Software for Incorporating Marker Data in Genetic Evaluations

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Software for Incorporating Marker Data in Genetic
Evaluations

• Kathy Hanford
• U.S. Meat Animal Research Center
• Agricultural Research Service
• U.S. Department of Agriculture

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Outline

• Introduction
• Mixed Models Incorporating Random QTL Effects
• Current/Future Modification to MTDFREMLQ
• Practical Limitations of MTDFREMLQ
• Applications

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Introduction

• Genetic evaluation
• genetic improvement of quantitative traits
  through selection
• currently use polygenic model
• genes at many loci each with a small effect
• measure the cumulative effect
• analysis with mixed models software available
• add genomic information

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Introduction

• Two phases in application of genomic data to
  livestock improvement

1) Statistical analysis of genomic information to
determine the potential importance of that
information (i.e. use of genetic markers to
quantify the effects of QTL on traits of economic
importance) 2) Include marker information in the
genetic evaluation of potential parents to
determine which will have the best progeny
(Marker Assisted Selection)
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Introduction

• QTL Identification
• methods needed for outbred populations
• daughter and granddaughter designs
• many half-sib families with QTL effects being
  estimated for each half-sib family
• Fernando and Grossman
• works with the outbred population as a whole,
  using both pedigree and marker information. Need
  complete marker data
• other methods
• such as MCMC, primarily been used only in
  simulations

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Mixed Model Incorporating Random QTL Effects
v 2nx1 vector of QTL alleleic effects   (a
ivp ivm iu i, v ivp i,vm i )
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BLUP equations for Fernando and Grossman model
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Numerator Relationship Matrix (A)

• The probability that alleles are IBD
• Probability between two half sibs is .25
• Need the inverse of A
• depends on pedigree information
• Computed directly (Henderson, 1976)
• Relatively few nonzero elements (sparse)

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Gametic (QTL) Correlation Matrix (M)

• The probability that alleles are IBD
• Need the inverse of M
• depends on pedigree information
• depends on probabilities QTL alleles are IBD
• Computed directly if complete marker information
  (Abdel-Azim and Freeman, 2001)

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Practical Issues in Calculating the QTL
Correlation Matrix

• Outbred population
• Sparse marker information
• Individuals with missing or incomplete marker
  data
• Some of which will be incorrect
• Large complex pedigrees (inbreeding and loops)

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Complex Pedigree
A
B
A1A2
??
D
C
A1A2

• Software
• MCMC
• LOKI
• DET
• Pong-Wong,et al.
• Allelic Peeling
• GenoProb

E
A1A2
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Size Considerations

• Each additional QTL increases the number of
  equations by 2 times the number of animals in the
  pedigree
• Sparse matrix storage
• Only store nonzero elements
• Polygenic (A-1) grows by 4 times the number of
  animals
• Gametic (M-1) grows by 15 times the number of
  animals

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MTDFREML

• Multiple Trait Derivative-free Restricted (or
  residual) Maximum Likelihood
• A set of programs to obtain estimates of
  variances and covariances
• USDA/ARS Dale Van Vleck
• Keith Boldman, Lisa Kriese, Curt Van Tassell,
  Steve Kachman, Joerg Dodenhoff

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MTDFREML

• MTDFNRM Calculate and output the inverse of the
  numerator relationship matrix
• MTDFPREP Set up the model for the analysis
• MTDFRUN Run the analysis using the files
  produced by MTDFNRM and MTDFPREP to obtain
  (co)variance estimates and breeding values

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Current Modifications to MTDFREML to Incorporate
QTL effects (MTDFREMLQ)

• MTDFNRMQ modified to calculate inverse of QTL
  correlation matrix (M-1) from IBD probability
  file (produced by Genoprob, Loki, etc)
• Non-inbred pedigree when marker data are
  incomplete
• Inbred pedigree when marker data are complete
• Genetic groups arising from different populations
  with different prior selection

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Current Modifications to MTDFREMLQ (cont.)

• MTDFPRPQ modified to include multiple QTL in
  the model (validated for single QTL)
• Multiple trait
• Gametic imprinting (coded, not validated)

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Current Modifications to MTDFREMLQ (cont.)

• MTDFRUNQ modified to include M-1 and associated
  between trait (co)variances for each QTL (V-1)
• Assumes independence between two QTLs

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Further Modifications to MTDFREMLQ

• Include inbred pedigree when marker data are
  incomplete (approximate M-1)
• Calculate standard errors for the parameters
  using the delta method
• Currently in MTDFREML
• In the testing/debugging stage
• appears to work for single-trait, single-QTL and
  two-trait, single-QTL cases.
• still need to test for multiple-QTL

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Practical Limitations of MTDFREMLQ

• Memory Limitations/animal/traits/qtl

50,000 1Trait 2 Traits 3 Traits 4 Traits
1 qtl lt268M 324M 778M 1.6G
2 qtls lt268M 552M 1.5G
3 qtls lt268M 919M
4 qtls 314M 1.4G
5 qtls 430M
100,000 1 Trait 2 Traits
1 qtl lt268M 562M
2 qtls lt268M 1.0G
3 qtls 376M
4 qtls 542M
5 qtls 775M
20,000 3 Traits 4 Traits 5 Traits
1 qtl 362M 698M 1.2G
2 qtls 642M 1.3G
3 qtls 1.1G
?Time Limitations
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Applications

• QTL detection
• Find and utilize QTL in a breed and include that
  information in national genetic evaluation.
• Marker Assisted Selection
• Experimental herds
• The twinning herd at MARC
• Currently producing about 50 twin calving
  compared to a normal range of 1-3
• 6000 in genetic evaluation, marker data from
  1994 on over 3000 animals in regions of 3 QTLs

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