Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP

By Jeffrey B. Endelman. 2011

1,895 citations recorded by the source corpus.

Many important traits in plant breeding are polygenic and therefore recalcitrant to traditional marker‐assisted selection. Genomic selection addresses this complexity by including all markers in the prediction model. A key method for the genomic prediction of breeding values is ridge regression (RR), which is equivalent to best linear unbiased prediction (BLUP) when the genetic covariance between lines is proportional to their similarity in genotype space. This additive model can be broadened to include epistatic effects by using other kernels, such as the Gaussian, which represent inner products in a complex feature space. To facilitate the use of RR and nonadditive kernels in plant breeding, a new software package for R called rrBLUP has been developed. At its core is a fast maximum‐likelihood algorithm for mixed models with a single variance component besides the residual error, which allows for efficient prediction with unreplicated training data. Use of the rrBLUP software is demonstrated through several examples, including the identification of optimal crosses based on superior progeny value. In cross‐validation tests, the prediction accuracy with nonadditive kernels was significantly higher than RR for wheat (Triticum aestivum L.) grain yield but equivalent for several maize (Zea mays L.) traits.

Subfields: Genetics, Plant Science

View Paper: https://www.semanticscholar.org/paper/c61e378c244020643944594ff4208ed20ce887ed

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Citations in the corpus

GAPIT Version 2: An Enhanced Integrated Tool for Genomic Association and Prediction (2016, methodology): “These large datasets require increasingly greater computing capabilities for performing analyses such as GWAS (Cantor et al., 2010) and genomic prediction of phenotypes from genotypes (VanRaden et al., 2009; Endelman, 2011; Poland et al., 2012).”
Feature selection methods for big data bioinformatics: A survey from the search perspective. (2016, methodology): “Mohapatra et al. [87] proposed two variations of kernel ridge regression (KRR) [88,89,90], namely wavelet kernel ridge regression (WKRR) and radial basis kernel ridge regression (RKRR) for classification of microarray medical datasets.”
Accuracy of Genomewide Selection for Different Traits with Constant Population Size, Heritability, and Number of Markers (2013, methodology): “8 (Endelman, 2011) for R version 2.”
Comparing genomic selection and marker-assisted selection for Fusarium head blight resistance in wheat (Triticum aestivum L.) (2016, methodology): “…division, with all breeding lines from the same cluster ending up in either TP or VP. Prediction accuracies were calculated in R (R Development Core Team 2013) using the ''lm()'' function for the MAS models and the ''mixed.solve()'' function of the rrBLUP package (Endelmann 2011) for the GS models.”
Genomic Selection for Crop Improvement (2017, positive): “Endelman et al. (2014) proposed using a response to selection metric Rmax based on the maximum genotypic value of selections instead of Rmean based on mean values for selection to analyze genetic gain in preliminary yield trials.”
Optimal Design of Preliminary Yield Trials with Genome-Wide Markers (2014, methodology): “Variance components were estimated by REML using R package rrBLUP, version 4.1 (Endelman, 2011; R Development Core Team, 2012).”
Genome-Assisted Prediction of Quantitative Traits Using the R Package sommer (2016, methodology): “…that allow genomic selection, there is few open source genomic selection or mixed model software that allows the modeling of several variance components at a time and particularly the modeling of SCA effects by likelihood methods, such as some popular R packages; regress, and EMM-REML [13,15 – 19].”
Genomic Prediction of Genetic Values for Resistance to Wheat Rusts (2012, methodology): “We used the package rrBLUP (Endelman, 2011), which calculates maximum likelihood (ML or REML) solutions for mixed models of the form”
Relatedness and Genotype × Environment Interaction Affect Prediction Accuracies in Genomic Selection: A Study in Cassava (2013, positive): “The A matrix was computed by using the rrBLUP function Amat (Endelman, 2011), which crop science, vol. 53, july–august 2013 www.crops.org 1317”
Genome‐wide Association for Plant Height and Flowering Time across 15 Tropical Maize Populations under Managed Drought Stress and Well‐Watered Conditions in Sub‐Saharan Africa (2016, methodology): “Genome-wide prediction was performed using the rrBLUP package for R (Endelman 2011; R Core Team 2015).”
GAPIT Version 3: Boosting Power and Accuracy for Genomic Association and Prediction (2020, methodology): “These packages include PLINK with GLM and logistic regression [23]; 127 TASSEL [24] with GLM and MLM; rrBLUP with ridge regression and gBLUP [25]; and BGLR 128”
Adding Genetically Distant Individuals to Training Populations Reduces Genomic Prediction Accuracy in Barley (2015, methodology): “The RR-BLUP model was implemented in the R package rrBLUP version 4.2 (R Development Core Team, 2012; Endelman, 2011 ).”
Genomic Selection in Wheat Breeding using Genotyping‐by‐Sequencing (2012, methodology): “A convergence threshold of 0.02 was used for all results. h e MVN-EM algorithm is available through R package rrBLUP version 3.8 or higher (Endelman, 2011).”