Originally published as Genetics Published Articles Ahead of Print on February 4, 2007.

Genetics, Vol. 175, 1895-1910, April 2007, Copyright © 2007
doi:10.1534/genetics.106.063743

Prediction of Breeding Values and Selection Responses With Genetic Heterogeneity of Environmental Variance

H. A. Mulder^*,1, P. Bijma^* and W. G. Hill

^* Animal Breeding and Genetics Group, Wageningen University, 6700 AH Wageningen, The Netherlands and Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3JT, United Kingdom

¹ Corresponding author: Animal Breeding and Genetics Group, Wageningen University, PO Box 338, 6700 AH Wageningen, The Netherlands.
E-mail: herman.mulder{at}wur.nl

There is empirical evidence that genotypes differ not only in mean, but also in environmental variance of the traits they affect. Genetic heterogeneity of environmental variance may indicate genetic differences in environmental sensitivity. The aim of this study was to develop a general framework for prediction of breeding values and selection responses in mean and environmental variance with genetic heterogeneity of environmental variance. Both means and environmental variances were treated as heritable traits. Breeding values and selection responses were predicted with little bias using linear, quadratic, and cubic regression on individual phenotype or using linear regression on the mean and within-family variance of a group of relatives. A measure of heritability was proposed for environmental variance to standardize results in the literature and to facilitate comparisons to "conventional" traits. Genetic heterogeneity of environmental variance can be considered as a trait with a low heritability. Although a large amount of information is necessary to accurately estimate breeding values for environmental variance, response in environmental variance can be substantial, even with mass selection. The methods developed allow use of the well-known selection index framework to evaluate breeding strategies and effects of natural selection that simultaneously change the mean and the variance.

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