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Originally published as Genetics Published Articles Ahead of Print on July 20, 2009.
Genetics, Vol. 183, 347-363, September 2009, Copyright © 2009
doi:10.1534/genetics.109.103952
Additive Genetic Variability and the Bayesian Alphabet
Daniel Gianola*,
,
,1,
Gustavo de los Campos*,
William G. Hill
,
Eduardo Manfredi and
Rohan Fernando**
* Department of Animal Sciences, University of Wisconsin, Madison, Wisconsin 53706, Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, N-1432 Ås, Norway, Institut National de la Recherche Agronomique, UR631 Station d'Amélioration Génétique des Animaux, BP 52627, 32326 Castanet-Tolosan, France, Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3JT, United Kingdom and ** Department of Animal Science, Iowa State University, Ames, Iowa 50011
1 Corresponding author: Department of Animal Sciences, 1675 Observatory Dr., Madison, WI 53706.
E-mail: gianola{at}ansci.wisc.edu
The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called "Bayes A") with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly.
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