Principal components analysis of genetic data has benefited from advances in random matrix theory. The Tracy-Widom distribution has been identified as the limiting distribution of the lead eigenvalue, enabling formal hypothesis testing of population structure. Additionally, a phase change exists between small and large eigenvalues, such that population divergence below a threshold of FST is impossible to detect and above which it is always detectable. I show that the plug-in estimate of the effective number of markers in the EIGENSOFT software often exceeds the rank of the sample covariance matrix, leading to a systematic overestimation of the number of significant principal components. I describe an alternative plug-in estimate that eliminates the problem. This improvement is not just an asymptotic result but is directly applicable to finite samples. The minimum average partial test, based on minimizing the average squared partial correlation between individuals, can detect population structure at smaller FST values than the corrected test. The minimum average partial test is applicable to both unadmixed and admixed samples, with arbitrary numbers of discrete subpopulations or parental populations, respectively. Application of the minimum average partial test to the 11 HapMap Phase III samples, comprising 8 unadmixed samples and 3 admixed samples, revealed 13 significant principal components.
© 2012 S. Karger AG, Basel
- Population stratification
- Population structure
- Principal components analysis
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Received: July 15, 2011
Accepted after revision: December 19, 2011
Published online: March 20, 2012
Number of Print Pages : 11
Number of Figures : 3, Number of Tables : 4, Number of References : 18
Human Heredity (International Journal of Human and Medical Genetics)
Vol. 73, No. 2, Year 2012 (Cover Date: May 2012)
Journal Editor: Devoto M. (Philadelphia, Pa./Rome)
ISSN: 0001-5652 (Print), eISSN: 1423-0062 (Online)
For additional information: http://www.karger.com/HHE
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