Understanding Admixture Fractions

Abstract

Estimation of admixture fractions has become one of the most commonly used computational tools in population genomics. However, 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.

Genome-wide Ancestry Patterns in Rapanui Suggest Pre-European Admixture with Native Americans

“…The length distribution of ancestry tracts therefore contains information regarding admixture times [35][36][37]. Additionally, due to sexual reproduction, ancestry tracts being exchanged among individuals leads to a more homogenous distribution of ancestry proportions among individuals as time passes [33,38].…”

“…As described below, all 27 were used for phasing, while only the 8 unrelated individuals were used for admixture analyses (using ADMIXTURE [31] and RFmix [32]) and for demographic inference (using tracts and the method described in [33]). We compiled a data set that includes genotype data from 58 Europeans (CEU), 15 New Guinea Highlanders, 17 Native Americans, 45 Chinese (CHB), 21 Borneans, 33 Polynesians (seven different locations: Futuna, Niue, Samoa, Tokelau, Tonga, Tuvalu, and Cook Islands), and 8 unrelated Rapanui.…”

Thinking about populations and races in time

“…However, the choice of the proxy populations is at least partially arbitrary, therefore each attribution of a specific genetic ancestry to an individual is in itself ambiguous" (THIS ISSUE, PG; emphasis in original, references deleted). 26 See Verdu and Rosenberg (2011) and Liang and Nielsen (2014) for methods that seek to take into account the history of population admixtures.…”

The Spatial Mixing of Genomes in Secondary Contact Zones

“…Under this simple model, the distribution of admixture tract lengths and the decay of admixture LD with respect to genetic distance are approximately exponential, with the rate parameter corresponding to the time in generations since admixture. However, violations of the assumptions of the single-pulse model can result in substantial departure between expected and observed rates of decay of coancestry with respect to time.Models incorporating multiple admixture times, or sustained migration (Pool and Nielsen 2009;Gravel 2012;Hellenthal et al 2014;Liang and Nielsen 2014b), have been built to address more complex admixture scenarios in single populations. However, these do not incorporate the fact that admixture often occurs in a geographic context-beginning at a given point in time, then spreading across space.…”

“…Models incorporating multiple admixture times, or sustained migration (Pool and Nielsen 2009;Gravel 2012;Hellenthal et al 2014;Liang and Nielsen 2014b), have been built to address more complex admixture scenarios in single populations. However, these do not incorporate the fact that admixture often occurs in a geographic context-beginning at a given point in time, then spreading across space.…”