Allele Age Under Non-Classical Assumptions is Clarified by an Exact Computational Markov Chain Approach

Bianca De Sanctis,A P Jason De Koning,Ivan Krukov

doi:10.1038/s41598-017-12239-0

Bianca De Sanctis, A P Jason De Koning + Show 1 more

Open Access

https://doi.org/10.1038/s41598-017-12239-0

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Abstract

Determination of the age of an allele based on its population frequency is a well-studied problem in population genetics, for which a variety of approximations have been proposed. We present a new result that, surprisingly, allows the expectation and variance of allele age to be computed exactly (within machine precision) for any finite absorbing Markov chain model in a matter of seconds. This approach makes none of the classical assumptions (e.g., weak selection, reversibility, infinite sites), exploits modern sparse linear algebra techniques, integrates over all sample paths, and is rapidly computable for Wright-Fisher populations up to Ne = 100,000. With this approach, we study the joint effect of recurrent mutation, dominance, and selection, and demonstrate new examples of “selective strolls” where the classical symmetry of allele age with respect to selection is violated by weakly selected alleles that are older than neutral alleles at the same frequency. We also show evidence for a strong age imbalance, where rare deleterious alleles are expected to be substantially older than advantageous alleles observed at the same frequency when population-scaled mutation rates are large. These results highlight the under-appreciated utility of computational methods for the direct analysis of Markov chain models in population genetics.

Highlights

Are expected to be recessive and weakly deleterious, and it is conceivable that this slowdown effect could thereby mislead attempts to make inferences about natural selection
To study the effects of non-classical parameter ranges on allele age, we develop a new exact approach capable of rapidly computing moments of the allele age distribution under any absorbing discrete-time Markov chain model of population genetics
Computational population genetics approaches offer the relatively straightforward ability to explore parameter ranges or assumptions that may be inaccessible to classical theory

Summary

Introduction

Are expected to be recessive and weakly deleterious, and it is conceivable that this slowdown effect could thereby mislead attempts to make inferences about natural selection. Messer and Petrov[21] have highlighted that most known cases of molecular adaptation across diverse organisms show signatures of soft selective sweeps (but see ref.22), where adaptive alleles have multiple origins either by recurrent mutation or migration These findings are potentially unexpected if evolution is strongly mutation-limited and may indicate that the effective population-scaled mutation rate is underestimated in many cases and/or that adaptation may tend to occur during periods of episodically large population size (and high θ)[23]. To study the effects of non-classical parameter ranges on allele age, we develop a new exact approach capable of rapidly computing moments of the allele age distribution under any absorbing discrete-time Markov chain model of population genetics This approach exploits sparsity, parallelism, and modern computational architectures[25], and is completely general with respect to the underlying model. We have implemented this method in our software package Wright-Fisher Exact Solver, WFES25 (available at https://github. com/dekoning-lab/wfes/)

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