G.R. Wiggans* and P.M. VanRadenAnimal Improvement Programs LaboratoryAgricultural Research Service, USDA Beltsville, MD*george.wiggans@ars.usda.gov

G.R. WiggansADSA 2010 (1)

Improved reliability approximation for genomic evaluations in the United States

Abstr.617

G.R. WiggansADSA 2010 (2)

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

G.R. WiggansADSA 2010 (3)

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

G.R. WiggansADSA 2010 (4)

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

G.R. WiggansADSA 2010 (5)

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

G.R. WiggansADSA 2010 (6)

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

G.R. WiggansADSA 2010 (7)

Coefficients to predict DEg

Breed Floor  Bulls* Cows* 

Young   animals*

*HolsteinJersey

20 0.058 0.056   0.051  10 0.088 0.086   0.072  

Brown Swiss   6 0.122 0.122   0.085    *Traditional evaluation

**No traditional evaluation

G.R. WiggansADSA 2010 (8)

Genotyped Holsteins

Date

Young animals**

All animal

sBulls* Cows*  Bulls     Heifers 

04-09 7,600  2,711     9,690       1,943 21,94401-10 8,974  4,348   14,061      6,031 33,41402-10 9,378  5,086   15,328      7,620 37,41204-10 9,770  7,415   16,007      8,630 41,82205-10 9,958  7,940   16,594      9,772 44,26406-10 9,958  8,122   17,507    10,713 46,30007-10 9,963  8,186   18,187    11,309 47,645  *Traditional evaluation

**No traditional evaluation

G.R. WiggansADSA 2010 (9)

REL for 18,187 young Holstein bulls

0500

100015002000250030003500400045005000

60616465666768697071727374757677787980

REL (%) for mlk yield

Bulls

(no

.)

G.R. WiggansADSA 2010 (10)

REL (%) for Holsteins born ≥2005Trait

Young animals**

Bulls* Cows*    Bulls     HeifersMilk 87  80    76    76Protein 87  79    76    76Productive life 72  68    65    64Somatic cell score 80  74    71    71Daughter pregnancy rate

68  65    62    62

PTA type 79  74    70    70Service-sire calving ease

82  71    72    70

Daughter calving ease 74  68    67    66Service-sire stillbirth 66  60    59    58Daughter stillbirth 67  62    59    59Net merit 79  73    70    70Animals, n 1,262  4,487    18,117   

 11,171

  *Traditional evaluation**No traditional evaluation

G.R. WiggansADSA 2010 (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

G.R. WiggansADSA 2010 (12)

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

G.R. WiggansADSA 2010 (13)

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

G.R. WiggansADSA 2010 (14)

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

G.R. WiggansADSA 2010 (15)

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