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. 2013 Nov:89:34-43.
doi: 10.1016/j.tpb.2013.08.004. Epub 2013 Aug 20.

Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulations

Katarzyna Bryc  1 , Wlodek Bryc, Jack W Silverstein
Affiliations

Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulations

Katarzyna Bryc et al. Theor Popul Biol. 2013 Nov.

Abstract

We present a mathematical model, and the corresponding mathematical analysis, that justifies and quantifies the use of principal component analysis of biallelic genetic marker data for a set of individuals to detect the number of subpopulations represented in the data. We indicate that the power of the technique relies more on the number of individuals genotyped than on the number of markers.

Keywords: Eigenanalysis; Eigenvalues; Number of subpopulations; Population structure; Principal components analysis.

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Figures

Figure 1
Figure 1
Histogram of the eigenvalues from PCA of Hapmap CEU, CHB, and YRI unrelated individuals (parents of trios), excluding the large eigenvalues (Λ ≫ 1), which are omitted to better illustrate the shape of the non-significant eigenvalues. Here, the largest three eigenvalues that correspond to subpopulation structure are Λ1 = 102.0, Λ2 = 14.55, Λ3 = 7.37.
Figure 2
Figure 2
Including related individuals perturbs the expected distribution of eigenvalues resulting from PCA. Left: A counts histogram of the eigenvalues from PCA using data generated via binomial simulation, where 29% of the individuals have been repeated. Large eigenvalues (corresponding to population structure) are not shown so as to better illustrate the effect on the distribution of the non-significant eigenvalues. Right: A histogram of the eigenvalues for PCA of three populations of HapMap (CEU, YRI, and CHB) including trios – 297 parents and their related 108 offspring. Large eigenvalues are not shown. Both simulated data and empirical genotype data show that inclusion of related individuals results in a multi-modal distribution of the eigenvalues, arising from the non-random correlations of individuals.
Figure 3
Figure 3
Histogram of the eigenvalues from PCA of all 11 populations in HapMap unrelated individuals. Nonautosomal markers with M = 924, N = 422253. The six largest eigenvalues Λ1 = 335.9, Λ2 = 37.4, Λ3 = 16.7, Λ4 = 2.5, Λ5 = 2.1, Λ6 = 1.7 are not shown.
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