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What is Population Genetics?

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Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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Inference in population genetics using forward and backward, discrete and continuous time processes.

Juraj Bergman¹, Dominik Schrempf¹, Carolin Kosiol²

¹Institut für Populationsgenetik, Vetmeduni Vienna, Veterinärplatz 1, Wien, A-1210, Austria; Vienna Graduate School of Population Genetics, Wien, A-1210, Austria.

Journal of Theoretical Biology

|December 13, 2017

Summary

This study combines forward and backward diffusion processes to efficiently calculate allele frequency distributions for population genetics. This method enables precise inference of evolutionary history and demographic parameters.

Keywords:

Bi-allelic mutation-drift model Exact inference Forward-backward algorithm Forward-backward diffusion Markov chain

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Area of Science:

Population genetics
Evolutionary biology
Computational biology

Background:

Population genetics aims to infer evolutionary history using models of allele frequency evolution.
Forward-in-time models (Wright-Fisher, Moran, diffusion) are common but backward-in-time processes are underutilized for parameter inference.

Purpose of the Study:

To demonstrate a novel method combining forward and backward diffusion processes.
To efficiently calculate exact joint probability distributions of allele frequencies over time.
To enable precise inference of population genetic parameters.

Main Methods:

Integration of forward and backward diffusion processes.
Analogy to the forward-backward algorithm in hidden Markov models.
Expansion of transition density in orthogonal polynomials for continuous models.

Main Results:

Exact joint probability distribution of sample and population allele frequencies obtained for discrete and continuous models.
Efficient inference of marginal likelihoods for population genetic parameters.
Calculation of conditional allele trajectories and marginal likelihoods for single and multiple populations.

Conclusions:

The combined forward-backward diffusion approach offers efficient maximum likelihood inference.
Applicable to a wide range of demographic scenarios in population genetics.
Advances the computational tools for studying evolutionary history.