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.
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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