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      Increased Prediction Accuracy in Wheat Breeding Trials Using a Marker × Environment Interaction Genomic Selection Model

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          Abstract

          Genomic selection (GS) models use genome-wide genetic information to predict genetic values of candidates of selection. Originally, these models were developed without considering genotype × environment interaction(G×E). Several authors have proposed extensions of the single-environment GS model that accommodate G×E using either covariance functions or environmental covariates. In this study, we model G×E using a marker × environment interaction (M×E) GS model; the approach is conceptually simple and can be implemented with existing GS software. We discuss how the model can be implemented by using an explicit regression of phenotypes on markers or using co-variance structures (a genomic best linear unbiased prediction-type model). We used the M×E model to analyze three CIMMYT wheat data sets (W1, W2, and W3), where more than 1000 lines were genotyped using genotyping-by-sequencing and evaluated at CIMMYT’s research station in Ciudad Obregon, Mexico, under simulated environmental conditions that covered different irrigation levels, sowing dates and planting systems. We compared the M×E model with a stratified ( i.e., within-environment) analysis and with a standard (across-environment) GS model that assumes that effects are constant across environments ( i.e., ignoring G×E). The prediction accuracy of the M×E model was substantially greater of that of an across-environment analysis that ignores G×E. Depending on the prediction problem, the M×E model had either similar or greater levels of prediction accuracy than the stratified analyses. The M×E model decomposes marker effects and genomic values into components that are stable across environments (main effects) and others that are environment-specific (interactions). Therefore, in principle, the interaction model could shed light over which variants have effects that are stable across environments and which ones are responsible for G×E. The data set and the scripts required to reproduce the analysis are publicly available as Supporting Information.

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          Integrating environmental covariates and crop modeling into the genomic selection framework to predict genotype by environment interactions.

          Development of models to predict genotype by environment interactions, in unobserved environments, using environmental covariates, a crop model and genomic selection. Application to a large winter wheat dataset. Genotype by environment interaction (G*E) is one of the key issues when analyzing phenotypes. The use of environment data to model G*E has long been a subject of interest but is limited by the same problems as those addressed by genomic selection methods: a large number of correlated predictors each explaining a small amount of the total variance. In addition, non-linear responses of genotypes to stresses are expected to further complicate the analysis. Using a crop model to derive stress covariates from daily weather data for predicted crop development stages, we propose an extension of the factorial regression model to genomic selection. This model is further extended to the marker level, enabling the modeling of quantitative trait loci (QTL) by environment interaction (Q*E), on a genome-wide scale. A newly developed ensemble method, soft rule fit, was used to improve this model and capture non-linear responses of QTL to stresses. The method is tested using a large winter wheat dataset, representative of the type of data available in a large-scale commercial breeding program. Accuracy in predicting genotype performance in unobserved environments for which weather data were available increased by 11.1% on average and the variability in prediction accuracy decreased by 10.8%. By leveraging agronomic knowledge and the large historical datasets generated by breeding programs, this new model provides insight into the genetic architecture of genotype by environment interactions and could predict genotype performance based on past and future weather scenarios.
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            Comparison Between Linear and Non-parametric Regression Models for Genome-Enabled Prediction in Wheat

            In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.
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              Perils of parsimony: properties of reduced-rank estimates of genetic covariance matrices.

              Eigenvalues and eigenvectors of covariance matrices are important statistics for multivariate problems in many applications, including quantitative genetics. Estimates of these quantities are subject to different types of bias. This article reviews and extends the existing theory on these biases, considering a balanced one-way classification and restricted maximum-likelihood estimation. Biases are due to the spread of sample roots and arise from ignoring selected principal components when imposing constraints on the parameter space, to ensure positive semidefinite estimates or to estimate covariance matrices of chosen, reduced rank. In addition, it is shown that reduced-rank estimators that consider only the leading eigenvalues and -vectors of the "between-group" covariance matrix may be biased due to selecting the wrong subset of principal components. In a genetic context, with groups representing families, this bias is inverse proportional to the degree of genetic relationship among family members, but is independent of sample size. Theoretical results are supplemented by a simulation study, demonstrating close agreement between predicted and observed bias for large samples. It is emphasized that the rank of the genetic covariance matrix should be chosen sufficiently large to accommodate all important genetic principal components, even though, paradoxically, this may require including a number of components with negligible eigenvalues. A strategy for rank selection in practical analyses is outlined.
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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
                6 February 2015
                April 2015
                : 5
                : 4
                : 569-582
                Affiliations
                [* ]Department of Plant, Soil and Microbial Sciences, Michigan State University (MSU), East Lansing, Michigan 4882,
                []International Maize and Wheat Improvement Center(CIMMYT), Mexico D.F., Mexico
                []Wheat Genetics Resource Center, Department of Plant Pathology and Department of Agronomy, Kansas State University (KSU), 4011 Throckmorton Hall, Manhattan, Kansas 66506
                [§ ]USDA-ARS and Department of Plant Breeding and Genetics, Cornell University, Ithaca, New York 14853, and
                [§§ ]Epidemiology & Biostatistics and Statistics departments, Michigan State University 909 Fee Road, East Lansing, Michigan 48824
                Author notes
                [1 ]Corresponding author: Department of Biostatistics, University of Alabama at Birmingham, 327L Ryals Public Health Bldg, 1665 University Boulevard, Birmingham, AL 35294. E-mail: gcampos@ 123456uab.edu
                Article
                GGG_016097
                10.1534/g3.114.016097
                4390573
                25660166
                aa881d28-2e7d-4a37-baaa-ea7b00a50379
                Copyright © 2015 Lopez-Cruz et al.

                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
                : 04 December 2014
                : 03 February 2015
                Page count
                Pages: 14
                Categories
                Genomic Selection

                Genetics
                genomic selection,multienvironment,genomic best linear unbiased prediction (gblup),marker × environment interaction,international bread wheat screening nursery,genpred,shared data resource

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