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Population structure and eigenanalysis.

Patterson N, Price AL, Reich D - PLoS Genet. (2006)

Bottom Line: Current methods for inferring population structure from genetic data do not provide formal significance tests for population differentiation.We place the method on a solid statistical footing, using results from modern statistics to develop formal significance tests.This means that we can predict the dataset size needed to detect structure.

View Article: PubMed Central - PubMed

Affiliation: Broad Institute of Harvard and MIT, Cambridge, Massachusetts, United States of America.

ABSTRACT
Current methods for inferring population structure from genetic data do not provide formal significance tests for population differentiation. We discuss an approach to studying population structure (principal components analysis) that was first applied to genetic data by Cavalli-Sforza and colleagues. We place the method on a solid statistical footing, using results from modern statistics to develop formal significance tests. We also uncover a general "phase change" phenomenon about the ability to detect structure in genetic data, which emerges from the statistical theory we use, and has an important implication for the ability to discover structure in genetic data: for a fixed but large dataset size, divergence between two populations (as measured, for example, by a statistic like FST) below a threshold is essentially undetectable, but a little above threshold, detection will be easy. This means that we can predict the dataset size needed to detect structure.

Show MeSH
LD Correction with no LD PresentP–P plots of the TW statistic, when no LD is present and after varying levels (k) of our LD correction. We first show this (A) for m = 500, n = 5,000, and then (B) for m = 200, n = 50,000. In both cases the LD correction makes little difference to the fit.
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pgen-0020190-g009: LD Correction with no LD PresentP–P plots of the TW statistic, when no LD is present and after varying levels (k) of our LD correction. We first show this (A) for m = 500, n = 5,000, and then (B) for m = 200, n = 50,000. In both cases the LD correction makes little difference to the fit.

Mentions: Set: Choose a to minimize and now calculate X = RR′ instead of MM′. It is first important to check that in the absence of LD the suggested correction does not seriously distort the Tracy–Widom statistic. In Figure 9A and 9B we show P–P plots, uncorrected, and with five levels (k = 1…5) of correction. The first figure is with 100 individuals and 5,000 markers, the second with 200 individuals and 50,000 markers. Then in Figure 10A and 10B we analyze a simulated dataset with severe LD. We generate blocks in perfect LD, in which the probability that a block contains L markers is 2−L. We show the corresponding plots. Note that here the uncorrected statistic is distributed quite differently than the Tracy–Widom distribution. Our suggested correction strategy seems to work well, and should be adequate in practice, especially as most large genotype arrays will attempt to avoid high levels of LD. We would recommend that before analyzing a very large dataset with dense genotyping, one should filter the data by removing a marker from every pair of markers that are in tight LD.


Population structure and eigenanalysis.

Patterson N, Price AL, Reich D - PLoS Genet. (2006)

LD Correction with no LD PresentP–P plots of the TW statistic, when no LD is present and after varying levels (k) of our LD correction. We first show this (A) for m = 500, n = 5,000, and then (B) for m = 200, n = 50,000. In both cases the LD correction makes little difference to the fit.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC1713260&req=5

pgen-0020190-g009: LD Correction with no LD PresentP–P plots of the TW statistic, when no LD is present and after varying levels (k) of our LD correction. We first show this (A) for m = 500, n = 5,000, and then (B) for m = 200, n = 50,000. In both cases the LD correction makes little difference to the fit.
Mentions: Set: Choose a to minimize and now calculate X = RR′ instead of MM′. It is first important to check that in the absence of LD the suggested correction does not seriously distort the Tracy–Widom statistic. In Figure 9A and 9B we show P–P plots, uncorrected, and with five levels (k = 1…5) of correction. The first figure is with 100 individuals and 5,000 markers, the second with 200 individuals and 50,000 markers. Then in Figure 10A and 10B we analyze a simulated dataset with severe LD. We generate blocks in perfect LD, in which the probability that a block contains L markers is 2−L. We show the corresponding plots. Note that here the uncorrected statistic is distributed quite differently than the Tracy–Widom distribution. Our suggested correction strategy seems to work well, and should be adequate in practice, especially as most large genotype arrays will attempt to avoid high levels of LD. We would recommend that before analyzing a very large dataset with dense genotyping, one should filter the data by removing a marker from every pair of markers that are in tight LD.

Bottom Line: Current methods for inferring population structure from genetic data do not provide formal significance tests for population differentiation.We place the method on a solid statistical footing, using results from modern statistics to develop formal significance tests.This means that we can predict the dataset size needed to detect structure.

View Article: PubMed Central - PubMed

Affiliation: Broad Institute of Harvard and MIT, Cambridge, Massachusetts, United States of America.

ABSTRACT
Current methods for inferring population structure from genetic data do not provide formal significance tests for population differentiation. We discuss an approach to studying population structure (principal components analysis) that was first applied to genetic data by Cavalli-Sforza and colleagues. We place the method on a solid statistical footing, using results from modern statistics to develop formal significance tests. We also uncover a general "phase change" phenomenon about the ability to detect structure in genetic data, which emerges from the statistical theory we use, and has an important implication for the ability to discover structure in genetic data: for a fixed but large dataset size, divergence between two populations (as measured, for example, by a statistic like FST) below a threshold is essentially undetectable, but a little above threshold, detection will be easy. This means that we can predict the dataset size needed to detect structure.

Show MeSH