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Restricted best linear unbiased prediction and a selection model.

T R Famula1

  • 1Department of Animal Science, University of California, 95616, Davis, CA, USA.

TAG. Theoretical and Applied Genetics. Theoretische Und Angewandte Genetik
|November 22, 2013
PubMed
Summary

Restricted selection provides an equivalence to selection models acting on residuals in mixed linear models. This reveals how restricted selection nonrandomly samples pleiotropic genes in genetic models.

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Area of Science:

  • Quantitative genetics
  • Statistical genetics
  • Animal breeding

Background:

  • Best linear unbiased prediction (BLUP) is a standard method for genetic evaluation.
  • Restricted selection index (RSI) is used to optimize selection across multiple traits under specific constraints.
  • Mixed linear models are fundamental for analyzing genetic data with complex structures.

Purpose of the Study:

  • To present an equivalence between restricted best linear unbiased prediction (RBLUP) and a specific selection model.
  • To elucidate the mechanism by which restricted selection influences gene sampling in multi-trait genetic models.
  • To provide a mathematical expression for a mixed linear model incorporating restrictions.

Main Methods:

  • Mathematical derivation of the equivalence between RBLUP and a selection model.
  • Analysis of selection on the residuals of a general mixed linear model.
  • Formulation of a mixed linear model that explicitly includes selection restrictions.

Main Results:

  • An equivalence is established between RBLUP (and RSI) and a selection model operating on the residuals of the general mixed linear model.
  • This demonstrates that restricted selection functions by nonrandomly sampling genes with pleiotropic effects.
  • An expression for a mixed linear model incorporating restrictions is derived.

Conclusions:

  • Restricted selection can be understood as a specific type of selection model applied to model residuals.
  • This framework clarifies the genetic consequences of imposing restrictions during selection, particularly concerning pleiotropy.
  • The presented model offers a new perspective on implementing and interpreting restricted selection in genetic analyses.