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Principal Components Analysis of Population Admixture

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  • Jianzhong Ma
  • Christopher I Amos

Abstract

With the availability of high-density genotype information, principal components analysis (PCA) is now routinely used to detect and quantify the genetic structure of populations in both population genetics and genetic epidemiology. An important issue is how to make appropriate and correct inferences about population relationships from the results of PCA, especially when admixed individuals are included in the analysis. We extend our recently developed theoretical formulation of PCA to allow for admixed populations. Because the sampled individuals are treated as features, our generalized formulation of PCA directly relates the pattern of the scatter plot of the top eigenvectors to the admixture proportions and parameters reflecting the population relationships, and thus can provide valuable guidance on how to properly interpret the results of PCA in practice. Using our formulation, we theoretically justify the diagnostic of two-way admixture. More importantly, our theoretical investigations based on the proposed formulation yield a diagnostic of multi-way admixture. For instance, we found that admixed individuals with three parental populations are distributed inside the triangle formed by their parental populations and divide the triangle into three smaller triangles whose areas have the same proportions in the big triangle as the corresponding admixture proportions. We tested and illustrated these findings using simulated data and data from HapMap III and the Human Genome Diversity Project.

Suggested Citation

  • Jianzhong Ma & Christopher I Amos, 2012. "Principal Components Analysis of Population Admixture," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-12, July.
  • Handle: RePEc:plo:pone00:0040115
    DOI: 10.1371/journal.pone.0040115
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    References listed on IDEAS

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    1. Gil McVean, 2009. "A Genealogical Interpretation of Principal Components Analysis," PLOS Genetics, Public Library of Science, vol. 5(10), pages 1-10, October.
    2. Kai Yu & Zhaoming Wang & Qizhai Li & Sholom Wacholder & David J Hunter & Robert N Hoover & Stephen Chanock & Gilles Thomas, 2008. "Population Substructure and Control Selection in Genome-Wide Association Studies," PLOS ONE, Public Library of Science, vol. 3(7), pages 1-14, July.
    3. Jianzhong Ma & Christopher I Amos, 2010. "Theoretical Formulation of Principal Components Analysis to Detect and Correct for Population Stratification," PLOS ONE, Public Library of Science, vol. 5(9), pages 1-14, September.
    4. Chao Tian & Robert M Plenge & Michael Ransom & Annette Lee & Pablo Villoslada & Carlo Selmi & Lars Klareskog & Ann E Pulver & Lihong Qi & Peter K Gregersen & Michael F Seldin, 2008. "Analysis and Application of European Genetic Substructure Using 300 K SNP Information," PLOS Genetics, Public Library of Science, vol. 4(1), pages 1-11, January.
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    Cited by:

    1. Jason Sawler & Bruce Reisch & Mallikarjuna K Aradhya & Bernard Prins & Gan-Yuan Zhong & Heidi Schwaninger & Charles Simon & Edward Buckler & Sean Myles, 2013. "Genomics Assisted Ancestry Deconvolution in Grape," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-1, November.
    2. Zheng, Xiuwen & Weir, Bruce S., 2016. "Eigenanalysis of SNP data with an identity by descent interpretation," Theoretical Population Biology, Elsevier, vol. 107(C), pages 65-76.

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