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      Genomic prediction of fruit texture and training population optimization towards the application of genomic selection in apple

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          Abstract

          Texture is a complex trait and a major component of fruit quality in apple. While the major effect of MdPG1, a gene controlling firmness, has already been exploited in elite cultivars, the genetic basis of crispness remains poorly understood. To further improve fruit texture, harnessing loci with minor effects via genomic selection is therefore necessary. In this study, we measured acoustic and mechanical features in 537 genotypes to dissect the firmness and crispness components of fruit texture. Predictions of across-year phenotypic values for these components were calculated using a model calibrated with 8,294 SNP markers. The best prediction accuracies following cross-validations within the training set of 259 genotypes were obtained for the acoustic linear distance (0.64). Predictions for biparental families using the entire training set varied from low to high accuracy, depending on the family considered. While adding siblings or half-siblings into the training set did not clearly improve predictions, we performed an optimization of the training set size and composition for each validation set. This allowed us to increase prediction accuracies by 0.17 on average, with a maximal accuracy of 0.81 when predicting firmness in the ‘Gala’ × ‘Pink Lady’ family. Our results therefore identified key genetic parameters to consider when deploying genomic selection for texture in apple. In particular, we advise to rely on a large training population, with high phenotypic variability from which a ‘tailored training population’ can be extracted using a priori information on genetic relatedness, in order to predict a specific target population.

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          Fitting Linear Mixed-Effects Models Using lme4

          Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer. Journal of Statistical Software, 67 (1) ISSN:1548-7660
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            MOLECULAR BIOLOGY OF FRUIT MATURATION AND RIPENING.

            The development and maturation of fruits has received considerable scientific scrutiny because of both the uniqueness of such processes to the biology of plants and the importance of fruit as a significant component of the human diet. Molecular and genetic analysis of fruit development, and especially ripening of fleshy fruits, has resulted in significant gains in knowledge over recent years. Great strides have been made in the areas of ethylene biosynthesis and response, cell wall metabolism, and environmental factors, such as light, that impact ripening. Discoveries made in Arabidopsis in terms of general mechanisms for signal transduction, in addition to specific mechanisms of carpel development, have assisted discovery in more traditional models such as tomato. This review attempts to coalesce recent findings in the areas of fruit development and ripening.
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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
                morgane.roth@inrae.fr
                Journal
                Hortic Res
                Hortic Res
                Horticulture Research
                Nature Publishing Group UK (London )
                2662-6810
                2052-7276
                1 September 2020
                1 September 2020
                2020
                : 7
                : 148
                Affiliations
                [1 ]GRID grid.417771.3, ISNI 0000 0004 4681 910X, Plant Breeding Research Division, , Agroscope, ; Wädenswil, Zurich, Switzerland
                [2 ]GRID grid.452456.4, ISNI 0000 0004 0613 5301, IRHS, INRAE, Agrocampus-Ouest, Université d’Angers, ; SFR 4207 QuaSaV, Beaucouzé, France
                [3 ]GRID grid.424414.3, ISNI 0000 0004 1755 6224, Department of Genomics and Biology of Fruit Crops, Research and Innovation Centre, , Fondazione Edmund Mach (FEM), ; Via E. Mach 1, 38010 San Michele all’Adige, Italy
                [4 ]GRID grid.8158.4, ISNI 0000 0004 1757 1969, Department of Agriculture, Food and Environment (Di3A), , University of Catania, ; Catania, Italy
                [5 ]Research Centre Laimburg, Laimburg 6, 39040 Auer, Italy
                [6 ]GRID grid.11696.39, ISNI 0000 0004 1937 0351, Center Agriculture Food Environment, , University of Trento, ; Via Mach 1, 38010 San Michele all’Adige, Italy
                [7 ]GRID grid.464148.b, ISNI 0000 0004 0502 233X, Present Address: GAFL, INRAE, ; 84140 Montfavet, France
                Author information
                http://orcid.org/0000-0003-1416-1078
                Article
                370
                10.1038/s41438-020-00370-5
                7459338
                31908804
                034ac8f5-a762-4324-91dd-43b919e73483
                © The Author(s) 2020

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as 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. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 10 January 2020
                : 18 July 2020
                : 24 July 2020
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                Custom metadata
                © The Author(s) 2020

                plant genetics,population genetics,plant breeding
                plant genetics, population genetics, plant breeding

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