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

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Presentation transcript:

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

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

FASS joint annual meeting, Phoenix, AZ, July 2012 (3) Paul VanRaden 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 G -1 – A Size of G and A 22 >200,000 and doubling each year

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)

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

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)

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

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 trend cows1644 New milk trend cows1430

FASS joint annual meeting, Phoenix, AZ, July 2012 (9) Paul VanRaden 2012 EvaluationRegression Squared Correlation Parent Average Multi-Step GPTA Step GPTA 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)

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

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

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

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