Large-scale single-step genomic evaluation for milk production traits

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Large-scale single-step genomic evaluation for
milk production traits

• B. L. Harris, A. M. Winkelman and D. L.
  JohnsonJune 2012

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Introduction
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• The single-step method simultaneously uses
  phenotypic, genomic and relationship information
• The pedigree-based relationship matrix is
  augmented by a genomic relationship matrix
• The scale of the augmented relationship matrix is
  adjusted to control the inflation of the genomic
  breeding values
• The augmented relationship matrix is incorporated
  into the mixed model equations

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Introduction
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• Aim of this study was to assess the single-step
  method for national genetic evaluation of
  production traits in New Zealand
• Across-breed evaluation
• Random regression test-day model Order 3
  Legendre polynomials for additive genetic and
  permanent environment effects
• Multiple lactations included as separate traits
  4 traits for additive genetic and 6 traits for
  the permanent environment effects
• MME order was approximately 550 million equations

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Introduction
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• Across-breed evaluation requires the genomic
  relationship matrix (GRM) to account for multiple
  breeds and their crosses
• Across breed GRM
• Adjustments to the matrix based on effect of
  breed fractions on the allele frequencies,
  variances and means of the base populations
  relative to numerator relationship matrix
• Euclidean distance matrix in a Gauss Kernel (EDM)
• No adjustments required for breeds

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Methods
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• The effect of including genomic information was
  assessed by comparing traditional BVs with GBVs
• Traditional BVs were from the national genetic
  evaluation of May 2012 (end of the 2011 season)
• The GBVs were from a single-step model using data
  up to the end of the 2009 season
• 525 test sires with first crop daughters
  completing their first lactation in the 2010 and
  2011 seasons
• 251 HF, 104 HFxJ and 170 J sires

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Data
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• 172 Million test-day records
• 22.5 Million animals
• 52 Holstein Friesian
• 18 Jersey
• 29 Jersey Holstein Friesian crosses
• 5,402 Genotyped sires on Illumina 50k Bovine chip
  (38k SNPs)

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Methods
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• The inverse of the augmented relationship matrix
  was calculated aswhere G GRM or EDM and
  is the scale parameter
• The scale parameter was varied from 0.7 to 0.3
  for GRM and 0.9 to 0.5 for the EDM
• Scaling parameter choice based on prior research
  Harris et al., (2011)

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Computational Strategy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• Preconditioned conjugate gradient (PCG) solver
  with iteration on data and code reordering
• The matrix
  was pre-calculated
• Direct matrix inversion using Intel MKL library
• The PCG solver for the single step model was
  identical to the traditional model except for
  single routine which computes

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Results
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• Single-step models converged within 500
  iterations
• Iteration time approximately 2 minutes 36 seconds
• Genomics added 5 seconds per iteration
• Inflation of GBVs of the test sires regardless
  whether GRM or EDM was used in the augmented
  relationship matrix
• The degree of inflation varied by trait and breed
  of test sire

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Results Inflation for Fat Yield
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
GRM
0.7
0.5
0.3
EDM
0.9
0.7
0.5
0.7
0.5
0.3
0.9
0.7
0.5
0.7
0.5
0.3
0.9
0.7
0.5
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Results Accuracy for Protein Yield
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
GRM
0.7
0.5
0.3
EDM
0.9
0.7
0.5
0.7
0.5
0.3
0.9
0.7
0.5
0.7
0.5
0.3
0.9
0.7
0.5
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Results
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• For all traits and breed of sire, inflation
  increased as the scaling parameter increased
• In some cases the inflation estimates were gt 1
  for the HFxJ crossbred sires indicating deflation
• The largest differences between the GRM and EDM
  for inflation were observed for fat yield where
  lower levels of inflation was found using the EDM
• Augmenting the relationship matrix with the GRM
  versus the EDM and changing the magnitude of the
  scale parameters had little impact on the
  accuracy of the evaluation.

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Results
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• A single value of the scaling parameter across
  breeds is a compromise
• if the weighted, across-breed mean of the
  inflation factor was close to unity then
• one or more breed(s) would have inflated GBVs and
  the remaining one(s) would have deflated BVs
• The within-breed correlations between the GBVs of
  the training sires (GRM vs EDM), were greater
  than 0.997 for all traits across all scenarios
• The correlations bewteen the GBVs of the test
  sires (GRM vs EDM) ranged between 0.90 and 0.99

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Conclusions
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy
Genomic breeding values with 55 accuracy

• The single-step procedure outlined in this paper
  was computationally feasible for a complex
  genetic evaluation model with a large amount of
  data
• Augmentation of the relationship matrix with an
  EDM tended to result in lower levels of inflation
  of the GBVs than did the GRM.
• The choice of the optimal scale parameters will
  be more challenging in across-breed genomic
  evaluations compared to single-breed evaluations

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Questions
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