Prediction error variance and expected response to selection, when selection is based on the best predictor – for Gaussian and threshold characters, traits following a Poisson mixed model and survival traits

  • Inge Riis KorsgaardEmail author
  • Anders Holst Andersen
  • Just Jensen
Open Access


In this paper, we consider selection based on the best predictor of animal additive genetic values in Gaussian linear mixed models, threshold models, Poisson mixed models, and log normal frailty models for survival data (including models with time-dependent covariates with associated fixed or random effects). In the different models, expressions are given (when these can be found – otherwise unbiased estimates are given) for prediction error variance, accuracy of selection and expected response to selection on the additive genetic scale and on the observed scale. The expressions given for non Gaussian traits are generalisations of the well-known formulas for Gaussian traits – and reflect, for Poisson mixed models and frailty models for survival data, the hierarchal structure of the models. In general the ratio of the additive genetic variance to the total variance in the Gaussian part of the model (heritability on the normally distributed level of the model) or a generalised version of heritability plays a central role in these formulas.


accuracy of selection best predictor expected response to selection heritability prediction error variance 

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© INRA, EDP Sciences 2002

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.

Authors and Affiliations

  • Inge Riis Korsgaard
    • 1
    Email author
  • Anders Holst Andersen
    • 2
  • Just Jensen
    • 1
  1. 1.Department of Animal Breeding and GeneticsDanish Institute of Agricultural SciencesTjeleDenmark
  2. 2.Department of Theoretical StatisticsUniversity of AarhusAarhus-CDenmark

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