A High-Order Cumulant Extension of Quasi-Linkage Equilibrium

Area of Science:

• Evolutionary Biology
• Population Genetics
• Quantitative Genetics

Background:

• Modeling genetically diverse populations requires tracking allele correlations (cumulants) across loci.
• The quasi-linkage equilibrium (QLE) approximation simplifies this by assuming weak correlations (low linkage disequilibrium).
• Standard QLE fails under strong selection, epistasis, or weak recombination.

Purpose of the Study:

• To extend the multilocus QLE framework to handle complex population dynamics.
• To develop a more robust approximation for allele frequency changes in evolutionary biology.
• To improve the modeling of genetic interactions and selection.

Main Methods:

• Developed an extended QLE (exQLE) framework allowing cumulants up to order K to evolve dynamically.
• Assumed higher-order cumulants rapidly equilibrate.
• Derived a general equation of motion for cumulants up to order K, paralleling standard QLE.

Main Results:

• The exQLE framework accurately captures cumulant dynamics, even with higher-order epistatic interactions (K=2).
• exQLE dynamics are driven by the average fitness gradient and genotype competition.
• The framework was successfully applied to infer fitness parameters from temporal sequence data.

Conclusions:

• exQLE offers a systematic and interpretable approximation scheme for population genetics.
• It reduces complexity by truncating higher-order cumulants.
• exQLE provides a powerful tool for analyzing evolutionary dynamics beyond the limitations of standard QLE.