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      Single-step genomic BLUP enables joint analysis of disconnected breeding programs: an example with Eucalyptus globulus Labill

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          Abstract

          Single-step GBLUP (HBLUP) efficiently combines genomic, pedigree, and phenotypic information for holistic genetic analyses of disjunct breeding populations. We combined data from two independent multigenerational Eucalyptus globulus breeding populations to provide direct comparisons across the programs and indirect predictions in environments where pedigreed families had not been evaluated. Despite few known pedigree connections between the programs, genomic relationships provided the connectivity required to create a unified relationship matrix, H, which was used to compare pedigree-based and HBLUP models. Stem volume data from 48 sites spread across three regions of southern Australia and wood quality data across 20 sites provided comparisons of model accuracy. Genotyping proved valuable for correcting pedigree errors and HBLUP more precisely defines relationships within and among populations, with relationships among the genotyped individuals used to connect the pedigrees of the two programs. Cryptic relationships among the native range populations provided evidence of population structure and evidence of the origin of landrace populations. HBLUP across programs improved the prediction accuracy of parents and genotyped individuals and enabled breeding value predictions to be directly compared and inferred in regions where little to no testing has been undertaken. The impact of incorporating genetic groups in the estimation of H will further align traditional genetic evaluation pipelines with approaches that incorporate marker-derived relationships into prediction models.

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          Efficient methods to compute genomic predictions.

          P VanRaden (2008)
          Efficient methods for processing genomic data were developed to increase reliability of estimated breeding values and to estimate thousands of marker effects simultaneously. Algorithms were derived and computer programs tested with simulated data for 2,967 bulls and 50,000 markers distributed randomly across 30 chromosomes. Estimation of genomic inbreeding coefficients required accurate estimates of allele frequencies in the base population. Linear model predictions of breeding values were computed by 3 equivalent methods: 1) iteration for individual allele effects followed by summation across loci to obtain estimated breeding values, 2) selection index including a genomic relationship matrix, and 3) mixed model equations including the inverse of genomic relationships. A blend of first- and second-order Jacobi iteration using 2 separate relaxation factors converged well for allele frequencies and effects. Reliability of predicted net merit for young bulls was 63% compared with 32% using the traditional relationship matrix. Nonlinear predictions were also computed using iteration on data and nonlinear regression on marker deviations; an additional (about 3%) gain in reliability for young bulls increased average reliability to 66%. Computing times increased linearly with number of genotypes. Estimation of allele frequencies required 2 processor days, and genomic predictions required <1 d per trait, and traits were processed in parallel. Information from genotyping was equivalent to about 20 daughters with phenotypic records. Actual gains may differ because the simulation did not account for linkage disequilibrium in the base population or selection in subsequent generations.
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            Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score.

            The first national single-step, full-information (phenotype, pedigree, and marker genotype) genetic evaluation was developed for final score of US Holsteins. Data included final scores recorded from 1955 to 2009 for 6,232,548 Holsteins cows. BovineSNP50 (Illumina, San Diego, CA) genotypes from the Cooperative Dairy DNA Repository (Beltsville, MD) were available for 6,508 bulls. Three analyses used a repeatability animal model as currently used for the national US evaluation. The first 2 analyses used final scores recorded up to 2004. The first analysis used only a pedigree-based relationship matrix. The second analysis used a relationship matrix based on both pedigree and genomic information (single-step approach). The third analysis used the complete data set and only the pedigree-based relationship matrix. The fourth analysis used predictions from the first analysis (final scores up to 2004 and only a pedigree-based relationship matrix) and prediction using a genomic based matrix to obtain genetic evaluation (multiple-step approach). Different allele frequencies were tested in construction of the genomic relationship matrix. Coefficients of determination between predictions of young bulls from parent average, single-step, and multiple-step approaches and their 2009 daughter deviations were 0.24, 0.37 to 0.41, and 0.40, respectively. The highest coefficient of determination for a single-step approach was observed when using a genomic relationship matrix with assumed allele frequencies of 0.5. Coefficients for regression of 2009 daughter deviations on parent-average, single-step, and multiple-step predictions were 0.76, 0.68 to 0.79, and 0.86, respectively, which indicated some inflation of predictions. The single-step regression coefficient could be increased up to 0.92 by scaling differences between the genomic and pedigree-based relationship matrices with little loss in accuracy of prediction. One complete evaluation took about 2h of computing time and 2.7 gigabytes of memory. Computing times for single-step analyses were slightly longer (2%) than for pedigree-based analysis. A national single-step genetic evaluation with the pedigree relationship matrix augmented with genomic information provided genomic predictions with accuracy and bias comparable to multiple-step procedures and could account for any population or data structure. Advantages of single-step evaluations should increase in the future when animals are pre-selected on genotypes. Copyright 2010 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.
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              A relationship matrix including full pedigree and genomic information.

