Cited by 2,094Genetic and phenotypic traits in livestockGenetic Mapping and Diversity in Plants and AnimalsGenetics and Plant Breeding

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

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Endelman, Jeffrey B.·2011·The Plant Genome

DOI 10.3835/plantgenome2011.08.0024

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Abstract

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 1 Analysis of line crosses. Each circle is the expected mean and standard deviation (SD) for the genomic-estimated breeding values (GEBVs) of the recombinant inbred progeny from one wheat cross. Results are shown for all 179,101 unique crosses between the 599 wheat lines, using the predicted marker effects in environment 1. In the top right of the fi gure are crosses between parents with high GEBV and complementary alleles, for which high levels of transgressive segregation are expected.CC-BY-NC-ND · From the PDF

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).CC-BY-NC-ND · From the PDF

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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)
DOI: 10.3835/plantgenome2011.08.0024
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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Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP

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