# Understanding Admixture Fractions

## TL;DR

This paper develops theoretical models to better understand and estimate admixture fractions in population genomics.

## Contribution

The paper introduces new theoretical results and a method to estimate admixture parameters using population genetic theory.

## Key findings

- Theoretical recurrence relations predict admixture fraction means and variances.
- Closed-form solutions are derived for special cases of admixture models.
- A model of constant gene flow fits African American population history better than a single admixture event.

## Abstract

Estimation of admixture fractions has become one of the most commonly used computational tools in population genomics. How ever, there is remarkably little population genetic theory on their statistical properties. We develop theoretical results that can accurately predict means and variances of admixture proportions within a population using models with recombination and genetic drift. Based on established theory on measures of multilocus disequilibrium, we show that there is a set of recurrence relations that can be used to derive expectations for higher moments of the admixture fraction distribution. We obtain closed form solutions for some special cases. Using these results, we develop a method for estimating admixture parameters from estimated admixture proportion obtained from programs such as Structure or Admixture. We apply this method to HapMap data and find that the population history of African Americans, as expected, is not best explained by a single admixture event between people of European and African ancestry. A model of constant gene flow for the past 11 generations until 2 generations ago gives a better fit.