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Combined Immunofluorescence and DNA FISH on 3D-preserved Interphase Nuclei to Study Changes in 3D Nuclear Organization

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TRACTABLE DIFFUSION AND COALESCENT PROCESSES FOR WEAKLY CORRELATED LOCI.

Paul A Jenkins¹, Paul Fearnhead², Yun S Song³

¹Department of Statistics, University of Warwick, Coventry CV4 7AL, UK, p.jenkins@warwick.ac.uk.

Electronic Journal of Probability

|July 5, 2016

Summary

This study introduces new, simplified multilocus population genetic models. These models, a diffusion and a coalescent process, offer closed-form solutions and capture key properties of existing complex models for large recombination rates.

Keywords:

coupling diffusion population genetics recombination sampling distribution

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Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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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.