Exact coalescent likelihoods for unlinked markers in finite-sites mutation models

TL;DR

This paper derives exact formulas for allele frequency spectra under coalescent models with mutation, enabling efficient analysis of unlinked biallelic markers for demographic and species inference.

Contribution

It introduces exact coalescent likelihood calculations for unlinked markers under finite-sites mutation models, extending previous methods.

Findings

Provides exact formulas for allele frequency spectra

Enables fast computations in multiple populations

Facilitates demographic and species tree inference

Abstract

We derive exact formulae for the allele frequency spectrum under the coalescent with mutation, conditioned on allele counts at some fixed time in the past. We consider unlinked biallelic markers mutating according to a finite sites, or infinite sites, model. This work extends the coalescent theory of unlinked biallelic markers, enabling fast computations of allele frequency spectra in multiple populations. Our results have applications to demographic inference, species tree inference, and the analysis of genetic variation in closely related species more generally.