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Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.

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      Abstract

      The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be over-dispersed by sampling error, where large eigenvalues are biased upwards, and small eigenvalues are biased downwards. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using REML in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW scale, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix.

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      Author and article information

      Affiliations
      [1 ] University of Queensland jsztepanacz@gmail.com.
      [2 ] University of Queensland.
      Journal
      Genetics
      Genetics
      Genetics Society of America
      1943-2631
      0016-6731
      May 05 2017
      28476865
      genetics.116.198606
      10.1534/genetics.116.198606

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