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 Predict April 2008 PTA from August 2003 PTA
 3,576 older Holstein bulls
 1,759 younger bulls (total = 5,335)
 Using 38,416 SNP from Illumina Bovine SNP50^{TM} Chip

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 Compare genomic to traditional relationships and inbreeding
 Formulas to compute G and A
 G – A differences for 5,335 bulls
 Compare genomic predictions using different estimates of frequency
 Estimate 38,416 allele frequencies
 Simple estimates vs. base population
 Or ignore frequency, use 0.5 instead

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 Detected clones, identical twins, and duplicate samples
 Detected incorrect DNA samples
 Detected incorrect pedigrees
 Identified correct source of DNA by genomic relationships with other
animals

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 Sum products of genotypes (g) adjusted for allele frequency (p)
 G1_{jk} = ∑ (g_{ij}p_{i}) (g_{ik}p_{i})
/ [2 ∑ p_{i}(1p_{i})]
 Or individually weighted by p
 G2_{jk} = ∑ (g_{ij}p_{i}) (g_{ik}p_{i})
/ 2p_{i}(1p_{i})
 Or scaled by intercept (b_{0}) and regression (b_{1}) on
A, using p = 0.5
 G3_{jk} = [∑ (g_{ij}  0.5) (g_{ik}  0.5) – b_{0}]
/ b_{1}

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 Correlations ranked G3 > G1 > G2 in simulation vs. G2 > G1 >
G3 with real data (opposite)
 G2 and G1 biased down, G3 up
 G1 and G2 can be adjusted toward A using b_{0} and b_{1},
similar to G3 formula
 After adjusting, mean G1 = 1.08 and G2 = 1.09 compared to G3 = 1.13 and
A = 1.05
 G1 was unbiased in simulation using true rather than estimated
frequencies

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 Base population frequencies
 Combine genotypes and pedigrees
 Efficient algorithm (Gengler, 2007)
 Simple frequency estimates
 Extra simple estimates (p = 0.5)
 Z = 0.5, 0, 0.5 in mixed model

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 Genomic relationships and inbreeding are more useful than Wright’s 1922
pedigree formulas
 Formulas to compute G have
 Large effects on inbreeding coefficients
 Small effects on reliability of predictions
 Estimates of allele frequencies
 For base population better than simple
 Not needed using regression of G on A

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 Funding:
 National Research Initiative grants
 CDDR Contributors (NAAB, Semex)
 Genotyping and DNA extraction:
 BFGL, U. Missouri, U. Alberta, GeneSeek, GIFV, and Illumina
 Computing from AIPL staff
 George Wiggans, Leigh Walton
