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Genetics, Vol. 178, 2289-2303, April 2008, Copyright © 2008
doi:10.1534/genetics.107.084285

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Reproducing Kernel Hilbert Spaces Regression Methods for Genomic Assisted Prediction of Quantitative Traits

Daniel Gianola*,{dagger},{ddagger},1 and Johannes B. C. H. M. van Kaam§

* Department of Animal Sciences, University of Wisconsin, Madison, Wisconsin 53706, {dagger} Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, N-1432 Ås, Norway, {ddagger} Scienze Entomologiche, Fitopatologiche, Microbiologiche Agrarie e Zootecniche, Universitá degli Studi di Palermo, 90128 Palermo, Italy and § Istituto Zooprofilattico Sperimentale della Sicilia "A. Mirri," 90129 Palermo, Italy

1 Corresponding author: Department of Animal Sciences, University of Wisconsin, 1675 Observatory Dr., Madison, WI 53706.
E-mail: gianola{at}ansci.wisc.edu

Reproducing kernel Hilbert spaces regression procedures for prediction of total genetic value for quantitative traits, which make use of phenotypic and genomic data simultaneously, are discussed from a theoretical perspective. It is argued that a nonparametric treatment may be needed for capturing the multiple and complex interactions potentially arising in whole-genome models, i.e., those based on thousands of single-nucleotide polymorphism (SNP) markers. After a review of reproducing kernel Hilbert spaces regression, it is shown that the statistical specification admits a standard mixed-effects linear model representation, with smoothing parameters treated as variance components. Models for capturing different forms of interaction, e.g., chromosome-specific, are presented. Implementations can be carried out using software for likelihood-based or Bayesian inference.




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O. Gonzalez-Recio, D. Gianola, N. Long, K. A. Weigel, G. J. M. Rosa, and S. Avendano
Nonparametric Methods for Incorporating Genomic Information Into Genetic Evaluations: An Application to Mortality in Broilers
Genetics, April 1, 2008; 178(4): 2305 - 2313.
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