Theoretical and Applied Genetics

, Volume 128, Issue 4, pp 693–703 | Cite as

Shrinkage estimation of the genomic relationship matrix can improve genomic estimated breeding values in the training set

  • Dominik Müller
  • Frank Technow
  • Albrecht E. Melchinger
Original Paper


Key message

We evaluated several methods for computing shrinkage estimates of the genomic relationship matrix and demonstrated their potential to enhance the reliability of genomic estimated breeding values of training set individuals.


In genomic prediction in plant breeding, the training set constitutes a large fraction of the total number of genotypes assayed and is itself subject to selection. The objective of our study was to investigate whether genomic estimated breeding values (GEBVs) of individuals in the training set can be enhanced by shrinkage estimation of the genomic relationship matrix. We simulated two different population types: a diversity panel of unrelated individuals and a biparental family of doubled haploid lines. For different training set sizes (50, 100, 200), number of markers (50, 100, 200, 500, 2,500) and heritabilities (0.25, 0.5, 0.75), shrinkage coefficients were computed by four different methods. Two of these methods are novel and based on measures of LD, the other two were previously described in the literature, one of which was extended by us. Our results showed that shrinkage estimation of the genomic relationship matrix can significantly improve the reliability of the GEBVs of training set individuals, especially for a low number of markers. We demonstrate that the number of markers is the primary determinant of the optimum shrinkage coefficient maximizing the reliability and we recommend methods eligible for routine usage in practical applications.


Conflict of interest

The authors declare no conflict of interest associated with this study.

Ethical standards

The authors declare that ethical standards are met, and all the experiments comply with the current laws of the country in which they were performed.

Supplementary material

122_2015_2464_MOESM1_ESM.pdf (2.7 mb)
Supplementary material 1 (pdf 2787 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of HohenheimStuttgartGermany
  2. 2.DuPont PioneerJohnstonUSA

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