Maximum likelihood estimators for scaled mutation rates in an equilibrium mutation-drift model

TL;DR

This paper derives maximum likelihood estimators for scaled mutation rates in equilibrium mutation-drift models, correcting previous errors and applying the method to Drosophila genetic data.

Contribution

It introduces corrected maximum likelihood estimators for mutation rates under various rate matrix models in equilibrium populations.

Findings

Corrected estimators for mutation rates in general, reversible, and strand-symmetric models.

Application to Drosophila intron data demonstrating practical utility.

Enhanced understanding of mutation rate estimation in population genetics.

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.