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 Nicolas Gengler^{1,2} & Paul VanRaden^{3}
 ^{1}Animal Science Unit, Gembloux Agricultural University,
Belgium
 ^{2}National Fund for Scientific Research (FNRS), Brussels,
Belgium
 ^{3}USDA Animal Improvement Programs Laboratory, Beltsville, MD

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 How to avoid any confusion in the mind of users?
 Do markets accept even more “blackbox”?
 How to create confidence?

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 Include data from other phenotyped relatives into the genotyped animals’
combined EBV, called hereafter “integration”
 Transfer information from genotyped to nongenotyped animals to allow
for them also computation of combined EBV,
called hereafter “propagation”

4

 Selection index to combine sources of information into a single set of
breeding values for genotyped animals
 Predict SNP gene content, then use it, alternatively predict genomic
breeding values than integrate these values using 1
 Integrate genomic breeding values as external information into genetic
evaluation using a Bayesian framework

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 Define three types of EBV (û_{1}, û_{2}, û_{3})
as components of information vector (û) by
 û_{1} = genomic EBV, known for genotyped animals, their data
being YD, DYD or DRP
 û_{2} = nongenomic EBV (PA), known for genotyped animals and
based on their data (YD, DYD, DRP)
 û_{3} = traditional EBV (PA) from national / intl. data
 Define combined EBV as û_{c}

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 Define needed variances and covariance as proportional to reliabilities
(R) and genetic variance:

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 Predicting û_{c} using standard SI
 Average SI coefficients (approximate)
 Intuitively eliminates double counting for PA
 Very similar to values obtained by multiple regression
 Achieves “Integration” (Goal 1)
 Solves doublecounting of PA for genotyped animals

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 Background
 SNP data only known for few animals
 First idea: propagation of gene content for all animals can be done
through out pedigree
 Conditional expectation of gene contents for SNP
for ungenotyped animals given molecular and pedigree
data
Gengler et al. JDS 2008 91: 1652 1659
 Leads directly to needed covariance structures combining genomic
relationship if known with pedigree relationships
 However basic idea can be extended easily
 Also presented here (Strategy 2b)

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 Predicted gene content for SNP can be used to predict individual genomic
EBV
 Leads directly to needed covariance structures combining genomic
relationship if known with pedigree relationships
 However method can also extended to predict directly individual genomic
EBV
 Also much simpler than estimating individual SNP gene contents

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 Equivalent BLUP model to predict û_{n}
 Solving of associated mixed model equations equivalent BLUP prediction
of û_{n}

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 Prediction of associated individual reliabilities for every û_{n }needed
 Transfers information from genotyped to nongenotyped animals,
achieves “Propagation” (Goal 2)
 To allow for nongenotyped animals also computation of combined EBV, use
of Method 1 (or other method) needed

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 Even by combining genomic EBV from Method 2 (including step from Method
1)
 Still not direct integration
 However Genomic EBV can also be considered external evaluation known a
priori for some animals
 Theory exists for Bayesian Integration as used in the beef genetic
evaluation systems

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 Following Legarra et al. (2007)
 Very similar to regular Mixed Model Equations, only two changes

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 Additional simplifications (assumptions) used :
 D = diagonal matrix whose elements proportional to REL and genetic
variance
 G_{gg} = diagonal matrix whose elements proportional to genetic
variance, represent maximum PEV
 Experience with Bayesian method
 Theory sound
 However strong assumptions
 Also practical experience finetuning needed

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 Strategy 1:
 Is used since April 2008 in the USA
 Achieves “Integration” (Goal 1)
 But does not propagate genomic EBV across the pedigree
 Strategy 2:
 Allows to propagate SNP gene content or even genomic EBV across the
pedigree (“Propagation”, Goal 2)
 Even if leads to combined genomic – pedigree relationships, their use
(inversion) not obvious with many animals
 Strategy 3:
 Achieves directly both “Integration” (Goal 1) and “Propagation” (Goal
2) because of modified Mixed Model Equations (relatives are also
affected, as are other effects in the model)
 Potentially a good compromise, also existing standard software can be
easily modified

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