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 Korsgaard^a, Anders Holst Andersen^b and Just Jensen<sup>a

a</sup>  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