Issue |
Genet. Sel. Evol.
Volume 34, Number 3, May-June 2002
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Page(s) | 307 - 333 | |
DOI | https://doi.org/10.1051/gse:2002010 |
Genet. Sel. Evol. 34 (2002) 307-333
DOI: 10.1051/gse:2002010
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 Korsgaarda, Anders Holst Andersenb and Just Jensenaa Department of Animal Breeding and Genetics, Danish Institute of Agricultural Sciences, P.O. Box 50, 8830 Tjele, Denmark
b Department of Theoretical Statistics, University of Aarhus, 8000 Aarhus-C, Denmark
(Received 9 January 2001; accepted 9 February 2002)
Abstract
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.
Key words: accuracy of selection / best predictor / expected response to selection / heritability / prediction error variance
Correspondence and reprints: Inge Riis Korsgaard
e-mail: IngeR.Korsgaard@agrsci.dk
© INRA, EDP Sciences 2002