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      Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

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          Abstract

          Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

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          Most cited references27

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          Performance of genomic selection in mice.

          Selection plans in plant and animal breeding are driven by genetic evaluation. Recent developments suggest using massive genetic marker information, known as "genomic selection." There is little evidence of its performance, though. We empirically compared three strategies for selection: (1) use of pedigree and phenotypic information, (2) use of genomewide markers and phenotypic information, and (3) the combination of both. We analyzed four traits from a heterogeneous mouse population (http://gscan.well.ox.ac.uk/), including 1884 individuals and 10,946 SNP markers. We used linear mixed models, using extensions of association analysis. Cross-validation techniques were used, providing assumption-free estimates of predictive ability. Sampling of validation and training data sets was carried out across and within families, which allows comparing across- and within-family information. Use of genomewide genetic markers increased predictive ability up to 0.22 across families and up to 0.03 within families. The latter is not statistically significant. These values are roughly comparable to increases of up to 0.57 (across family) and 0.14 (within family) in accuracy of prediction of genetic value. In this data set, within-family information was more accurate than across-family information, and populational linkage disequilibrium was not a completely accurate source of information for genetic evaluation. This fact questions some applications of genomic selection.
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            Accuracy of Genomic Selection Methods in a Standard Data Set of Loblolly Pine (Pinus taeda L.)

            Genomic selection can increase genetic gain per generation through early selection. Genomic selection is expected to be particularly valuable for traits that are costly to phenotype and expressed late in the life cycle of long-lived species. Alternative approaches to genomic selection prediction models may perform differently for traits with distinct genetic properties. Here the performance of four different original methods of genomic selection that differ with respect to assumptions regarding distribution of marker effects, including (i) ridge regression–best linear unbiased prediction (RR–BLUP), (ii) Bayes A, (iii) Bayes Cπ, and (iv) Bayesian LASSO are presented. In addition, a modified RR–BLUP (RR–BLUP B) that utilizes a selected subset of markers was evaluated. The accuracy of these methods was compared across 17 traits with distinct heritabilities and genetic architectures, including growth, development, and disease-resistance properties, measured in a Pinus taeda (loblolly pine) training population of 951 individuals genotyped with 4853 SNPs. The predictive ability of the methods was evaluated using a 10-fold, cross-validation approach, and differed only marginally for most method/trait combinations. Interestingly, for fusiform rust disease-resistance traits, Bayes Cπ, Bayes A, and RR–BLUB B had higher predictive ability than RR–BLUP and Bayesian LASSO. Fusiform rust is controlled by few genes of large effect. A limitation of RR–BLUP is the assumption of equal contribution of all markers to the observed variation. However, RR-BLUP B performed equally well as the Bayesian approaches.The genotypic and phenotypic data used in this study are publically available for comparative analysis of genomic selection prediction models.
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              Bayesian LASSO for quantitative trait loci mapping.

              The mapping of quantitative trait loci (QTL) is to identify molecular markers or genomic loci that influence the variation of complex traits. The problem is complicated by the facts that QTL data usually contain a large number of markers across the entire genome and most of them have little or no effect on the phenotype. In this article, we propose several Bayesian hierarchical models for mapping multiple QTL that simultaneously fit and estimate all possible genetic effects associated with all markers. The proposed models use prior distributions for the genetic effects that are scale mixtures of normal distributions with mean zero and variances distributed to give each effect a high probability of being near zero. We consider two types of priors for the variances, exponential and scaled inverse-chi(2) distributions, which result in a Bayesian version of the popular least absolute shrinkage and selection operator (LASSO) model and the well-known Student's t model, respectively. Unlike most applications where fixed values are preset for hyperparameters in the priors, we treat all hyperparameters as unknowns and estimate them along with other parameters. Markov chain Monte Carlo (MCMC) algorithms are developed to simulate the parameters from the posteriors. The methods are illustrated using well-known barley data.
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                Author and article information

                Journal
                G3 (Bethesda)
                Genetics
                G3: Genes, Genomes, Genetics
                G3: Genes, Genomes, Genetics
                G3: Genes, Genomes, Genetics
                G3: Genes|Genomes|Genetics
                Genetics Society of America
                2160-1836
                1 September 2013
                September 2013
                : 3
                : 9
                : 1511-1523
                Affiliations
                [* ]Department of Agricultural Sciences, University of Helsinki, Helsinki FIN-00014
                []Department of Mathematical Sciences, University of Oulu, Oulu FIN-90014, Finland
                []Department of Biology and Biocenter Oulu, University of Oulu, Oulu FIN-90014, Finland
                Author notes

                Supporting information is available online at http://www.g3journal.org/lookup/suppl/doi:10.1534/g3.113.007096/-/DC1

                [1 ]Corresponding author: Department of Mathematical Sciences and Department of Biology, P. O. Box 3000, University of Oulu, Oulu FIN-90014, Finland. E-mail: mjs@ 123456rolf.helsinki.fi
                Article
                GGG_007096
                10.1534/g3.113.007096
                3755911
                23821618
                c56b36f1-33b4-4247-a9d6-6b5650108b56
                Copyright © 2013 Kärkkäinen and Sillanpää

                This is an open-access article distributed under the terms of the Creative Commons Attribution Unported License ( http://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 28 March 2013
                : 24 June 2013
                Page count
                Pages: 13
                Categories
                Genomic Selection
                Custom metadata
                v1

                Genetics
                genomic selection,multiocus association model,g-blup,threshold model,ordinal,binary,censored gaussian,genpred,shared data resources

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