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      FW: An R Package for Finlay–Wilkinson Regression that Incorporates Genomic/Pedigree Information and Covariance Structures Between Environments

      G3: Genes|Genomes|Genetics
      Genetics Society of America
      bayesian, finlay–wilkinson, genomic/environment, correlation, genotype by environment interaction, reaction norm, genpred, genomic selection, shared data resource

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          Abstract

          The Finlay–Wilkinson regression (FW) is a popular method among plant breeders to describe genotype by environment interaction. The standard implementation is a two-step procedure that uses environment (sample) means as covariates in a within-line ordinary least squares (OLS) regression. This procedure can be suboptimal for at least four reasons: (1) in the first step environmental means are typically estimated without considering genetic-by-environment interactions, (2) in the second step uncertainty about the environmental means is ignored, (3) estimation is performed regarding lines and environment as fixed effects, and (4) the procedure does not incorporate genetic (either pedigree-derived or marker-derived) relationships. Su et al. proposed to address these problems using a Bayesian method that allows simultaneous estimation of environmental and genotype parameters, and allows incorporation of pedigree information. In this article we: (1) extend the model presented by Su et al. to allow integration of genomic information [e.g., single nucleotide polymorphism (SNP)] and covariance between environments, (2) present an R package (FW) that implements these methods, and (3) illustrate the use of the package using examples based on real data. The FW R package implements both the two-step OLS method and a full Bayesian approach for Finlay–Wilkinson regression with a very simple interface. Using a real wheat data set we demonstrate that the prediction accuracy of the Bayesian approach is consistently higher than the one achieved by the two-step OLS method.

          Most cited references4

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          Genomic-Enabled Prediction Based on Molecular Markers and Pedigree Using the Bayesian Linear Regression Package in R.

          The availability of dense molecular markers has made possible the use of genomic selection in plant and animal breeding. However, models for genomic selection pose several computational and statistical challenges and require specialized computer programs, not always available to the end user and not implemented in standard statistical software yet. The R-package BLR (Bayesian Linear Regression) implements several statistical procedures (e.g., Bayesian Ridge Regression, Bayesian LASSO) in a unifi ed framework that allows including marker genotypes and pedigree data jointly. This article describes the classes of models implemented in the BLR package and illustrates their use through examples. Some challenges faced when applying genomic-enabled selection, such as model choice, evaluation of predictive ability through cross-validation, and choice of hyper-parameters, are also addressed.
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            Joint analysis of genotypic and environmental effects.

            A definition of jointly contributing genotypic and environmental effects is introduced, from which a new concept of genotype × environment interactions is derived. Interaction is defined to be the failure of genotypic or environmental response functions to be separable. For separable response functions, the contributions of the genotypic and environmental effects must be related in terms of an operator which can describe their joint actions. A scale-free method of determining the simplest operator is developed in terms of comparative norms of reaction and a characteristic of the operator is given for several operators. With a defined operator, the genetic and environmental contributions can be derived, and biologically interpreted. These methods are applied to published data on Pinus caribaea.
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              Environmental and genotype-environmental components of variability. 3. Multiple lines and crosses.

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                Author and article information

                Journal
                26715095
                4777122
                10.1534/g3.115.026328
                http://creativecommons.org/licenses/by/4.0/

                Genetics
                bayesian,finlay–wilkinson,genomic/environment,correlation,genotype by environment interaction,reaction norm,genpred,genomic selection,shared data resource

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