              Dense molecular markers are being used in genetic evaluation for parts of the population. This requires a two-step procedure where pseudo-data (for instance, daughter yield deviations) are computed from full records and pedigree data and later used for genomic evaluation. This results in bias and loss of information. One way to incorporate the genomic information into a full genetic evaluation is by modifying the numerator relationship matrix. A naive proposal is to substitute the relationships of genotyped animals with the genomic relationship matrix. However, this results in incoherencies because the genomic relationship matrix includes information on relationships among ancestors and descendants. In other words, using the pedigree-derived covariance between genotyped and ungenotyped individuals, with the pretense that genomic information does not exist, leads to inconsistencies. It is proposed to condition the genetic value of ungenotyped animals on the genetic value of genotyped animals via the selection index (e.g., pedigree information), and then use the genomic relationship matrix for the latter. This results in a joint distribution of genotyped and ungenotyped genetic values, with a pedigree-genomic relationship matrix H. In this matrix, genomic information is transmitted to the covariances among all ungenotyped individuals. The matrix is (semi)positive definite by construction, which is not the case for the naive approach. Numerical examples and alternative expressions are discussed. Matrix H is suitable for iteration on data algorithms that multiply a vector times a matrix, such as preconditioned conjugated gradients.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                G3 (Bethesda)
                Genetics
                g3journal
                G3: Genes|Genomes|Genetics
                Oxford University Press
                2160-1836
                October 2021
                16 July 2021
                16 July 2021
                : 11
                : 10
                : jkab253
                Affiliations
                [1 ]Treehouse Forest Research LLC , Check, VA 24072, USA
                [2 ]Australian Bluegum Plantations , Albany, WA 6330, Australia
                [3 ]HVP Plantations , Churchill, VIC 3842, Australia
                [4 ]Sassafras Group Pty Ltd , Yarraville, VIC 3013, Australia
                [5 ]Plant Pathology, University of Florida , Gainesville, FL 32611, USA
                Author notes
                Corresponding author: Email: andrew@ 123456treehouse-research.com
                Author information
                https://orcid.org/0000-0001-9914-7712
                Article
                jkab253
                10.1093/g3journal/jkab253
                8473980
                34568915
                2c2e573f-fc94-45c5-a042-46b31296d0f6
                © The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.

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

                History
                : 23 March 2021
                : 08 July 2021
                : 22 September 2021
                Page count
                Pages: 13
                Funding
                Funded by: Forest and Wood Products Australia, DOI 10.13039/501100001073;
                Award ID: PNC378-1516
                Funded by: Australian Bluegum Plantations;
                Funded by: HVP Plantations;
                Categories
                Investigation
                AcademicSubjects/SCI01180
                AcademicSubjects/SCI01140
                AcademicSubjects/SCI00010
                AcademicSubjects/SCI00960
                AcademicSubjects/SCI01180
                AcademicSubjects/SCI01140
                AcademicSubjects/SCI00010
                AcademicSubjects/SCI00960

                Genetics
                breeding value accuracy,forest tree breeding,genomic relationship matrix,genomic selection,hblup,myrtaceae,mpp,multiparental populations

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