Paul VanRaden Animal Improvement Programs Laboratory Agricultural Research Service, USDA Beltsville, MD 2013 Paul VanRaden University of Maryland Animal Science seminar (1) Computation of Large-Scale Genomic Evaluations

Paul VanRaden 2013 University of Maryland Animal Science seminar (2) Early genomic theory l Nejati-Javaremi et al (1997) tested use of genomic relationship matrix in BLUP l Meuwissen et al (2001) tested linear and nonlinear estimation of haplotype effects l Both studies assumed that few (<1,000) markers could explain all genetic variance (no polygenic effects in model) l Polygenic variance was only 5% with 50,000 SNP (VanRaden, 2008), but 50% with 1,000

Paul VanRaden 2013 University of Maryland Animal Science seminar (3) Multi-step genomic evaluations l Traditional evaluations computed first and used as input data to genomic equations l Allele effects estimated for 45,187 markers by multiple regression, assuming equal prior variance l Polygenic effect estimated for genetic variation not captured by markers, assuming pedigree covariance l Selection index step combines genomic info with traditional info from non-genotyped parents l Applied to 30 yield, fitness, calving and type traits

Paul VanRaden 2013 University of Maryland Animal Science seminar (4) l Benefits of 1-step genomic evaluation w Account for genomic pre-selection w Expected Mendelian Sampling ≠ 0 w Improve accuracy and reduce bias w Include many genotyped animals l Redesign animal model software used since 1989 Single-step genomic evaluation

Paul VanRaden 2013 University of Maryland Animal Science seminar (5) Pedigree: Parents, Grandparents, etc. Manfred O-Man Jezebel O-Style Teamster Deva Dima

Paul VanRaden 2013 University of Maryland Animal Science seminar (6) O-Style Haplotypes chromosome 15

Paul VanRaden 2013 University of Maryland Animal Science seminar (7) Expected Relationship Matrix 1 PGSPGDMGSMGDSireDamBull Manfred Jezebel Teamster Dima O-Man Deva O-Style Calculated assuming that all grandparents are unrelated 1HO9167 O-Style

Paul VanRaden 2013 University of Maryland Animal Science seminar (8) Pedigree Relationship Matrix PGSPGDMGSMGDSireDamBull Manfred Jezebel Teamster Dima O-Man Deva O-Style HO9167 O-Style

Paul VanRaden 2013 University of Maryland Animal Science seminar (9) Genomic Relationship Matrix PGSPGDMGSMGDSireDamBull Manfred Jezebel Teamster Dima O-Man Deva O-Style HO9167 O-Style

Paul VanRaden 2013 University of Maryland Animal Science seminar (10) Difference (Genomic – Pedigree) PGSPGDMGSMGDSireDamBull Manfred Jezebel Teamster Dima O-Man Deva O-Style HO9167 O-Style

Paul VanRaden 2013 University of Maryland Animal Science seminar (11) Pseudocolor Plots ― O-Style

Paul VanRaden 2013 University of Maryland Animal Science seminar (12) 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 >300,000 and doubling each year Size of A is 60 million animals 1 – Step Equations Aguilar et al., 2010

Paul VanRaden 2013 University of Maryland Animal Science seminar (13) 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) Legarra and Ducrocq, 2011 Modified 1-Step Equations

Paul VanRaden 2013 University of Maryland Animal Science seminar (14) l 1-step genomic model w Add extra equations for γ and φ (Legarra and Ducrocq) w Converged ok for JE, bad for HO w Extended to MT using block diagonal w Invert 3x3 A -1 u, G γ, -A 22 φ blocks? NO w PCG iteration (hard to debug) Maybe Genomic Algorithms Tested

Paul VanRaden 2013 University of Maryland Animal Science seminar (15) l Multi-step insertion of GEBV w [W’R -1 W + A -1 k] u = W’R -1 y (without G) w Previous studies added genomic information to W’R -1 W and W’R -1 y w Instead: insert GEBV into u, iterate l 1-step genomic model using DYD w Solve SNP equations from DYD & YD w May converge faster, but approximate Genomic Algorithms (continued)

