Computation of Large-Scale Genomic Evaluations

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

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

Benefits of 1-step genomic evaluation
Account for genomic pre-selection
Expected Mendelian Sampling ≠ 0
Improve accuracy and reduce bias
Include many genotyped animals
Redesign animal model software used since 1989
Single-step genomic evaluation

Pedigree: Parents, Grandparents, etc.

O-Style Haplotypes
chromosome 15

Expected Relationship Matrix1
1Calculated assuming that all grandparents are unrelated
1HO9167 O-Style

Pedigree Relationship Matrix
1HO9167 O-Style

Genomic Relationship Matrix
1HO9167 O-Style

Difference (Genomic – Pedigree)
1HO9167 O-Style

Pseudocolor Plots ― O-Style

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
b
u
=
X’ R-1 y
W’ R-1 y
H-1 = A-1 +
0 0
0 G-1 – A22-1
Size of G and A22 >300,000 and doubling each year
Size of A is 60 million animals
1 – Step Equations
Aguilar et al., 2010

X’R-1X X’R-1W 0 0
W’R-1X W’R-1W+A-1k Q Q
0 Q’ -G/k 0
0 Q’ 0 A22/k
To avoid inverses, add equations for γ, φ
Use math opposite of absorbing effects
b
u
γ
φ
=
X’ R-1 y
W’ R-1 y
0
0
Iterate for γ using G = Z Z’ / [ 2 Σp(1-p)]
Iterate for φ using A22 multiply (Colleau)
Q’ = [ 0 I ] (I for genotyped animals)
Legarra and Ducrocq, 2011
Modified 1-Step Equations

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-1u, Gγ, -A22φ blocks? NO
PCG iteration (hard to debug) Maybe
Genomic Algorithms Tested

Multi-step insertion of GEBV
[W’R-1W + A-1k] u = W’R-1y (without G)
Previous studies added genomic information to W’R-1W and W’R-1y
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)

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

Jersey Results
New = 1-step GPTA milk, Old = multi-step GPTA milk

Multi-step regressions also improved by modified selection index weights
Data cutoff in August 2008
1-Step vs Multi-Step: Results

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

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

Steps to prepare genotypes
Nominate animal for genotyping
Collect blood, hair, semen, nasal swab, or ear punch
Blood may not be suitable for twins
Extract DNA at laboratory
Prepare DNA and apply to BeadChip
Do amplification and hybridization, 3-day process
Read red/green intensities from chip and call genotypes from clusters

Ancestor Validation and Discovery
Ancestor discovery can accurately confirm, correct, or discover parents and more distant ancestors for most dairy animals because most sires are genotyped.
Animal checked against all candidates
SNP test and haplotype test both used
Parents and MGS are suggested to breed associations and breeders since December 2011 to improve pedigrees.

Ancestor Discovery Results by Breed
*Confirmation = top MGS candidate matched true pedigree MGS.
†50K genotyped animals only.

One step model includes:
72 million lactation phenotypes
50 million animals in pedigree
29 million permanent environment
7 million herd mgmt groups
11 million herd by sire interactions
7 traits: Milk, Fat, Protein, SCS, longevity, fertility
Genotypes not yet included
Data (Yield and Health)

Model options now include:
Multi-trait models
Multiple class and regress variables
Suppress some factors / each trait
Random regressions
Foreign data
Parallel processing
Genomic information
Renumber factors in same program
New Features Added

CPU for all-breed model (7 traits)
ST: 4 min / round with 7 processors and ~1000 rounds (2.8 days)
MT: 15 min / round and ~1000 rounds
~200 rounds for updates using priors
Little extra cost to include foreign
Memory required
ST or MT: 32 Gbytes (256 available)
Computation Required: Evaluation

Impute 636,967 markers for 103,070 animals
Required 10 hours with 6 processors (findhap)
Required 50 Gbytes memory
Program FImpute from U. Guelph slightly better
Impute 1 million markers on 1 chromosome (sequences) for 1,000 animals
Required 15 minutes with 6 processors
Required 4 Gbytes memory
Computation Required: Imputation

Methods to Trace Inheritance
Few markers
Pedigree needed
Prob (paternal or maternal alleles inherited) computed within families
Many markers
Can find matching DNA segments without pedigree
Prob (haplotypes are identical) mostly near 0 or 1 if segments contain many markers

with Few Markers (12 SNP / chromosome)
Haplotype Probabilities

with More Markers (50 SNP / chromosome)
Haplotype Probabilities

Haplotyping Program: findhap.f90
Population haplotyping
Divide chromosomes into segments
List haplotypes by genotype match
Similar to FastPhase, IMPUTE, or long range phasing
Pedigree haplotyping
Look up parent or grandparent haplotypes
Detect crossovers, fix noninheritance
Impute nongenotyped ancestors

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

Population Haplotyping Steps
Put first genotype into haplotype list
Check next genotype against list
Do any homozygous loci conflict?
If haplotype conflicts, continue search
If match, fill any unknown SNP with homozygote
2nd haplotype = genotype minus 1st haplotype
Search for 2nd haplotype in rest of list
If no match in list, add to end of list
Sort list to put frequent haplotypes 1st

Check New Genotype Against List
1st segment of chromosome 15
5.16% 022222222020020022002020200020000200202000022022222202220
4.37% 022020220202200020022022200002200200200000200222200002202
4.36% 022020022202200200022020220000220202200002200222200202220
3.67% 022020222020222002022022202020000202220000200002020002002
3.66% 022222222020222022020200220000020222202000002020220002022
Get 2nd haplotype by removing 1st from genotype:
022002222002220022022020220020200202202000202020020002020
Search for 1st haplotype that matches genotype:
022112222011221022021110220010110212202000102020120002021
3.65% 022020022202200200022020220000220202200002200222200202222
3.51% 022002222020222022022020220200222002200000002022220002220
3.42% 022002222002220022022020220020200202202000202020020002020
3.24% 022222222020200000022020220020200202202000202020020002020
3.22% 022002222002220022002020002220000202200000202022020202220

Net Merit by Chromosome
Freddie - highest Net Merit bull

Net Merit by Chromosome
O Man – Sire of Freddie

Net Merit by Chromosome
Die-Hard - maternal grandsire

Net Merit by Chromosome
Planet – high Net Merit bull

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

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

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