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      Modeling genotype × environment interaction for single and multitrait genomic prediction in potato ( Solanum tuberosum L.)

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          Abstract

          In this study, we extend research on genomic prediction (GP) to polysomic polyploid plant species with the main objective to investigate single-trait (ST) and multitrait (MT) multienvironment (ME) models using field trial data from 3 locations in Sweden [Helgegården (HEL), Mosslunda (MOS), Umeå (UM)] over 2 years (2020, 2021) of 253 potato cultivars and breeding clones for 5 tuber weight traits and 2 tuber flesh quality characteristics. This research investigated the GP of 4 genome-based prediction models with genotype × environment interactions (GEs): (1) ST reaction norm model ( M1), (2) ST model considering covariances between environments ( M2), (3) ST M2 extended to include a random vector that utilizes the environmental covariances ( M3), and (4) MT model with GE ( M4). Several prediction problems were analyzed for each of the GP accuracy of the 4 models. Results of the prediction of traits in HEL, the high yield potential testing site in 2021, show that the best-predicted traits were tuber flesh starch (%), weight of tuber above 60 or below 40 mm in size, and the total tuber weight. In terms of GP, accuracy model M4 gave the best prediction accuracy in 3 traits, namely tuber weight of 40–50 or above 60 mm in size, and total tuber weight, and very similar in the starch trait. For MOS in 2021, the best predictive traits were starch, weight of tubers above 60, 50–60, or below 40 mm in size, and the total tuber weight. MT model M4 was the best GP model based on its accuracy when some cultivars are observed in some traits. For the GP accuracy of traits in UM in 2021, the best predictive traits were the weight of tubers above 60, 50–60, or below 40 mm in size, and the best model was MT M4, followed by models ST M3 and M2.

          Most cited references50

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          Efficient methods to compute genomic predictions.

          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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            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 ∼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 (Ne = 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.
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              Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP

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                Author and article information

                Contributors
                Role: editor
                Journal
                G3 (Bethesda)
                Genetics
                g3journal
                G3: Genes|Genomes|Genetics
                Oxford University Press (US )
                2160-1836
                February 2023
                08 December 2022
                08 December 2022
                : 13
                : 2
                : jkac322
                Affiliations
                Departamento de Energía, Universidad Autónoma del Estado de Quintana Roo , Chetumal, Quintana Roo 77019, México
                Department of Plant Breeding, Swedish University of Agricultural Sciences (SLU) , P.O. Box 190, Lomma SE 23436, Sweden
                International Maize and Wheat Improvement Center (CIMMYT) , Carretera México-Veracruz Km. 45, El Batán, Texcoco 56237, Edo. de Mexico, Mexico
                Colegio de Postgraduados, Montecillos , Edo. de México 56230, México
                Department of Plant Breeding, Swedish University of Agricultural Sciences (SLU) , P.O. Box 190, Lomma SE 23436, Sweden
                Author notes
                Corresponding author: Sveriges Lantbruksuniversitet, Inst. för Växtförädling, Box 190, SE 23 422 Lomma, Sweden. Email: rodomiro.ortiz@ 123456slu.se

                Conflict of interest The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

                Author information
                https://orcid.org/0000-0002-0685-2867
                https://orcid.org/0000-0001-9429-5855
                https://orcid.org/0000-0002-1739-7206
                Article
                jkac322
                10.1093/g3journal/jkac322
                9911059
                36477309
                e30f3d37-110e-4632-a32d-32dc2f4f7b9f
                © The Author(s) 2022. Published by Oxford University Press on behalf of the Genetics Society of America.

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

                History
                : 09 August 2022
                : 28 November 2022
                : 25 January 2023
                Page count
                Pages: 13
                Funding
                Funded by: Swedish University of Agricultural Sciences, doi 10.13039/501100004360;
                Funded by: SLU, doi 10.13039/100010390;
                Funded by: Swedish Research Council Formas, doi 10.13039/501100001862;
                Categories
                Genomic Prediction
                Genomic Prediction
                AcademicSubjects/SCI01180
                AcademicSubjects/SCI01140

                Genetics
                solanum tuberosum,genomic prediction in potato,genomic × environment interaction,multienvironment modeling,multiple trait modeling,single-environment modeling,single-trait modeling

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