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Chunk #136 — Discussion — The Spectrum of the Covariance Matrix

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Population structure and eigenanalysis.
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Consider sampling a marker from samples belonging to K populations. Suppose the allele has frequency pi in population i. We sample diploid genotypes, obtaining counts Cj of the variant allele from sample j. We suppose sample j belongs to population i = i(j), and that the sample size for population i is M(i). We discuss the spectrum (eigenvalues) of the covariance matrix of the raw counts Cj. Note that this is for the theoretical covariance not the sample covariance.