• Understanding these effects is crucial for interpreting patterns of genetic variation in populations.

Purpose of the Study:

• To develop a theoretical framework for approximating the ancestral recombination graph (ARG) during a selective sweep.
• To analyze the joint genealogies of two partially linked neutral loci under strong selection.
• To provide accurate predictions for allele frequency distributions and associations.

Main Methods:

• Extension of existing work on marked Yule trees to model genealogies linked to a beneficial allele.
• Focus on large selection coefficients and specific recombination rates between loci.
• Probabilistic approximation of the genealogy with a defined accuracy.

Main Results:

• A full description of the joint genealogy at two linked neutral loci during a selective sweep.
• The developed method achieves a probabilistic accuracy of theta((log alpha)(-2)).
• Derivation of the expectation of Lewontin's D to quantify non-random allele association.

Conclusions:

• The study provides a robust theoretical tool for analyzing genetic diversity patterns under strong selection.
• The findings offer insights into how selective sweeps shape the joint distribution of alleles at linked loci.
• The derived expectation of Lewontin's D can be used to detect historical selective events.