a1 Department of Animal Sciences, University of Wisconsin-Madison, Madison, WI 53706, USA
a2 Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, N-1432 Ås, Norway
a3 Institut National de la Recherche Agronomique, UR631 Station d'Amélioration Génétique des Animaux, BP 52627, 32326 Castanet-Tolosan, France
a4 Institut für Tierzucht und Haustiergenetik, Georg-August-Universität, Göttingen, Federal Republic of Germany
Inferences about genetic values and prediction of phenotypes for a quantitative trait in the presence of complex forms of gene action, issues of importance in animal and plant breeding, and in evolutionary quantitative genetics, are discussed. Current methods for dealing with epistatic variability via variance component models are reviewed. Problems posed by cryptic, non-linear, forms of epistasis are identified and discussed. Alternative statistical procedures are suggested. Non-parametric definitions of additive effects (breeding values), with and without employing molecular information, are proposed, and it is shown how these can be inferred using reproducing kernel Hilbert spaces regression. Two stylized examples are presented to demonstrate the methods numerically. The first example falls in the domain of the infinitesimal model of quantitative genetics, with additive and dominance effects inferred both parametrically and non-parametrically. The second example tackles a non-linear genetic system with two loci, and the predictive ability of several models is evaluated.
(Received July 08 2008)
(Revised September 17 2008)
(Revised October 02 2008)