Paul VanRaden 2013 University of Maryland Animal Science seminar (16) l National U.S. Jersey data w 4.4 million lactation phenotypes w 4.1 million animals in pedigree w Multi-trait milk, fat, protein yields w 5,364 male, 11,488 female genotypes l Deregressed MACE evaluations for 7,072 bulls with foreign daughters (foreign dams not yet included) Data for 1-Step Test

Paul VanRaden 2013 University of Maryland Animal Science seminar (17) 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

Paul VanRaden 2013 University of Maryland Animal Science seminar (18) EvaluationRegression Squared Correlation Parent Average Multi-Step GPTA Step GPTA Expected.93 Multi-step regressions also improved by modified selection index weights Data cutoff in August Step vs Multi-Step: Results

Paul VanRaden 2013 University of Maryland Animal Science seminar (19) l CPU time for 3 trait ST model w JE took 11 sec / round including G w HO took 1.6 min / round including G w JE needed ~1000 rounds (3 hours) w HO needed >5000 rounds (>5 days) l Memory required for HO w 30 Gigabytes (256 available) Computation Required

Paul VanRaden 2013 University of Maryland Animal Science seminar (20) l Difficult to match G and A across breeds l Nonlinear model (Bayes A) possible with SNP effect algorithm l Interbull validation not designed for genomic models l MACE results may become biased Remaining Issues

Paul VanRaden 2013 University of Maryland Animal Science seminar (21) Steps to prepare genotypes l Nominate animal for genotyping l Collect blood, hair, semen, nasal swab, or ear punch w Blood may not be suitable for twins l Extract DNA at laboratory l Prepare DNA and apply to BeadChip l Do amplification and hybridization, 3-day process l Read red/green intensities from chip and call genotypes from clusters

Paul VanRaden 2013 University of Maryland Animal Science seminar (22) Ancestor Validation and Discovery l Ancestor discovery can accurately confirm, correct, or discover parents and more distant ancestors for most dairy animals because most sires are genotyped. l Animal checked against all candidates l SNP test and haplotype test both used l Parents and MGS are suggested to breed associations and breeders since December 2011 to improve pedigrees.

Paul VanRaden 2013 University of Maryland Animal Science seminar (23) Ancestor Discovery Results by Breed SNP TestHaplotype Test MGS MGGS Breed% Confirmed * % Confirmed Holstein95 (98) † 9792 Jersey91 (92)95 Brown Swiss94 (95)9785 *Confirmation = top MGS candidate matched true pedigree MGS. † 50K genotyped animals only.

Paul VanRaden 2013 University of Maryland Animal Science seminar (24) l One step model includes: w 72 million lactation phenotypes w 50 million animals in pedigree w 29 million permanent environment w 7 million herd mgmt groups w 11 million herd by sire interactions w 7 traits: Milk, Fat, Protein, SCS, longevity, fertility w Genotypes not yet included Data (Yield and Health)

Paul VanRaden 2013 University of Maryland Animal Science seminar (25) l Model options now include: w Multi-trait models w Multiple class and regress variables w Suppress some factors / each trait w Random regressions w Foreign data w Parallel processing w Genomic information l Renumber factors in same program New Features Added

Paul VanRaden 2013 University of Maryland Animal Science seminar (26) l CPU for all-breed model (7 traits) w ST: 4 min / round with 7 processors and ~1000 rounds (2.8 days) w MT: 15 min / round and ~1000 rounds w ~200 rounds for updates using priors w Little extra cost to include foreign l Memory required w ST or MT: 32 Gbytes (256 available) Computation Required: Evaluation

Paul VanRaden 2013 University of Maryland Animal Science seminar (27) l Impute 636,967 markers for 103,070 animals w Required 10 hours with 6 processors (findhap) w Required 50 Gbytes memory w Program FImpute from U. Guelph slightly better l Impute 1 million markers on 1 chromosome (sequences) for 1,000 animals w Required 15 minutes with 6 processors w Required 4 Gbytes memory Computation Required: Imputation

