Combination of genotype, pedigree, local and foreign information

(1)

Combination of genotype, pedigree,

local and foreign information

J. Vandenplas

1,2

_{, F.G. Colinet}

1

_{, N. Gengler}

1,*

1 _{University of Liège, Gembloux Agro‐Bio Tech, Belgium} 2 _{National Fund for Scientific Research, Brussels, Belgium} 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013

Introduction

For genomic prediction

To get reliable GEBV use of multiple sources needed

Traditional traits (i.e., in dairy cattle)

Local genomic evaluations  MACE

Novel traits

(e.g., milk quality, feed efficiency, methane) Combining different sources of often locally sparse phenotypic data even more needed 2 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013

 Adapting strategies to use multiple sources

Aims

To develop strategies to use simultaneously:

Genotypes, Pedigree, Local phenotypes and, Foreign phenotypes

By combining and adapting:

Single‐step genomic evaluations (ssGBLUP) and, Bayesian procedure to integrate external information* *Vandenplas, J., & Gengler, N. (2012). J. Dairy Sci. 95: 1513‐1526

Aims

To develop strategies to use simultaneously:

Genotypes, Pedigree, Phenotypes from multiple sources



_ssGBAYES

(2)

ssGBLUP

Single‐step genomic evaluation (ssGBLUP)

Allows direct combination of genomic, pedigree and phenotypic information

However: current limitation

Only available local phenotypic records can be used 5 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013

ssGBLUP

Single‐step genomic evaluation (ssGBLUP)

However: current limitation

Only available local phenotypic records can be used 6 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013

 In opposition to multi‐step methods

(e.g., use of local‐EBV and MACE‐EBV in prediction equation step)

ssGBLUP

Single‐step genomic evaluation (ssGBLUP)

However: current limitation

Only available local phenotypic records can be used

Reason for this limitation

Local ssGBLUP based on modified system of mixed model equations (MME) 7 64th_{annual EAAP Meeting, Nantes, France, August 26}th_{– 30}th₂₀₁₃

Modified MME

ssGBLUP

 : inverse of combined genomic‐ pedigree based (co)variances matrix  : vector of local phenotypes

 : vector of estimated local fixed effects

 : vector of estimated local GEBV

 8 64th_{annual EAAP Meeting, Nantes, France, August 26}th_{– 30}th₂₀₁₃                            L 1 L 1 * L * L 1 * 1 1 1 1 y R Z' y R X' u β G Z R Z' X R Z' Z R X' X R X' ˆ ˆ 1 0 1 1 * G H G     L y * L βˆ * L uˆ

 

*



*1



L 0,G u p  MVN 

(3)

As alternative to introduce phenotypes

Also allowing for foreign information

However avoiding double counting

E.g. MACE‐EBV contain our phenotypes

Also avoiding deregression

Potential source of trouble

Be simple and flexible

Allowing to extend to multiple sources

Alternative

9 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013



Concept of “Hybrid” ssGBLUP

10 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013



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       L 1 L 1 * L * L 1 * 1 1 1 1

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 More details later

Assumption: a priori known information on

Source of phenotypic information

Vector of local EBV:  “external”*_information Prediction error (co)variances matrix:

Allows use of simplified models

E.g., Test‐day model  lactation EBV

Bayesian priors

* L uˆ L uˆ L D



y

L

replaced by and

uˆ

_L

D

L * “external” = outside of original system of MME

Using only local information as source





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L 1 L * L L 1 *

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=

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“Hybrid” ssGBLUP  ssGBAYES

Least square part of LHS of hypothetical BLUP generating local information RHS of hypothetical BLUP generating local information



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       L 1 L 1 * L * L 1 * 1 1 1 1

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(4)

Assumption: a priori known information on

Extended to 2 sources of phenotypic information

Vector of local EBV:  1st_{“external”}*_information

Vector of foreign EBV:  2nd_{“external”}*_information Prediction error (co)variances matrices: , Issue: only available for some animals  , , and : (partially) unknown

Bayesian priors

13 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013 * L uˆ L uˆ D_L D_F L uˆ F uˆ L D DF F uˆ * “external” = outside of original system of MME

Methods

For both sources: estimation of

(i=L,F) Available EBV of some animals (so‐called “external” ) “Internal” animals: prediction of EBV ( ) : genetic (co)variances matrix  14 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013 i uˆ E i uˆ

 



 

1



, ˆ ˆ ˆ   II  E EE IE E I i i 1 i i i i u G G u G u MVN p



_'



