Shrinkage estimation of the genomic relationship matrix can improve genomic estimated breeding values in the training set
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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.
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.
- Bernardo R, Yu J (2007) Prospects for genomewide selection for quantitative traits in Maize. Crop Sci 47(3):1082. doi: 10.2135/cropsci2006.11.0690. https://www.crops.org/publications/cs/abstracts/47/3/1082
- de Los Campos G, Hickey JM, Pong-Wong R, Daetwyler HD, Calus MPL (2013) Whole-genome regression and prediction methods applied to plant and animal breeding. Genetics 193(2), pp. 327–45. doi: 10.1534/genetics.112.143313. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3567727&tool=pmcentrez&rendertype=abstract
- Endelman JB (2011) Ridge regression and other kernels for genomic selection with R Package rrBLUP. Plant Genome J 4(3):250. doi: 10.3835/plantgenome2011.08.0024. https://www.crops.org/publications/tpg/abstracts/4/3/250
- Endelman JB, Jannink JL (2012) Shrinkage estimation of the realized relationship matrix. G3 2(11):1405–13. doi: 10.1534/g3.112.004259. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3484671&tool=pmcentrez&rendertype=abstract
- Frisch M, Melchinger AE (2007) Variance of the parental genome contribution to inbred lines derived from biparental crosses. Genetics 176(1):477–88, doi: 10.1534/genetics.106.065433. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1893034&tool=pmcentrez&rendertype=abstract
- Habier D, Fernando RL, Dekkers JCM (2007) The impact of genetic relationship information on genome-assisted breeding values. Genetics 177(4):2389–97. doi: 10.1534/genetics.107.081190. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2219482&tool=pmcentrez&rendertype=abstract
- Henderson CR (1973) Sire evaluation and genetic trends. J Anim Sci, pp 10–41Google Scholar
- Hill W, Robertson A (1968) Linkage disequilibrium in finite populations. Theor Appl Genet 38(6):226–231. http://link.springer.com/article/10.1007/BF01245622
- Hill WG (2010) Understanding and using quantitative genetic variation. Philos Trans R Soc Lond Ser B Biol Sci 365(1537);73–85. doi: 10.1098/rstb.2009.0203. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2842708&tool=pmcentrez&rendertype=abstract
- Hill WG, Weir BS (2011) Variation in actual relationship as a consequence of Mendelian sampling and linkage. Genet Res 93(1):47–64. doi: 10.1017/S0016672310000480. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3070763&tool=pmcentrez&rendertype=abstract
- Kang HM, Zaitlen Na, Wade CM, Kirby A, Heckerman D, Daly MJ, Eskin E (2008) Efficient control of population structure in model organism association mapping. Genetics 178(3):1709–23. doi: 10.1534/genetics.107.080101. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2278096&tool=pmcentrez&rendertype=abstract
- Lande R, Thompson R (1990) Efficiency of marker-assisted selection in the improvement of quantitative traits. Genetics 124(3):743–56. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1203965&tool=pmcentrez&rendertype=abstract
- Lynch M, Walsh B (1998) Genetics and analysis of quantitative traits, 1st edn. Sinauer Associates, SunderlandGoogle Scholar
- Meuwissen THE, Hayes BJ, Goddard ME (2001) Prediction of total genetic value using genome-wide dense marker maps. Genetics 157(4):1819–1829. http://www.genetics.org/content/157/4/1819.abstract
- R Core Team (2014) R: a language and environment for statistical computing. http://www.r-project.org/
- Riedelsheimer C, Technow F, Melchinger AE (2012) Comparison of whole-genome prediction models for traits with contrasting genetic architecture in a diversity panel of maize inbred lines. BMC genomics 13(1):452. doi: 10.1186/1471-2164-13-452. http://www.mendeley.com/research/comparison-of-whole-genome-prediction-models-for-traits-with-contrasting-genetic-architecture-in-a-d-1/
- Smith JSC, Hussain T, Jones ES, Graham G, Podlich D, Wall S, Williams M (2008) Use of doubled haploids in maize breeding: implications for intellectual property protection and genetic diversity in hybrid crops. Mol Breed 22(1):51–59. doi: 10.1007/s11032-007-9155-1. http://link.springer.com/10.1007/s11032-007-9155-1
- Technow F (2013) hypred: simulation of genomic data in applied genetics. http://cran.r-project.org/web/packages/hypred/
- Yang J, Benyamin B, McEvoy BP, Gordon S, Henders AK, Nyholt DR, Madden Pa, Heath AC, Martin NG, Montgomery GW, Goddard ME, Visscher PM (2010) Common SNPs explain a large proportion of the heritability for human height. Nat Genet 42(7):565–9. doi: 10.1038/ng.608. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3232052&tool=pmcentrez&rendertype=abstract