The multivariate Wright-Fisher process with mutation: Moment-based analysis and inference using a hierarchical Beta model

Theoretical Population Biology
Asger Hobolth, Jukka Sirén


We consider the diffusion approximation of the multivariate Wright-Fisher process with mutation. Analytically tractable formulas for the first-and second-order moments of the allele frequency distribution are derived, and the moments are subsequently used to better understand key population genetics parameters and modeling frameworks. In particular we investigate the behavior of the expected homozygosity (the probability that two randomly sampled genes are identical) in the transient and stationary phases, and how appropriate the Dirichlet distribution is for modeling the allele frequency distribution at different evolutionary time scales. We find that the Dirichlet distribution is adequate for the pure drift model (no mutations allowed), but the distribution is not sufficiently flexible for more general mutation models. We suggest a new hierarchical Beta distribution for the allele frequencies in the Wright-Fisher process with a mutation model on the nucleotide level that distinguishes between transitions and transversions.


May 2, 2006·Statistical Applications in Genetics and Molecular Biology·Asger Hobolth, Jens Ledet Jensen
Mar 25, 2009·Trends in Ecology & Evolution·James H Degnan, Noah A Rosenberg
Nov 13, 2009·Molecular Biology and Evolution·Joseph Heled, Alexei J Drummond
Sep 8, 2010·Molecular Biology and Evolution·Jukka SirénJukka Corander
May 14, 2011·Molecular Ecology Resources·Oscar E Gaggiotti, Matthieu Foll
Mar 17, 2012·Molecular Biology and Evolution·David BryantArindam RoyChoudhury
Sep 21, 2012·Molecular Biology and Evolution·Jukka SirénJukka Corander
Nov 21, 2012·PLoS Genetics·Joseph K Pickrell, Jonathan K Pritchard
Aug 3, 2013·Molecular Biology and Evolution·Nicola De MaioCarolin Kosiol
Jul 26, 2015·Systematic Biology·Nicola De MaioCarolin Kosiol


Feb 9, 2019·Journal of Mathematical Biology·Maria Simonsen SpeedAsger Hobolth

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