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Originally published as Genetics Published Articles Ahead of Print on March 21, 2005.
Genetics, Vol. 170, 465-480, May 2005, Copyright © 2005
doi:10.1534/genetics.104.039354
Bayesian Shrinkage Estimation of Quantitative Trait Loci Parameters
Hui Wang*,
Yuan-Ming Zhang*,
Xinmin Li
,
Godfred L. Masinde
,
Subburaman Mohan,
David J. Baylink and
Shizhong Xu*,1
* Department of Botany and Plant Sciences, University of California, Riverside, California 92521
Functional Genomics Facility, University of Chicago, Chicago, Illinois 60637
Molecular Genetics Division, Musculoskeletal Disease Center, J. L. Pettis Veterans Administration Medical Center and Loma Linda University, Loma Linda, California 92357
1 Corresponding author: Department of Botany and Plant Sciences, 900 University Ave., University of California, Riverside, California 92521.
E-mail: xu{at}genetics.ucr.edu
Mapping multiple QTL is a typical problem of variable selection in an oversaturated model because the potential number of QTL can be substantially larger than the sample size. Currently, model selection is still the most effective approach to mapping multiple QTL, although further research is needed. An alternative approach to analyzing an oversaturated model is the shrinkage estimation in which all candidate variables are included in the model but their estimated effects are forced to shrink toward zero. In contrast to the usual shrinkage estimation where all model effects are shrunk by the same factor, we develop a Bayesian method that allows the shrinkage factor to vary across different effects. The new shrinkage method forces marker intervals that contain no QTL to have estimated effects close to zero whereas intervals containing notable QTL have estimated effects subject to virtually no shrinkage. We demonstrate the method using both simulated and real data for QTL mapping. A simulation experiment with 500 backcross (BC) individuals showed that the method can localize closely linked QTL and QTL with effects as small as 1% of the phenotypic variance of the trait. The method was also used to map QTL responsible for wound healing in a family of a (MRL/MPJ x SJL/J) cross with 633 F2 mice derived from two inbred lines.
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