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      Prediction of Multiple-Trait and Multiple-Environment Genomic Data Using Recommender Systems

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          Abstract

          In genomic-enabled prediction, the task of improving the accuracy of the prediction of lines in environments is difficult because the available information is generally sparse and usually has low correlations between traits. In current genomic selection, although researchers have a large amount of information and appropriate statistical models to process it, there is still limited computing efficiency to do so. Although some statistical models are usually mathematically elegant, many of them are also computationally inefficient, and they are impractical for many traits, lines, environments, and years because they need to sample from huge normal multivariate distributions. For these reasons, this study explores two recommender systems: item-based collaborative filtering (IBCF) and the matrix factorization algorithm (MF) in the context of multiple traits and multiple environments. The IBCF and MF methods were compared with two conventional methods on simulated and real data. Results of the simulated and real data sets show that the IBCF technique was slightly better in terms of prediction accuracy than the two conventional methods and the MF method when the correlation was moderately high. The IBCF technique is very attractive because it produces good predictions when there is high correlation between items (environment–trait combinations) and its implementation is computationally feasible, which can be useful for plant breeders who deal with very large data sets.

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          Genomic selection.

          Genomic selection is a form of marker-assisted selection in which genetic markers covering the whole genome are used so that all quantitative trait loci (QTL) are in linkage disequilibrium with at least one marker. This approach has become feasible thanks to the large number of single nucleotide polymorphisms (SNP) discovered by genome sequencing and new methods to efficiently genotype large number of SNP. Simulation results and limited experimental results suggest that breeding values can be predicted with high accuracy using genetic markers alone but more validation is required especially in samples of the population different from that in which the effect of the markers was estimated. The ideal method to estimate the breeding value from genomic data is to calculate the conditional mean of the breeding value given the genotype of the animal at each QTL. This conditional mean can only be calculated by using a prior distribution of QTL effects so this should be part of the research carried out to implement genomic selection. In practice, this method of estimating breeding values is approximated by using the marker genotypes instead of the QTL genotypes but the ideal method is likely to be approached more closely as more sequence and SNP data is obtained. Implementation of genomic selection is likely to have major implications for genetic evaluation systems and for genetic improvement programmes generally and these are discussed.
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            A Genomic Bayesian Multi-trait and Multi-environment Model

            When information on multiple genotypes evaluated in multiple environments is recorded, a multi-environment single trait model for assessing genotype × environment interaction (G × E) is usually employed. Comprehensive models that simultaneously take into account the correlated traits and trait × genotype × environment interaction (T × G × E) are lacking. In this research, we propose a Bayesian model for analyzing multiple traits and multiple environments for whole-genome prediction (WGP) model. For this model, we used Half- t priors on each standard deviation term and uniform priors on each correlation of the covariance matrix. These priors were not informative and led to posterior inferences that were insensitive to the choice of hyper-parameters. We also developed a computationally efficient Markov Chain Monte Carlo (MCMC) under the above priors, which allowed us to obtain all required full conditional distributions of the parameters leading to an exact Gibbs sampling for the posterior distribution. We used two real data sets to implement and evaluate the proposed Bayesian method and found that when the correlation between traits was high (>0.5), the proposed model (with unstructured variance–covariance) improved prediction accuracy compared to the model with diagonal and standard variance–covariance structures. The R-software package Bayesian Multi-Trait and Multi-Environment (BMTME) offers optimized C++ routines to efficiently perform the analyses.
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              A Bayesian Poisson-lognormal Model for Count Data for Multiple-Trait Multiple-Environment Genomic-Enabled Prediction

              When a plant scientist wishes to make genomic-enabled predictions of multiple traits measured in multiple individuals in multiple environments, the most common strategy for performing the analysis is to use a single trait at a time taking into account genotype × environment interaction (G × E), because there is a lack of comprehensive models that simultaneously take into account the correlated counting traits and G × E. For this reason, in this study we propose a multiple-trait and multiple-environment model for count data. The proposed model was developed under the Bayesian paradigm for which we developed a Markov Chain Monte Carlo (MCMC) with noninformative priors. This allows obtaining all required full conditional distributions of the parameters leading to an exact Gibbs sampler for the posterior distribution. Our model was tested with simulated data and a real data set. Results show that the proposed multi-trait, multi-environment model is an attractive alternative for modeling multiple count traits measured in multiple environments.
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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
                04 January 2018
                January 2018
                : 8
                : 1
                : 131-147
                Affiliations
                [* ]Facultad de Telemática, Universidad de Colima, 28040 Colima, México
                []Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI), Universidad de Guadalajara, 44430 Jalisco, México
                []International Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, 06600 México City, México
                [§ ]Departamento de Estadística, Centro de Investigación en Matemáticas (CIMAT), 36240 Guanajuato, México
                [** ]Department of Entomology, Michigan State University, East Lancing, Michigan 48824
                [†† ]Department of Computer Science, Aalto University, FI-00076, Finland
                Author notes
                [1 ]Corresponding authors: Facultad de Telemática, Universidad de Colima, 28040 Colima, México. E-mail: oamontes1@ 123456ucol.mx ; and Biometrics and Statistics Unit, International Maize and Wheat Improvement Center (CIMMYT), Apdo. postal 6-641, Apdo. Postal 6-641, 06600 México City, México. E-mail: j.crossa@ 123456cgiar.org
                Author information
                http://orcid.org/0000-0001-9429-5855
                Article
                GGG_300309
                10.1534/g3.117.300309
                5765342
                29097376
                2d423c56-9825-463f-985b-fc2336b22370
                Copyright © 2018 Montesinos-Lopez et al.

                This is an open-access article 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 the original work is properly cited.

                History
                : 27 September 2017
                : 31 October 2017
                Page count
                Figures: 3, Tables: 11, Equations: 11, References: 11, Pages: 17
                Categories
                Genomic Selection

                Genetics
                genomic information,item-based collaborative filtering,matrix factorization,multi-trait,genotype,environment interaction,prediction accuracy,collaborative filtering,genpred,shared data resources,genomic selection

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