## Abstract

The stationary sampling distribution of a neutral decoupled Moran or Wright–Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this distribution as a starting point we derive results for maximum likelihood estimates of scaled mutation rates from site frequency data under three model assumptions: a twelve-parameter general rate matrix, a nine-parameter reversible rate matrix, and a six-parameter strand-symmetric rate matrix. The site frequency spectrum is assumed to be sampled from a fixed size population in equilibrium, and to consist of allele frequency data at a large number of unlinked sites evolving with a common mutation rate matrix without selective bias. We correct an error in a previous treatment of the same problem (Burden and Tang, 2017) affecting the estimators for the general and strand-symmetric rate matrices. The method is applied to a biological dataset consisting of a site frequency spectrum extracted from short autosomal introns in a sample of Drosophila melanogaster individuals.

Original language | English |
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Pages (from-to) | 106-118 |

Number of pages | 13 |

Journal | Theoretical Population Biology |

Volume | 134 |

Early online date | 18 Jun 2020 |

DOIs | |

Publication status | Published - Aug 2020 |

## Keywords

- Decoupled Moran diffusion
- Mutation–drift model
- Scaled mutation parameters
- Strand-symmetry
- Wright–Fisher diffusion