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Shrinkage estimation of the realized relationship matrix
Jeffrey B Endelman1, Jean-Luc Jannink
1Robert W. Holley Center for Agriculture and Health, USDA-ARS, Cornell University, Ithaca, NY 14853, USA. j.endelman@gmail.com
G3 (Bethesda, Md.)
|November 23, 2012
Summary
Shrinkage estimation of the additive relationship matrix improves genomic breeding value (GEBV) predictions accuracy when using low-density markers and moderate-accuracy phenotypes. This method enhances genetic gain in genomic selection candidates.
Area of Science:
- Quantitative genetics
- Animal breeding
- Genomic selection
Background:
- The additive relationship matrix is crucial for mixed model prediction of breeding values.
- Scaling of the realized relationship matrix (XX') derived from genotype data is often ambiguous.
- Accurate estimation of genomic relationships is vital for effective genomic selection.
Purpose of the Study:
- To derive a proper scaling for the realized relationship matrix where the mean diagonal element equals 1+f (f = inbreeding coefficient).
- To investigate if shrinkage estimation of the genomic covariance matrix improves genomic estimated breeding value (GEBV) prediction accuracy with low-density markers.
Main Methods:
- Derived a formula for relationship matrix scaling involving the covariance matrix of genomic loci sampling.
- Employed shrinkage estimation for the covariance matrix using an analytically derived optimal shrinkage intensity.
- Conducted simulations and analyzed a commercial pig population dataset for GEBV accuracy assessment.
Main Results:
- Shrinkage estimation significantly increased GEBV accuracy for phenotyped lines in unstructured populations, especially with low-density markers.
- The accuracy gain from shrinkage was dependent on heritability, becoming less relevant at high heritability (> 0.6).
- In a pig population, shrinkage improved average GEBV accuracy from 0.56 to 0.62 (phenotypic accuracy 0.58) using 384 markers.
Conclusions:
- Shrinkage estimation of the relationship matrix offers a valuable improvement for GEBV accuracy when moderate-accuracy phenotypes and low-density markers are available.
- This approach can enhance genetic gain in candidates undergoing genomic selection.
- The findings are robust and validated in both simulated and real-world animal breeding data.
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