TRACTABLE DIFFUSION AND COALESCENT PROCESSES FOR WEAKLY CORRELATED LOCI

Area of Science:

• Population genetics
• Mathematical biology
• Evolutionary genetics

Background:

• The Wright-Fisher diffusion and Kingman's coalescent are standard multilocus population genetics models.
• Existing models lack closed-form sampling distributions and are computationally intensive.

Purpose of the Study:

• To derive new, simplified multilocus population genetic models.
• To develop models that are computationally tractable while retaining key properties of existing models.
• To provide closed-form solutions for sampling distributions.

Main Methods:

• Derivation of a new diffusion model using a central limit theorem for density-dependent processes.
• Development of a new coalescent process via probabilistic coupling of the ancestral recombination graph.
• Analysis of sampling distributions as asymptotic expansions in inverse powers of the recombination parameter.

Main Results:

• The new diffusion model yields a sampling distribution as a linear combination of Gaussian moments, providing a closed-form solution.
• The new coalescent process simplifies the dynamics of the ancestral recombination graph.
• The derived models agree with standard models up to the second order for large recombination rates.

Conclusions:

• The new models offer significant computational advantages over existing multilocus population genetics models.
• These simplified models accurately approximate complex dynamics, particularly for large recombination rates.
• The closed-form solutions facilitate theoretical and empirical applications in population genetics research.