2012 ADSA-ASAS Joint Annual Meeting Phoenix, AZ, July 15-19 Extension of Bayesian procedures to integrate and to blend multiple external information into genetic evaluations J. Vandenplas 1,2 , N. Gengler 1

1 University of Liège, Gembloux Agro-Bio Tech, Belgium 2 National Fund for Scientific Research, Brussels, Belgium

Introduction

• Most reliable EBV if estimated from all available sources • Most situations – Multiple sources (e.g., dairy breeds) • Traditional genetic evaluations • International second step (Interbull)  Animals with few (or no) local data: low accuracy – Development of genomic selection  New genomic information sources  Strategies for integration / blending of those multiple external evaluations

External information

• Most situations – EBV and REL from other genetic evaluations – Information not taken into account by a local BLUP  No double-counting between local and external evaluations – Only available for some animals • Having, or not, phenotypic information in the local BLUP • Present in the pedigree of the local BLUP • Special case: MACE-EBV

Aim

To integrate/blend multiple a priori known external information into a local evaluation

 Using a Bayesian approach – Based on • • • Legarra et al. (2007) Quaas and Zhang (2006) Vandenplas and Gengler (2012)

Regular BLUP

• Mixed model equations   

X' Z' R R



1 X



1 X X' R Z' R



1 Z



1 Z



G



1

      ˆ ˆ

L L

      

X' Z' R R



1 y L



1 y L

   –

G -1

– – – – 

H -1



G -1 0

: Inverse of genetic (co)variances matrix

y

ˆ

L L

: vector of local observations : vector of estimated local fixed effects ˆ

L

p

u L

: vector of estimated local EBV 

MVN

Methods

• Assumption: –

A priori

known information of

u L

n

sources of external information: •

n

vector of external EBV

E 1

,...,

u E i

,...,

E n

•

n

prediction error (co)variances matrices

D E 1

,...,

D E i ,..., D E n

– Issue: only available for some animals 

E i

and : (partially) unknown

E i

Methods

• For each source

i

: Estimation of

u E i

– Available : External EBV of external animals ( )

EE i

– Local animals : prediction

p

(

ˆ

EL i * EE i )



MVN



G * LE i

of external EBV ( )

EL i G *



1 EE i u * EE i , (G *EE i )



1

  ˆ

E i

    

u

ˆ

EL i * EE i

   

Predicted external EBV Available external EBV

 Correct propagation of external information

Methods

• For each source

i:

Estimation of

D E i D



1 E i



G



1



Λ E i G



1



A



1



G 0



1

: Inverse of genetic (co)variances matrix of

u E i Λ E i

 block diag

( Δ j G 0



1 Δ j )

; i  1,..., n sources; j  1,..., a animals For For external animals animals with :

Δ j

 diag

( REL ijk

only local informatio n :

Δ

(

1 

j



REL ijk )

0

)

; k  1,..., t traits

Methods

• Integration of

n

external information   

X' R Z' R



1 X



1 X Z' X' R R



1 Z



1 Z



G



1

      ˆ

L L

      

X' R Z' R



1 y L



1 y L

      

X' Z' R R



1 X



1 X X' R



1 Z Z' R



1 Z



G



1



n



i



1 Λ E i

       ˆ

L L

       

Z' R X' R



1 y L

 

1 i n

 

1 y L



D



1 E i u E i

    

Sum of n least square parts of LHS of n hypothetical BLUP of n sources of external EBV Sum of n RHS of n hypothetical BLUP of n sources of external EBV

Methods

• Blending of

n

external information – Assumption: no local records in

y L

 

G



1



i n

 

1 Λ E i

  ˆ

L

  

i n

 

1



D E



1 i

ˆ

E i

  

Methods

• Issue: double-counting of information among external animals  Estimation of contributions due to relationships and due to own records 

Λ i

Simulation: blending

• 100 replicates • 2 populations – ±1000 animals/population – 5 generations – Random matings / cullings – Observations (Van Vleck, 1994) • Milk yield for the first lactation • Heritability : 0.25

– Fixed effect • Random herd effect within population

Simulation: blending

• Performed evaluations

Information Pedigree External population Local population + 50 external sires used locally Phenotypes External observations Local observations External information External EBV and REL (50 external sires) Local EBV and REL (all population) External BLUP

 

Local BLUP Blending BLUP Joint BLUP

Simulation: blending

• Performed evaluations

Information Pedigree External population Local population + 50 external sires used locally Phenotypes External observations Local observations External information External EBV and REL (50 external sires) Local EBV and REL (all population) External BLUP

 

Local BLUP

 

Blending BLUP Joint BLUP

Simulation: blending

• Performed evaluations

Information Pedigree External population Local population + 50 external sires used locally Phenotypes External observations Local observations External information External EBV and REL (50 external sires) Local EBV and REL (all population) External BLUP

 

Local BLUP

 

Blending BLUP Joint BLUP

  

Simulation: blending

• Performed evaluations

Information Pedigree External population Local population + 50 external sires used locally Phenotypes External observations Local observations External information External EBV and REL (50 external sires) Local EBV and REL (all population) External BLUP

