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Application of approximate variances of variance components and their ratios in genetic tests

Theoretical and Applied Genetics volume 91, pages 15–24 (1995)Cite this article

Abstract

The application and underlying assumptions of formulae used to estimate the variance of variance components and ratios of variance components are fully described for (1) variance components estimated using Henderson's Method 3 (HM3) and Restricted Maximum Likelihood (REML) and (2) ratios of variance components commonly used in genetic tests — biased and unbiased heritabilities. A first-order Taylor series approximation is often used to estimate the variance of a ratio of two random variables (e.g., heritability), however the formula is complicated, thus making calculations prone to errors. Dickerson's approximation is considerably simpler, though relatively rarely used. In case studies using data from 148 slash pine full-sib progeny tests, Dickerson's method was found to be slightly more conservative than the Taylor series approximation when estimating the variance of heritability estimates, regardless of test size, age, or the trait (volume, which is a continuous trait, and rust resistance, which is a bernoulli trait). Both the Taylor series and Dickerson approximations compared favorably with an empirical estimate of the variance of heritability estimates, however there is some evidence of small-sample bias associated with the use of the asymptotic variance-covariances from REML variance component estimation.

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Author notes

  1. M. J. Dieters

    Present address: Queensland Forest Research Institute, MS 483 Fraser Road, QLD 4570, Gympie, Australia

Affiliations

  1. Department of Forestry, University of Florida, 32611, Gainesville, FL, USA

    M. J. Dieters, T. L. White & G. R. Hodge

  2. Department of Statistics, University of Florida, 32611, Gainesville, FL, USA

    R. C. Littell

Authors
  1. M. J. Dieters
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  2. T. L. White
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  3. R. C. Littell
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  4. G. R. Hodge
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Additional information

This is Florida Agricultural Experiment Station Journal Series No. R-03964 of the Institute of Food and Agricultural Sciences, University of Florida, Gainesville, FL 32611, USA

Communicated by P. M. A. Tigerstedt

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Dieters, M.J., White, T.L., Littell, R.C. et al. Application of approximate variances of variance components and their ratios in genetic tests. Theoret. Appl. Genetics 91, 15–24 (1995). https://doi.org/10.1007/BF00220853

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  • DOI: https://doi.org/10.1007/BF00220853

Key words

  • Variance of ratios
  • Heritability
  • Taylor series
  • Variance components
  • REML