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      Efficiency of multi-trait, indirect, and trait-assisted genomic selection for improvement of biomass sorghum

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          Abstract

          Key message

          We compare genomic selection methods that use correlated traits to help predict biomass yield in sorghum, and find that trait-assisted genomic selection performs best.

          Abstract

          Genomic selection (GS) is usually performed on a single trait, but correlated traits can also help predict a focal trait through indirect or multi-trait GS. In this study, we use a pre-breeding population of biomass sorghum to compare strategies that use correlated traits to improve prediction of biomass yield, the focal trait. Correlated traits include moisture, plant height measured at monthly intervals between planting and harvest, and the area under the growth progress curve. In addition to single- and multi-trait direct and indirect GS, we test a new strategy called trait-assisted GS, in which correlated traits are used along with marker data in the validation population to predict a focal trait. Single-trait GS for biomass yield had a prediction accuracy of 0.40. Indirect GS performed best using area under the growth progress curve to predict biomass yield, with a prediction accuracy of 0.37, and did not differ from indirect multi-trait GS that also used moisture information. Multi-trait GS and single-trait GS yielded similar results, indicating that correlated traits did not improve prediction of biomass yield in a standard GS scenario. However, trait-assisted GS increased prediction accuracy by up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$50\%$$\end{document} when using plant height in both the training and validation populations to help predict yield in the validation population. Coincidence between selected genotypes in phenotypic and genomic selection was also highest in trait-assisted GS. Overall, these results suggest that trait-assisted GS can be an efficient strategy when correlated traits are obtained earlier or more inexpensively than a focal trait.

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          The online version of this article (10.1007/s00122-017-3033-y) contains supplementary material, which is available to authorized users.

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          Best linear unbiased estimation and prediction under a selection model.

          Mixed linear models are assumed in most animal breeding applications. Convenient methods for computing BLUE of the estimable linear functions of the fixed elements of the model and for computing best linear unbiased predictions of the random elements of the model have been available. Most data available to animal breeders, however, do not meet the usual requirements of random sampling, the problem being that the data arise either from selection experiments or from breeders' herds which are undergoing selection. Consequently, the usual methods are likely to yield biased estimates and predictions. Methods for dealing with such data are presented in this paper.
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            Increased accuracy of artificial selection by using the realized relationship matrix.

            Dense marker genotypes allow the construction of the realized relationship matrix between individuals, with elements the realized proportion of the genome that is identical by descent (IBD) between pairs of individuals. In this paper, we demonstrate that by replacing the average relationship matrix derived from pedigree with the realized relationship matrix in best linear unbiased prediction (BLUP) of breeding values, the accuracy of the breeding values can be substantially increased, especially for individuals with no phenotype of their own. We further demonstrate that this method of predicting breeding values is exactly equivalent to the genomic selection methodology where the effects of quantitative trait loci (QTLs) contributing to variation in the trait are assumed to be normally distributed. The accuracy of breeding values predicted using the realized relationship matrix in the BLUP equations can be deterministically predicted for known family relationships, for example half sibs. The deterministic method uses the effective number of independently segregating loci controlling the phenotype that depends on the type of family relationship and the length of the genome. The accuracy of predicted breeding values depends on this number of effective loci, the family relationship and the number of phenotypic records. The deterministic prediction demonstrates that the accuracy of breeding values can approach unity if enough relatives are genotyped and phenotyped. For example, when 1000 full sibs per family were genotyped and phenotyped, and the heritability of the trait was 0.5, the reliability of predicted genomic breeding values (GEBVs) for individuals in the same full sib family without phenotypes was 0.82. These results were verified by simulation. A deterministic prediction was also derived for random mating populations, where the effective population size is the key parameter determining the effective number of independently segregating loci. If the effective population size is large, a very large number of individuals must be genotyped and phenotyped in order to accurately predict breeding values for unphenotyped individuals from the same population. If the heritability of the trait is 0.3, and N(e)=100, approximately 12474 individuals with genotypes and phenotypes are required in order to predict GEBVs of un-phenotyped individuals in the same population with an accuracy of 0.7 [corrected].
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              Shrinkage Estimation of the Realized Relationship Matrix