' i ' i i uE uI uˆ  ˆ ˆ 0 G A G  I i uˆ

 Correct propagation of information

Methods

For both sources: estimation of

(i=L,F) 15 64th_{annual EAAP Meeting, Nantes, France, August 26}th_{– 30}th₂₀₁₃ i

D

i 1 i G Λ D   









          0 Δ Δ Δ R Δ Λ j j j 1 0 j i : animals internal For traits ,..., 1 ; : animals external For animals ,..., 1 ; t k RE diag n j diag block k

 All matrices depend only on contributions

due to own records

i

Λ

Issue

Non‐Independence of information sources

E.g., Local information included in MACE‐EBV 16 64th_{annual EAAP Meeting, Nantes, France, August 26}th_{– 30}th₂₀₁₃ Lc 1 Lc F 1 F Ff 1 Ff

u

D

u

D

u

D



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

ˆ

Vector of foreign EBV free of local information Vector of foreign EBV Vector of local EBV contributing to foreign information

 Estimation of external information

free from local information

(5)

Combination of genotype, pedigree, local and

foreign information (ssGBayes)





Lc 1 Lc F 1 F L 1 L * L Lc F L 1 *

u

D

u

D

u

D

=

u

Λ

+

Λ

+

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

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Methods

17 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013 Least square part of LHS of hypothetical BLUP of local information Least square part of LHS of hypothetical BLUP of foreign information free of local information RHS of hypothetical BLUP of local information RHS of hypothetical BLUP of foreign information free of local information

 No double counting of contributions

Example :

Walloon genomic evaluation

 ssGBAYES results for milk yield But already used for all INTERBULL traits  1,909 genotyped Holstein bulls and cows  16,234 animals (genotyped and ancestors) 12,046 animals with Walloon EBV (EBVW) 1,981 bulls with MACE EBV (EBVM) 601 bulls with Walloon EBV contributing to MACE (EBVWc)  Reliabilities (REL) for GEBV obtained through inversion of left‐hand side 18 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013

Results

 Averaged REL (SD) associated to EBV_W, GEBV_Wand GEBV_W+M‐Wcfor genotyped bulls for milk yield Class of RELw N EBVW 1 No. of publishable bulls GEBVW 2 No. of publishable bulls GEBVW+M‐Wc3 No. of publishable bulls < 0.50 647 0.25 (0.12) 0 0.44 (0.09) 194 0.80 (0.09) 628 0.50 – 0.74 173 0.63 (0.07) 173 0.69 (0.06) 173 0.87 (0.05) 173 ≥ 0.75 390 0.90 (0.07) 390 0.91 (0.06) 390 0.94 (0.04) 390 1_{REL obtained from Walloon polygenic evaluation}

2_{REL obtained from Walloon genomic evaluation using only EBV} W 3_{REL obtained from Walloon genomic evaluation using EBV}

W, EBVMand EBVWc 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.200.30 0.40 0.500.60 0.70 0.800.90 1.00 GRELW+M‐Wc REL

Results

 Bulls  Cows

 Bulls not yet included in national polygenic evaluation  Increase of REL for genotyped animals without MACE

(6)

Conclusions

Applied to Walloon dairy genomic evaluations

Bayesian approach integrates well MACE results into ssGBLUP Recovers large amount of phenotypic information More accurate predictions for genotyped animals and their progeny Correct propagation of all available information 21 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013

Combining “s” sources of information



   













s 1, i i 1 i * C s 1, i i 1 *

₊

_Λ

_u

₌

_D

_u

G

ˆ

General notation

22 64thannual EAAP Meeting, Nantes, France, August 26th– 30th2013 Least square part of LHS of hypothetical BLUP for information source i RHS of hypothetical BLUP for information source i

 Potential to improve current

genomic prediction strategies

Further implications ssGBayes

No deregression

Direct use of EBV from multiple sources

Applicable to multi‐trait models

E.g., external information for correlated and/or

predictor traits

Open general framework, can be modified to

accomodate latest genomic models, e.g.:

GWAS models based on ssGBLUP

SNP based single‐step models

23 64th_{annual EAAP Meeting, Nantes, France, August 26}th_{– 30}th₂₀₁₃ ₆₄th_{annual EAAP Meeting, Nantes, France, August 26}th_{– 30}th₂₀₁₃

Thank you for your attention

Acknowledgments for financial support

 Service Public of Wallonia SPW – DGO3 through project D31‐1274 DairySNP  National Fund for Scientific Research and Wallonie Brussels Internationalfor scientific stays

Acknowledgments

 Animal Breeding Association for providing data  CECI for computational resources  Animal and Dairy Science Department, University of Georgia, Athens, USA  Animal Science Department, University of Ljubljana, Slovenia