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      A Bayesian Genomic Multi-output Regressor Stacking Model for Predicting Multi-trait Multi-environment Plant Breeding Data

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          In this paper we propose a Bayesian multi-output regressor stacking (BMORS) model that is a generalization of the multi-trait regressor stacking method. The proposed BMORS model consists of two stages: in the first stage, a univariate genomic best linear unbiased prediction (GBLUP including genotype × environment interaction GE) model is implemented for each of the L traits under study; then the predictions of all traits are included as covariates in the second stage, by implementing a Ridge regression model. The main objectives of this research were to study alternative models to the existing multi-trait multi-environment (BMTME) model with respect to (1) genomic-enabled prediction accuracy, and (2) potential advantages in terms of computing resources and implementation. We compared the predictions of the BMORS model to those of the univariate GBLUP model using 7 maize and wheat datasets. We found that the proposed BMORS produced similar predictions to the univariate GBLUP model and to the BMTME model in terms of prediction accuracy; however, the best predictions were obtained under the BMTME model. In terms of computing resources, we found that the BMORS is at least 9 times faster than the BMTME method. Based on our empirical findings, the proposed BMORS model is an alternative for predicting multi-trait and multi-environment data, which are very common in genomic-enabled prediction in plant and animal breeding programs.

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          Most cited references 28

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          A Robust, Simple Genotyping-by-Sequencing (GBS) Approach for High Diversity Species

          Advances in next generation technologies have driven the costs of DNA sequencing down to the point that genotyping-by-sequencing (GBS) is now feasible for high diversity, large genome species. Here, we report a procedure for constructing GBS libraries based on reducing genome complexity with restriction enzymes (REs). This approach is simple, quick, extremely specific, highly reproducible, and may reach important regions of the genome that are inaccessible to sequence capture approaches. By using methylation-sensitive REs, repetitive regions of genomes can be avoided and lower copy regions targeted with two to three fold higher efficiency. This tremendously simplifies computationally challenging alignment problems in species with high levels of genetic diversity. The GBS procedure is demonstrated with maize (IBM) and barley (Oregon Wolfe Barley) recombinant inbred populations where roughly 200,000 and 25,000 sequence tags were mapped, respectively. An advantage in species like barley that lack a complete genome sequence is that a reference map need only be developed around the restriction sites, and this can be done in the process of sample genotyping. In such cases, the consensus of the read clusters across the sequence tagged sites becomes the reference. Alternatively, for kinship analyses in the absence of a reference genome, the sequence tags can simply be treated as dominant markers. Future application of GBS to breeding, conservation, and global species and population surveys may allow plant breeders to conduct genomic selection on a novel germplasm or species without first having to develop any prior molecular tools, or conservation biologists to determine population structure without prior knowledge of the genome or diversity in the species.
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            TASSEL: software for association mapping of complex traits in diverse samples.

            Association analyses that exploit the natural diversity of a genome to map at very high resolutions are becoming increasingly important. In most studies, however, researchers must contend with the confounding effects of both population and family structure. TASSEL (Trait Analysis by aSSociation, Evolution and Linkage) implements general linear model and mixed linear model approaches for controlling population and family structure. For result interpretation, the program allows for linkage disequilibrium statistics to be calculated and visualized graphically. Database browsing and data importation is facilitated by integrated middleware. Other features include analyzing insertions/deletions, calculating diversity statistics, integration of phenotypic and genotypic data, imputing missing data and calculating principal components.
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              Prediction of total genetic value using genome-wide dense marker maps.

              Recent advances in molecular genetic techniques will make dense marker maps available and genotyping many individuals for these markers feasible. Here we attempted to estimate the effects of approximately 50,000 marker haplotypes simultaneously from a limited number of phenotypic records. A genome of 1000 cM was simulated with a marker spacing of 1 cM. The markers surrounding every 1-cM region were combined into marker haplotypes. Due to finite population size N(e) = 100, the marker haplotypes were in linkage disequilibrium with the QTL located between the markers. Using least squares, all haplotype effects could not be estimated simultaneously. When only the biggest effects were included, they were overestimated and the accuracy of predicting genetic values of the offspring of the recorded animals was only 0.32. Best linear unbiased prediction of haplotype effects assumed equal variances associated to each 1-cM chromosomal segment, which yielded an accuracy of 0.73, although this assumption was far from true. Bayesian methods that assumed a prior distribution of the variance associated with each chromosome segment increased this accuracy to 0.85, even when the prior was not correct. It was concluded that selection on genetic values predicted from markers could substantially increase the rate of genetic gain in animals and plants, especially if combined with reproductive techniques to shorten the generation interval.

                Author and article information

                G3 (Bethesda)
                G3: Genes, Genomes, Genetics
                G3: Genes, Genomes, Genetics
                G3: Genes, Genomes, Genetics
                G3: Genes|Genomes|Genetics
                Genetics Society of America
                19 August 2019
                October 2019
                : 9
                : 10
                : 3381-3393
                [* ]Facultad de Telemática, Universidad de Colima, Colima, Colima, 28040, México,
                []Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI), Universidad de Guadalajara, Guadalajara, Jalisco, 44430, México,
                []International Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, Ciudad de México, 06600, México,
                [§ ]Universidad de Quintana Roo, Chetumal, Quintana Roo, México,
                [** ]Departamento de Estadística, Centro de Investigación en Matemáticas, Guanajuato, Guanajuato, 36023, México, and
                [†† ]Department of Plant Sciences, Norwegian University of Life Sciences, IHA/CIGENE, P.O. Box 5003, NO-1432 Ås, Norway
                Author notes
                [1 ]Corresponding authors: Biometrics and Statistics Unit, International Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, Ciudad de México, 06600, México. E-mail: j.crossa@ . Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI), Universidad de Guadalajara, Guadalajara, Jalisco, 44430, México. E-mail: aml_uach@
                Copyright © 2019 Montesinos-Lopez et al.

                This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                Page count
                Figures: 7, Tables: 3, Equations: 3, References: 33, Pages: 13
                Genomic Prediction


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