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2007 Paul VanRaden Animal Improvement Programs Lab, Beltsville, MD Iterative combination of national phenotype, genotype, pedigree,

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Presentation on theme: "2007 Paul VanRaden Animal Improvement Programs Lab, Beltsville, MD Iterative combination of national phenotype, genotype, pedigree,"— Presentation transcript:

1 2007 Paul VanRaden Animal Improvement Programs Lab, Beltsville, MD Paul.VanRaden@ars.usda.gov Iterative combination of national phenotype, genotype, pedigree, and foreign information

2 FASS joint annual meeting, Phoenix, AZ, July 2012 (2) Paul VanRaden 2012  Develop 1-step genomic evaluation Account for genomic pre-selection Expected Mendelian Sampling ≠ 0 Improve accuracy and reduce bias Include many genotyped animals  Redesign software used since 1989 (see Mel Tooker’s talk) Goals

3 FASS joint annual meeting, Phoenix, AZ, July 2012 (3) Paul VanRaden 2012 1-Step Equations Aguilar et al., 2010 X’ R -1 X X’ R -1 W W’ R -1 X W’ R -1 W + H -1 k Model: y = X b + W u + e + other random effects not shown bubu = X’ R -1 y W’ R -1 y H -1 = A -1 + 0 0 G -1 – A 22 -1 Size of G and A 22 >200,000 and doubling each year

4 FASS joint annual meeting, Phoenix, AZ, July 2012 (4) Paul VanRaden 2012 Modified 1-Step Equations Legarra and Ducrocq, 2011 X’R -1 X X’R -1 W 0 0 W’R -1 X W’R -1 W+A -1 k Q Q 0 Q’ -G/k 0 0 Q’ 0 A 22 /k To avoid inverses, add equations for γ, φ Use math opposite of absorbing effects buγφbuγφ = X’ R -1 y W’ R -1 y 0 Iterate for γ using G = Z Z’ / [ 2 Σp(1-p)] Iterate for φ using A 22 multiply (Colleau) Q’ = [ 0 I ] (I for genotyped animals)

5 FASS joint annual meeting, Phoenix, AZ, July 2012 (5) Paul VanRaden 2012  1-step genomic model Add extra equations for γ and φ (Legarra and Ducrocq) Converged ok for JE, bad for HO Extended to MT using block diagonal Invert 3x3 A -1 u, Gγ, -A 22 φ blocks? NO PCG iteration (hard to debug) Maybe Genomic Algorithms Tested

6 FASS joint annual meeting, Phoenix, AZ, July 2012 (6) Paul VanRaden 2012  Multi-step insertion of GEBV [W’R -1 W + A -1 k] u = W’R -1 y (without G) Previous studies added genomic information to W’R -1 W and W’R -1 y Instead: insert GEBV into u, iterate  1-step genomic model using DYD Solve SNP equations from DYD & YD May converge faster, but approximate Genomic Algorithms (continued)

7 FASS joint annual meeting, Phoenix, AZ, July 2012 (7) Paul VanRaden 2012  National U.S. Jersey data 4.4 million lactation phenotypes 4.1 million animals in pedigree Multi-trait milk, fat, protein yields 5,364 male, 11,488 female genotypes  Deregressed MACE evaluations for 7,072 bulls with foreign daughters (foreign dams not yet included) Data for 1-Step Test

8 FASS joint annual meeting, Phoenix, AZ, July 2012 (8) Paul VanRaden 2012 Jersey Results New = 1-step GPTA milk, Old = multi-step GPTA milk StatisticAnimals Corr(New, Old)All bulls0.994 Corr(New, Old)Genotyped bulls0.992 Corr(DYD g, DYD)Genotyped bulls0.999 Corr(New, Old)Young genomic0.966 SD old PTA milkYoung genomic540 SD new PTA milkYoung genomic552 Old milk trend1995-2005 cows1644 New milk trend1995-2005 cows1430

9 FASS joint annual meeting, Phoenix, AZ, July 2012 (9) Paul VanRaden 2012 EvaluationRegression Squared Correlation Parent Average.73.436 Multi-Step GPTA.75.520 1-Step GPTA.85.520 Expected.93 1-Step vs Multi-Step: Results Data cutoff in August 2008 Multi-step regressions also improved by modified selection index weights (Jan Wright’s poster)

10 FASS joint annual meeting, Phoenix, AZ, July 2012 (10) Paul VanRaden 2012  CPU time for 3 trait ST model JE took 11 sec / round including G HO took 1.6 min / round including G JE needed ~1000 rounds (3 hours) HO needed >5000 rounds (>5 days)  Memory required for HO 30 Gigabytes (256 available) Computation Required

11 FASS joint annual meeting, Phoenix, AZ, July 2012 (11) Paul VanRaden 2012  Difficult to match G and A across breeds  Nonlinear model (Bayes A) possible with SNP effect algorithm  Interbull validation not designed for genomic models  MACE results may become biased Remaining Issues

12 FASS joint annual meeting, Phoenix, AZ, July 2012 (12) Paul VanRaden 2012 Conclusions  1-step genomic evaluations tested Inversion avoided using extra equations Converged well for JE but not for HO Same accuracy, less bias than multi- step Foreign data from MACE included  Further work needed on algorithms Including genomic information Extending to all-breed evaluation

13 FASS joint annual meeting, Phoenix, AZ, July 2012 (13) Paul VanRaden 2012  George Wiggans, Ignacy Misztal, and Andres Legara provided advice on algorithms  Mel Tooker assisted with computation and program design  Members of the Council on Dairy Cattle Breeding provided data Acknowledgments

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