Additive Genetic Variability and the Bayesian Alphabet
Copyright Ó 2009 by the Genetics Society of America 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 A˚ s, Norway, ‡Institut National de la Recherche Agronomique, UR631 Station d’Ame´lioration Ge´ne´tique 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 Manuscript received April 14, 2009 Accepted for publication July 16, 2009 ABSTRACT 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.
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