Statistical Inference in the Wright–Fisher Model Using Allele Frequency Data
Paula Tataru†, Maria Simonsen†, Thomas Bataillon and Asger Hobolth*
- Author Affiliations
Bioinformatics Research Centre, Aarhus University, Aarhus, 8000, Denmark.
↵*Correspondence to be sent to: Bioinformatics Research Centre, Aarhus University, C.F. Møllers Allé 8, Aarhus C 8000, Denmark; E-mail: asger@birc.au.dk
Received December 4, 2015 Revision received May 31, 2016 Accepted June 6, 2016.
Abstract
The Wright–Fisher model provides an elegant mathematical framework for understanding allele frequency data. In particular, the model can be used to infer the demographic history of species and identify loci under selection. A crucial quantity for inference under the Wright–Fisher model is the distribution of allele frequencies (DAF). Despite the apparent simplicity of the model, the calculation of the DAF is challenging. We review and discuss strategies for approximating the DAF, and how these are used in methods that perform inference from allele frequency data. Various evolutionary forces can be incorporated in the Wright–Fisher model, and we consider these in turn. We begin our review with the basic bi-allelic Wright–Fisher model where random genetic drift is the only evolutionary force. We then consider mutation, migration, and selection. In particular, we compare diffusion-based and moment-based methods in terms of accuracy, computational efficiency, and analytical tractability. We conclude with a brief overview of the multi-allelic process with a general mutation model.
[Allele frequency, diffusion, inference, moments, selection, Wright–Fisher.]
© The Author(s) 2016. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.
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