 

Local BLUP

 

Blending BLUP Joint BLUP

      

Comparison with joint BLUP

• Rank correlations (r+SD)

Evaluation Without external information Local BLUP Only external information Blending BLUP With double-counting Without double-counting Local animals 0.95

± 0.02

0.99

>0.99

± ± 0.004

0.000

External sires 0.54

± 0.11

0.97

>0.99

± ± 0.01

0.001

 Rankings more similar to those of the joint BLUP

Comparison with joint BLUP

• Mean squared errors (MSE+SD) - Expressed as a percentage of the local MSE

Evaluation Without external information Local BLUP Only external information Blending BLUP With double-counting Without double-counting Local animals External sires 100.00

± 26.7

100.00

± 24.5

21.20

0.48

± ± 6.2

0.2

6.83

0.23

± ± 1.9

0.1

 Importance of double-counting

Conclusion

• Bayesian Mixed Model Equations  Rankings most similar to those of a joint BLUP – Importance of double-counting among animals

Conclusion

• Bayesian Mixed Model Equations  Rankings most similar to those of a joint BLUP – Importance of double-counting among animals  Bayesian procedure – Reliable integration/blending of multiple external information – Simple modifications of current programs – Applicable to multi-traits models

Special case: MACE

• Integration of MACE-EBV – Genetic evaluations – Single-step genomic evaluations (cf. oral presentation at this meeting)  Issue: included local information  Estimation of external information free of local information:

D E



1

ˆ

E

 

1 D M

ˆ

M



D L *



1

ˆ

* L

Special case: MACE

• Integration of MACE-EBV    

X' Z' L L R



1 X L R



1 X L Z' L R



1 Z L X' L



R G



1



1 Z L



D M



1



D L *



1

       

β u

ˆ ˆ

L L

        

Z' L R



1 y L X' L



R



1 y D



1 M u

ˆ

M L



D L *



1 u

ˆ

* L

   

Special case: MACE

• Integration of MACE-EBV    

X' Z' L L R



1 X L R



1 X L Z' L R



1 Z L X' L



R G



1



1 Z L



D M



1



D L *



1

       

β u

ˆ ˆ

L L

        

Z' L R



1 y L X' L



R



1 y L D M



1 u

ˆ

M



D L *



1 u

ˆ

* L

   

Inverse of (combined genomic -) pedigree based (co)variances matrix

Special case: MACE

• Integration of MACE-EBV    

X' Z' L L R



1 X L R



1 X L Z' L R



1 Z L X' L



R G



1



1 Z L



D M



1



D L *



1

       

β u

ˆ ˆ

L L

        

Z' L R



1 y L X' L



R



1 y L D M



1 u

ˆ

M



D L *



1 u

ˆ

* L

   

Inverse of (combined genomic -) pedigree based (co)variances matrix Inverse of prediction error (co)variances matrix of MACE-EBV

Special case: MACE

• Integration of MACE-EBV    

X' Z' L L R



1 X L R



1 X L Z' L R



1 Z L X' L



R G



1



1 Z L



D M



1



D L *



1

       

β u

ˆ ˆ

L L

        

Z' L R



1 y L X' L



R



1 y L D M



1 u

ˆ

M



D L *



1 u

ˆ

* L

   

Inverse of (combined genomic -) pedigree based (co)variances matrix Inverse of prediction error (co)variances matrix of MACE-EBV Inverse of prediction error (co)variances matrix of local EBV

Special case: MACE

• Integration of MACE-EBV    

X' Z' L L R



1 X L R



1 X L Z' L R



1 Z L X' L



R G



1



1 Z L



D M



1



D L *



1

       

β u

ˆ ˆ

L L

        

Z' L R



1 y L X' L



R



1 y L D M



1 u

ˆ

M



D L *



1 u

ˆ

* L

   

Inverse of (combined genomic -) pedigree based (co)variances matrix RHS Inverse of prediction error (co)variances matrix of MACE-EBV Inverse of prediction error (co)variances matrix of local EBV of an hypothetical BLUP of MACE-EBV

Special case: MACE

• Integration of MACE-EBV    

X' Z' L L R



1 X L R



1 X L Z' L R



1 Z L X' L



R G



1



1 Z L



D M



1



D L *



1

       

β u

ˆ ˆ

L L

        

Z' L R



1 y L X' L



R



1 y L D M



1 u

ˆ

M



D L *



1 u

ˆ

* L

   

Inverse of (combined genomic -) pedigree based (co)variances matrix RHS Inverse of prediction error (co)variances matrix of MACE-EBV Inverse of prediction error (co)variances matrix of local EBV of an hypothetical BLUP of MACE-EBV RHS of an hypothetical BLUP of local EBV

Acknowledgements

• Animal and Dairy Science (ADS) Department, University of Georgia Athens (UGA), USA • Animal Breeding and Genetics Group of Animal Science Unit, Gembloux Agro-Bio Tech University of Liège (ULg – GxABT), Belgium • National Fund for Scientific Research (FNRS), Belgium