# Ancestral inference from haplotypes and mutations

## TL;DR

This paper develops methods for inferring the evolutionary history of DNA sequences based on haplotype and mutation data, using coalescent theory and sampling techniques, with applications to human Y chromosome data.

## Contribution

It introduces new theoretical results and sampling algorithms for ancestral inference from haplotypes and segregating sites, extending existing formulas and accommodating variable population sizes.

## Key findings

- Effective inference methods demonstrated on human Y chromosome data
- Extension of Ewens Sampling Formula for haplotype configurations
- Implementation of rejection and importance sampling schemes

## Abstract

We consider inference about the history of a sample of DNA sequences, conditional upon the haplotype counts and the number of segregating sites observed at the present time. After deriving some theoretical results in the coalescent setting, we implement rejection sampling and importance sampling schemes to perform the inference. The importance sampling scheme addresses an extension of the Ewens Sampling Formula for a configuration of haplotypes and the number of segregating sites in the sample. The implementations include both constant and variable population size models. The methods are illustrated by two human Y chromosome data sets.