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Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP
Open accessAbstract
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.
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![Figure 2 Performance of the Gaussian model (GAUSS). The fi gure depicts the effect of the Gaussian scale parameter ( θ in Eq. [6]) on the restricted log-likelihood (LL), the training population accuracy ( r train ), and the cross-validation accuracy ( r pred ) when predicting sets 5 or 6 in environment 1. For set 5 the restricted maximum likelihood solution for θ ( θ REML ) = 0.5, and for set 6 θ REML = 0.4. In both cases r train approached 1 as θ → 0, but the trends for r pred were different. For set 5 r pred exhibited an interior maximum near θ REML , while for set 6 r pred increased monotonically with θ . Because GAUSS is approximately ridge regression (RR) when θ is large, the contrasting behavior in this fi gure illustrates why GAUSS had higher r pred than RR for set 5 but vice versa for set 6 (see Table 2).](/paper-figures/eb5657fa983040d490573ea2a9864980/ridge-regression-and-other-kernels-for-genomic-selection-with-r-package-rrblup-figure-2.png)
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“Endelman (2011) developed the R -package rrBLUP that allows convenient restricted maximum likelihood (REML) estimation of the bandwidth, but only in the context of LMMs with a single genetic variance component, i.e., no G × E or G × E × M interaction models.”
From REML implementations of kernel-based genomic prediction models for genotype x environment x management interactions (2025) · cites this paper as Endelman (2011)
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Metadata
- Authors
- Endelman, J. B.
- Affiliations
- Washington State University (US)
- Corresponding author
- Endelman, Jeffrey B.
- ORCID
- Endelman, Jeffrey B.
- Venue
- The Plant Genome
- Publisher
- Wiley
- Published
- 2011-11
- Volume
- 4
- Issue
- 3
- Pages
- 250-255
- ISSN
- 1940-3372 (ISSN-L)
- OpenAlex
- W2064013109
- Cited by
- 2,094
- References
- 29
- Citations by year
- 2026: 198 · 2025: 202 · 2024: 204 · 2023: 206 · 2022: 226 · 2021: 234 · 2020: 204 · 2019: 144 · 2018: 110 · 2017: 112 · 2016: 99 · 2015: 82 · 2014: 36 · 2013: 23 · 2012: 9
- FWCI
- 14.37
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by-nc-nd
- doi.wiley.com/10.1002/tdm_license_1.1 (tdm)
- Locations
- The Plant Genome (publishedVersion, cc-by-nc-nd)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic and phenotypic traits in livestock
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Mapping and Diversity in Plants and Animals
- Life Sciences › Agricultural and Biological Sciences › Plant Science › Genetics and Plant Breeding
- Keywords
- genomic selection, ridge regression, BLUP, Gaussian kernel, breeding value estimation, plant breeding, wheat grain yield, cross-validation
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