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      Genomic Selection in Multi-environment Crop Trials

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          Abstract

          Genomic selection in crop breeding introduces modeling challenges not found in animal studies. These include the need to accommodate replicate plants for each line, consider spatial variation in field trials, address line by environment interactions, and capture nonadditive effects. Here, we propose a flexible single-stage genomic selection approach that resolves these issues. Our linear mixed model incorporates spatial variation through environment-specific terms, and also randomization-based design terms. It considers marker, and marker by environment interactions using ridge regression best linear unbiased prediction to extend genomic selection to multiple environments. Since the approach uses the raw data from line replicates, the line genetic variation is partitioned into marker and nonmarker residual genetic variation ( i.e., additive and nonadditive effects). This results in a more precise estimate of marker genetic effects. Using barley height data from trials, in 2 different years, of up to 477 cultivars, we demonstrate that our new genomic selection model improves predictions compared to current models. Analyzing single trials revealed improvements in predictive ability of up to 5.7%. For the multiple environment trial (MET) model, combining both year trials improved predictive ability up to 11.4% compared to a single environment analysis. Benefits were significant even when fewer markers were used. Compared to a single-year standard model run with 3490 markers, our partitioned MET model achieved the same predictive ability using between 500 and 1000 markers depending on the trial. Our approach can be used to increase accuracy and confidence in the selection of the best lines for breeding and/or, to reduce costs by using fewer markers.

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          Most cited references9

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          Natural variation in a homolog of Antirrhinum CENTRORADIALIS contributed to spring growth habit and environmental adaptation in cultivated barley.

          As early farming spread from the Fertile Crescent in the Near East around 10,000 years before the present, domesticated crops encountered considerable ecological and environmental change. Spring-sown crops that flowered without the need for an extended period of cold to promote flowering and day length-insensitive crops able to exploit the longer, cooler days of higher latitudes emerged and became established. To investigate the genetic consequences of adaptation to these new environments, we identified signatures of divergent selection in the highly differentiated modern-day spring and winter barleys. In one genetically divergent region, we identify a natural variant of the barley homolog of Antirrhinum CENTRORADIALIS (HvCEN) as a contributor to successful environmental adaptation. The distribution of HvCEN alleles in a large collection of wild and landrace accessions indicates that this involved selection and enrichment of preexisting genetic variants rather than the acquisition of mutations after domestication.
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            Factors affecting accuracy from genomic selection in populations derived from multiple inbred lines: a Barley case study.

            We compared the accuracies of four genomic-selection prediction methods as affected by marker density, level of linkage disequilibrium (LD), quantitative trait locus (QTL) number, sample size, and level of replication in populations generated from multiple inbred lines. Marker data on 42 two-row spring barley inbred lines were used to simulate high and low LD populations from multiple inbred line crosses: the first included many small full-sib families and the second was derived from five generations of random mating. True breeding values (TBV) were simulated on the basis of 20 or 80 additive QTL. Methods used to derive genomic estimated breeding values (GEBV) were random regression best linear unbiased prediction (RR-BLUP), Bayes-B, a Bayesian shrinkage regression method, and BLUP from a mixed model analysis using a relationship matrix calculated from marker data. Using the best methods, accuracies of GEBV were comparable to accuracies from phenotype for predicting TBV without requiring the time and expense of field evaluation. We identified a trade-off between a method's ability to capture marker-QTL LD vs. marker-based relatedness of individuals. The Bayesian shrinkage regression method primarily captured LD, the BLUP methods captured relationships, while Bayes-B captured both. Under most of the study scenarios, mixed-model analysis using a marker-derived relationship matrix (BLUP) was more accurate than methods that directly estimated marker effects, suggesting that relationship information was more valuable than LD information. When markers were in strong LD with large-effect QTL, or when predictions were made on individuals several generations removed from the training data set, however, the ranking of method performance was reversed and BLUP had the lowest accuracy.
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              Technical note: Derivation of equivalent computing algorithms for genomic predictions and reliabilities of animal merit.

              Conventional prediction of dairy cattle merit involves setting up and solving linear equations with the number of unknowns being the number of animals, typically millions, multiplied by the number of traits being simultaneously assessed. The coefficient matrix has been large and sparse and iteration on data has been the method of choice, whereby the coefficient matrix is not stored but recreated as needed. In contrast, genomic prediction involves assessment of the merit of genome fragments characterized by single nucleotide polymorphism genotypes, currently some 50,000, which can then be used to predict the merit of individual animals according to the fragments they have inherited. The prediction equations for chromosome fragments typically have fewer than 100,000 unknowns, but the number of observations used to predict the fragment effects can be one-tenth the number of fragments. The coefficient matrix tends to be dense and the resulting system of equations can be ill behaved. Equivalent computing algorithms for genomic prediction were derived. The number of unknowns in the equivalent system grows with number of genotyped animals, usually bulls, rather than the number of chromosome fragment effects. In circumstances with fewer genotyped animals than single nucleotide polymorphism genotypes, these equivalent computations allow the solving of a smaller system of equations that behaves numerically better. There were 3 solving strategies compared: 1 method that formed and stored the coefficient matrix in memory and 2 methods that iterate on data. Finally, formulas for reliabilities of genomic predictions of merit were developed.
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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
                11 March 2016
                May 2016
                : 6
                : 5
                : 1313-1326
                Affiliations
                [* ]Division of Plant Sciences, University of Dundee at the James Hutton Institute, Invergowrie, Dundee DD2 5DA, Scotland, UK
                []National Institute for Applied Statistics Research Australia, University of Wollongong, NSW, 2522, Australia
                [§ ]Rothamsted Research, Harpenden, Hertfordshire AL5 3JQ, UK
                [** ]Department of Cell and Molecular Sciences, The James Hutton Institute, Invergowrie, Dundee DD2 5DA, Scotland, UK
                Author notes
                [1]

                Present address: Biomathematics and Statistics Scotland (BioSS), The James Hutton Institute, Dundee, DD2 5DA Scotland, UK.

                [2]

                Present address: Limagrain, Biopôle Clermont-Limagne, Rue Henri Mondor, 63360 Saint-Beauzire, France.

                [3 ]Corresponding authors: Division of Plant Sciences, School of Life Sciences, University of Dundee at the James Hutton Institute, Invergowrie, Dundee, DD2 5DA, UK. E-mails: c.halpin@ 123456dundee.ac.uk , and r.waugh@ 123456dundee.ac.uk
                Author information
                http://orcid.org/0000-0002-1808-8130
                Article
                GGG_027524
                10.1534/g3.116.027524
                4856083
                26976443
                d0bad455-07da-4dd7-ba69-29d52e185f72
                Copyright © 2016 Oakey et al.

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

                History
                : 03 October 2015
                : 05 March 2016
                Page count
                Figures: 3, Tables: 7, Equations: 13, References: 42, Pages: 14
                Categories
                Genomic Selection

                Genetics
                multi-environment trial,genomic selection,random ridge regression,gebv,barley,genpred,shared data resource

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