              The additive relationship matrix plays an important role in mixed model prediction of breeding values. For genotype matrix X (loci in columns), the product XX′ is widely used as a realized relationship matrix, but the scaling of this matrix is ambiguous. Our first objective was to derive a proper scaling such that the mean diagonal element equals 1+f, where f is the inbreeding coefficient of the current population. The result is a formula involving the covariance matrix for sampling genomic loci, which must be estimated with markers. Our second objective was to investigate whether shrinkage estimation of this covariance matrix can improve the accuracy of breeding value (GEBV) predictions with low-density markers. Using an analytical formula for shrinkage intensity that is optimal with respect to mean-squared error, simulations revealed that shrinkage can significantly increase GEBV accuracy in unstructured populations, but only for phenotyped lines; there was no benefit for unphenotyped lines. The accuracy gain from shrinkage increased with heritability, but at high heritability (> 0.6) this benefit was irrelevant because phenotypic accuracy was comparable. These trends were confirmed in a commercial pig population with progeny-test-estimated breeding values. For an anonymous trait where phenotypic accuracy was 0.58, shrinkage increased the average GEBV accuracy from 0.56 to 0.62 (SE < 0.00) when using random sets of 384 markers from a 60K array. We conclude that when moderate-accuracy phenotypes and low-density markers are available for the candidates of genomic selection, shrinkage estimation of the relationship matrix can improve genetic gain.
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                Author and article information

                Contributors
                samuelf@illinois.edu
                Journal
                Theor Appl Genet
                Theor. Appl. Genet
                TAG. Theoretical and Applied Genetics. Theoretische Und Angewandte Genetik
                Springer Berlin Heidelberg (Berlin/Heidelberg )
                0040-5752
                1432-2242
                7 December 2017
                7 December 2017
                2018
                : 131
                : 3
                : 747-755
                Affiliations
                [1 ]ISNI 0000 0004 1936 9991, GRID grid.35403.31, Department of Crop Sciences, , University of Illinois, ; 1206 W Gregory Drive, IL Urbana, 61801 USA
                [2 ]ISNI 0000 0004 1937 0722, GRID grid.11899.38, Department of Genetics, Luiz de Queiroz College of Agriculture, , University of São Paulo, ; PO Box 83, Piracicaba, SP 13400-970 Brazil
                [3 ]ISNI 0000 0000 8816 9513, GRID grid.411269.9, Departamento de Estatística, , Universidade Federal de Lavras, ; 3037, Lavras, MG 37200-000 Brazil
                Author notes

                Communicated by Ian D. Godwin.

                Article
                3033
                10.1007/s00122-017-3033-y
                5814553
                29218378
                e4513ce3-3d27-4743-9804-9106d3690cad
                © The Author(s) 2017

                Open AccessThis article is 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 you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

                History
                : 10 May 2017
                : 1 December 2017
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/100006132, Office of Science;
                Award ID: DE-SC0012400
                Funded by: FundRef http://dx.doi.org/10.13039/501100002322, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior;
                Funded by: FundRef http://dx.doi.org/10.13039/501100004901, Fundação de Amparo á Pesquisa do Estado de Minas Gerais;
                Funded by: Conselho Nacional de Desenvolvimento Cientófico e Tecnológico (BR)
                Funded by: FundRef http://dx.doi.org/10.13039/501100001807, Fundação de Amparo ó Pesquisa do Estado de São Paulo;
                Award ID: 2016/12977-7
                Award Recipient :
                Categories
                Original Article
                Custom metadata
                © Springer-Verlag GmbH Germany, part of Springer Nature 2018

                Genetics
                Genetics

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