Duality between the two-locus Wright-Fisher Diffusion Model and the Ancestral Process with Recombination

TL;DR

This paper explores the duality between the two-locus Wright-Fisher diffusion model and the ancestral process with recombination, providing numerical and analytical methods to compute moments and studying properties of the ancestral recombination graph.

Contribution

It introduces new numerical and analytical methods for computing moments and analyzes properties of the ancestral recombination graph using duality.

Findings

Numerical methods for moment computation via Markov chain Monte Carlo

Closed-form expressions for moments of the diffusion model

Insights into the properties of the ancestral recombination graph

Abstract

Known results on the moments of the distribution generated by the two-locus Wright-Fisher diffusion model and a duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical methods for computing moments by a Markov chain Monte Carlo and a method to compute closed-form expressions of the moments are presented. By using the duality argument properties of the ancestral recombination graph are studied in terms of the moments.