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Principal component analysis
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=== Population genetics === In 1978 [[Luigi Luca Cavalli-Sforza|Cavalli-Sforza]] and others pioneered the use of principal components analysis (PCA) to summarise data on variation in human gene frequencies across regions. The components showed distinctive patterns, including gradients and sinusoidal waves. They interpreted these patterns as resulting from specific ancient migration events. Since then, PCA has been ubiquitous in population genetics, with thousands of papers using PCA as a display mechanism. Genetics varies largely according to proximity, so the first two principal components actually show spatial distribution and may be used to map the relative geographical location of different population groups, thereby showing individuals who have wandered from their original locations.<ref>{{Cite journal |last1=Novembre |first1=John |last2=Stephens |first2=Matthew |date=2008 |title=Interpreting principal component analyses of spatial population genetic variation |journal=Nat Genet |volume=40 |issue=5 |pages=646β49 |doi=10.1038/ng.139 |pmid=18425127 |pmc=3989108 }}</ref> PCA in genetics has been technically controversial, in that the technique has been performed on discrete non-normal variables and often on binary allele markers. The lack of any measures of standard error in PCA are also an impediment to more consistent usage. In August 2022, the molecular biologist [[Eran Elhaik]] published a theoretical paper in [[Scientific Reports]] analyzing 12 PCA applications. He concluded that it was easy to manipulate the method, which, in his view, generated results that were 'erroneous, contradictory, and absurd.' Specifically, he argued, the results achieved in population genetics were characterized by cherry-picking and [[circular reasoning]].<ref>{{cite journal | first = Eran | last = Elhaik | author-link = Eran Elhaik | doi = 10.1038/s41598-022-14395-4 | title = Principal Component Analyses (PCA)βbased findings in population genetic studies are highly biased and must be reevaluated | journal = [[Scientific Reports]] | volume = 12 | at = 14683 | year = 2022| issue = 1 | pmid = 36038559 | pmc = 9424212 | bibcode = 2022NatSR..1214683E | s2cid = 251932226 | doi-access = free }}</ref>
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