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Neural Networks for self-adjusting Mutation Rate Estimation when the Recombination Rate is unknown

Klara Elisabeth Burger, View ORCID ProfilePeter Pfaffelhuber, View ORCID ProfileFranz Baumdicker
doi: https://doi.org/10.1101/2021.09.02.457550
Klara Elisabeth Burger
1Cluster of Excellence “Machine Learning: New Perspectives for Science”, University of Tübingen, Germany
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Peter Pfaffelhuber
2Department of Mathematical Stochastics, University of Freiburg, Germany
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Franz Baumdicker
1Cluster of Excellence “Machine Learning: New Perspectives for Science”, University of Tübingen, Germany
3Cluster of Excellence “Controlling Microbes to Fight Infections”, Mathematical and Computational Population Genetics, University of Tübingen, Germany
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  • For correspondence: franz.baumdicker@uni-tuebingen.de
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Abstract

Estimating the mutation rate, or equivalently effective population size, is a common task in population genetics. If recombination is low or high, optimal linear estimation methods are known and well understood. For intermediate recombination rates, the calculation of optimal estimators is more challenging. As an alternative to model-based estimation, neural networks and other machine learning tools could help to develop good estimators in these involved scenarios. However, if no benchmark is available it is difficult to assess how well suited these tools are for different applications in population genetics.

Here we investigate feedforward neural networks for the estimation of the mutation rate based on the site frequency spectrum and compare their performance with model-based estimators. For this we use the model-based estimators introduced by Fu, Futschik et al., and Watterson that minimize the variance or mean square error for no and free recombination. We find that neural networks reproduce these estimators if provided with the appropriate features and training sets. Remarkably, using the model-based estimators to adjust the weights of the training data, only one hidden layer is necessary to obtain a single estimator that performs almost as well as model-based estimators for low and high recombination rates, and at the same time provides a superior estimation method for intermediate recombination rates. We apply the method to simulated data based on the human chromosome 2 recombination map, highlighting its robustness in a realistic setting where local recombination rates vary and/or are unknown.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • Section on human recombination map added; Comparison to other methods added; Supplemental files added

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted May 17, 2022.
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Neural Networks for self-adjusting Mutation Rate Estimation when the Recombination Rate is unknown
Klara Elisabeth Burger, Peter Pfaffelhuber, Franz Baumdicker
bioRxiv 2021.09.02.457550; doi: https://doi.org/10.1101/2021.09.02.457550
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Neural Networks for self-adjusting Mutation Rate Estimation when the Recombination Rate is unknown
Klara Elisabeth Burger, Peter Pfaffelhuber, Franz Baumdicker
bioRxiv 2021.09.02.457550; doi: https://doi.org/10.1101/2021.09.02.457550

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