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GENERAL MOMENT CLOSURE FOR THE NEUTRAL TWO-LOCUS WRIGHT-FISHER DYNAMICS.

Raunak Kundagrami^1,2, Sean Yetter³, Matthias Steinrücken^2,4

¹Program in Biophysics, Harvard University, Boston, Massachusetts, USA.

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|February 6, 2026

Summary

Researchers developed a new method using coordinate transformation to solve the moment closure problem in population genetics. This approach accurately models genetic drift, mutation, and recombination dynamics for better parameter inference.

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Area of Science:

Population Genetics
Theoretical Biology
Computational Biology

Background:

The Wright-Fisher diffusion and coalescent process are fundamental in population genetics.
Current methods use ordinary differential equations to study genetic drift, mutation, and recombination dynamics.
A key challenge is the 'moment closure problem' where higher-order moments are needed to compute lower-order ones, especially under recombination.

Purpose of the Study:

To address the moment closure problem in population genetics.
To develop a more accurate and extensible method for analyzing population genetic processes.
To enable efficient computation of population genetic parameters and statistics.

Main Methods:

Applied a coordinate transformation to the diffusion generator of the Wright-Fisher model.
Derived a system of differential equations for canonical moments in the transformed coordinates.
Utilized simulations to verify the accuracy and efficiency of the new method.

Main Results:

The coordinate transformation yields a closed system of equations for the moments.
This closed system allows for more accurate numerical computations compared to previous approaches.
Simulations confirm the ability to accurately capture moment dynamics and compute diversity/linkage statistics.

Conclusions:

The novel coordinate transformation effectively solves the moment closure problem.
This method offers a more robust and generalizable framework for population genetic analyses.
The approach facilitates efficient inference of demographic histories and recombination rates.