Paul VanRaden 2013 University of Maryland Animal Science seminar (28) Methods to Trace Inheritance l Few markers w Pedigree needed w Prob (paternal or maternal alleles inherited) computed within families l Many markers w Can find matching DNA segments without pedigree w Prob (haplotypes are identical) mostly near 0 or 1 if segments contain many markers

Paul VanRaden 2013 University of Maryland Animal Science seminar (29) with Few Markers (12 SNP / chromosome) Haplotype Probabilities

Paul VanRaden 2013 University of Maryland Animal Science seminar (30) with More Markers (50 SNP / chromosome) Haplotype Probabilities

Paul VanRaden 2013 University of Maryland Animal Science seminar (31) Haplotyping Program: findhap.f90 l Population haplotyping w Divide chromosomes into segments w List haplotypes by genotype match w Similar to FastPhase, IMPUTE, or long range phasing l Pedigree haplotyping w Look up parent or grandparent haplotypes w Detect crossovers, fix noninheritance w Impute nongenotyped ancestors

Paul VanRaden 2013 University of Maryland Animal Science seminar (32) Coding of Alleles and Segments l Genotypes w 0 = BB, 1 = AB or BA, 2 = AA, 5 = __ (missing) w Allele frequency used for missing l Haplotypes w 0 = B, 1 = not known, 2 = A l Segment inheritance (example) w Son has haplotype numbers 5 and 8 w Sire has haplotype numbers 8 and 21 w Son got haplotype number 5 from dam

Paul VanRaden 2013 University of Maryland Animal Science seminar (33) Population Haplotyping Steps l Put first genotype into haplotype list l Check next genotype against list w Do any homozygous loci conflict? − If haplotype conflicts, continue search − If match, fill any unknown SNP with homozygote − 2 nd haplotype = genotype minus 1 st haplotype − Search for 2 nd haplotype in rest of list w If no match in list, add to end of list l Sort list to put frequent haplotypes 1st

Paul VanRaden 2013 University of Maryland Animal Science seminar (34) Check New Genotype Against List 1st segment of chromosome % % % % % Get 2 nd haplotype by removing 1 st from genotype: Search for 1 st haplotype that matches genotype: % % % % %

Paul VanRaden 2013 University of Maryland Animal Science seminar (35) Net Merit by Chromosome Freddie - highest Net Merit bull

Paul VanRaden 2013 University of Maryland Animal Science seminar (36) Net Merit by Chromosome O Man – Sire of Freddie

Paul VanRaden 2013 University of Maryland Animal Science seminar (37) Net Merit by Chromosome Die-Hard - maternal grandsire

Paul VanRaden 2013 University of Maryland Animal Science seminar (38) Net Merit by Chromosome Planet – high Net Merit bull

Paul VanRaden 2013 University of Maryland Animal Science seminar (39) What’s the best cow we can make? A “Supercow” constructed from the best haplotypes in the Holstein population would have an EBV(NM$) of $7515

Paul VanRaden 2013 University of Maryland Animal Science seminar (40) Conclusions l 1-step genomic evaluations tested w Inversion avoided using extra equations w Converged well for JE but not for HO w Same accuracy, less bias than multi-step w Foreign data from MACE included l Further work needed on algorithms w Including genomic information w Extending to all-breed evaluation

Paul VanRaden 2013 University of Maryland Animal Science seminar (41) Conclusions l Foreign data can add to national evaluations w In one step model instead of post-process w High correlations of national with MACE l Multi-trait all-breed model developed w Replace software used since 1989 w Many new features added w Correlations ~.99 with traditional AM w Tested with 7 yield and health traits w Also tested with 14 JE conformation traits

Paul VanRaden 2013 University of Maryland Animal Science seminar (42) l George Wiggans, Ignacy Misztal, and Andres Legara provided advice on algorithms l Mel Tooker, Tabatha Cooper, and Jan Wright assisted with computation, program design, and ancestor discovery l Members of the Council on Dairy Cattle Breeding provided data Acknowledgments