Improved reliability approximation for genomic evaluations in the United States

1. Improved reliability approximation for genomic evaluations in the United States Abstr.617

2. Beltsville Agricultural Research Center Centennial • 1910-2010 Reliability (REL) • Measure of amount of information in an evaluation • Squared correlation between EBV and true breeding value • May be expressed as daughter equivalents (DE = k*Rel/(1-Rel), where k = variance ratio) • Diagonal element of inverse of coefficient matrix • Approximation used when computing inverse is too time consuming

3. Beltsville Agricultural Research Center Centennial • 1910-2010 Approximation of REL • Time to compute inverse increases cubically with number of genotyped animals • When inversion discontinued in 2009, all animals given same contribution from genomics • Genomic relationship (G) with predictor animals measures information contributed • REL of predictor animal evaluation used for weighting

4. Beltsville Agricultural Research Center Centennial • 1910-2010 Approximation procedure • Convert traditional reliability to DE • Remove contribution from parents • Convert back to reliability for weighting genomic relationship • Sum weighted relationships across predictor animals (∑Gw). Similar to genomic future inbreeding

5. Beltsville Agricultural Research Center Centennial • 1910-2010 Conversion of ∑Gw to reliability • August 2009 reliabilities from inverse converted to DE and genomic contribution (DEg) extracted • DEg predicted from ∑Gw for 3 Holstein groups • 8,353 bulls with traditional evaluations • 3,559 cows with traditional evaluations • 16,135 animals without traditional evaluations

6. Beltsville Agricultural Research Center Centennial • 1910-2010 Conversion of ∑Gw(continued) • Straight line fit well except for low∑Gw • Floor set at 30 DEg • Slopes and floor differ by breed • Applicable across traits because same k used to calculate DEg

7. Beltsville Agricultural Research Center Centennial • 1910-2010 Coefficients to predict DEg *Traditional evaluation **No traditional evaluation

8. Beltsville Agricultural Research Center Centennial • 1910-2010 Genotyped Holsteins *Traditional evaluation **No traditional evaluation

9. 5000 4500 4000 Beltsville Agricultural Research Center Centennial • 1910-2010 3500 3000 Bulls (no.) 2500 2000 1500 1000 500 0 60 61 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 REL (%) for mlk yield REL for 18,187 young Holstein bulls

10. Beltsville Agricultural Research Center Centennial • 1910-2010 REL (%) for Holsteins born ≥2005 *Traditional evaluation **No traditional evaluation

11. G matrix • Computing time increases by (number of SNP)*(number of genotyped animals)2 • Options for calculating genomic relationships • Get faster computer • Run program in parallel • Compute relationships before evaluations • Calculate only for new animals; store old ones • Calculate based only on SNP from 3K chip • Use Eigenvalues & Eigenvectors to reduce processing • If G used to calculate EBV greater precision needed

12. Beltsville Agricultural Research Center Centennial • 1910-2010 Genotype quality and reliability • Problems – greater with imputation • Missing genotypes • Genotype incorrect • Remedies • Discount for missing SNP genotypes • Consider if parents were genotyped • Discount uniformly for 3K chip

13. Beltsville Agricultural Research Center Centennial • 1910-2010 Implementation of 3K chip • Chip expected to ship this week • 2,882 usable SNP, plus 14 on Y Chromosome • Unofficial evaluations expected Sept. 7 • Large initial use expected • New genotyping laboratories

14. Beltsville Agricultural Research Center Centennial • 1910-2010 Conclusions • Improved REL approximation implemented April 2010 • REL reduced for animals less related to predictor population • MN control-line bulls • Foreign bulls • Approximation relies on G matrix • Modification planned to account for loss in accuracy from imputation

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