Integration of Multiple External Information into Genetic Evaluations
This study focuses on extending Bayesian procedures to integrate and blend various external sources of information into genetic evaluations, aiming to enhance the accuracy of estimated breeding values. The approach involves incorporating a priori known external information using mixed model equations and prediction error covariances matrices. Methods are outlined for estimating external EBVs, predicting EBVs for local animals, and ensuring correct propagation of external information.
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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. Vandenplas1,2, N. Gengler1 1University of Li ge, Gembloux Agro-Bio Tech, Belgium 2National 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 1 1 1 X' R X X' R Z X' R y L = L + 1 1 1 1 Z' R X Z' R Z G Z' R y u L L = -1 -1 -1 0 G H G : Inverse of genetic (co)variances matrix : vector of local observations : vector of estimated local fixed effects : vector of estimated local EBV ( ) ( ) G 0, uL MVN = y L u L L p
Methods Assumption: A priori known information of n sources of external information: n vector of external EBV u u u ,..., ,..., u L E E E 1 i n n prediction error (co)variances matrices D ,..., D ,..., D E E E 1 i n Issue: only available for some animals u and : (partially) unknown i E D E i
Methods u For each source i: Estimation of Available: External EBV of external animals ( ) E i * EEi u u Local animals: prediction of external EBV ( ) EL i ( ) *EE = * EE * LE * EE 1 * EE 1 u ( u u p MVN ) G G , (G ) i EL i i i i i u Predicted external EBV EL = u i E * EE u i Available external EBV i Correct propagation of external information
Methods D For each source i: Estimation of E i = + 1 1 D G E E i i = 1 1 1 G A G : Inverse of genetic (co)variances matrix of i E u 0 = = = 1 block diag i ; 1,..., sources; n j 1,..., animals a ( G ) Ei j 0 j = = For external animals : diag ( REL ( 1 REL ) ) k ; 1,..., traits t local ijk ijk j = For animals with only informatio n : 0 j
Methods Integration of n external information R Z' X R Z' 1 1 1 X' R X X' R Z X' R y L = L + 1 1 1 1 Z G Z' R y u L L 1 1 1 X' R X X' R Z X' R y L = L ( ) n n = i = i E + + + 1 1 1 1 1 u Z' R X Z' R Z G Z' R y D u E L E L i i i 1 1 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 ( ) n n = i = i E + = 1 1 u u G D E L E i i i 1 1
Methods Issue: double-counting of information among external animals Estimation of contributions due to relationships and due to own records All only depend on contributions due to own records i E
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 External BLUP Local BLUP Blending BLUP Joint BLUP 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)
Simulation: blending Performed evaluations Information External BLUP Local BLUP Blending BLUP Joint BLUP 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)
Simulation: blending Performed evaluations Information External BLUP Local BLUP Blending BLUP Joint BLUP 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)
Simulation: blending Performed evaluations Information External BLUP Local BLUP Blending BLUP Joint BLUP 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)
Comparison with joint BLUP Rank correlations (r+SD) Evaluation Local animals External sires Without external information Local BLUP 0.95 0.02 0.54 0.11 Only external information Blending BLUP With double-counting 0.99 0.004 0.97 0.01 Without double-counting >0.99 0.000 >0.99 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 Local animals External sires Without external information Local BLUP 100.00 26.7 100.00 24.5 Only external information Blending BLUP With double-counting 21.20 6.2 6.83 1.9 Without double-counting 0.48 0.2 0.23 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: = 1 1 * L 1 * L u u u D D D E E M M
Special case: MACE Integration of MACE-EBV 1 1 1 X' R X X' R Z X' R y L L L L D L L = L M M + + + 1 1 1 1 * L 1 1 1 * L 1 * L u u Z' R X Z' R Z G D Z' R y D D u L L L L L L M L
Special case: MACE Integration of MACE-EBV 1 1 1 X' R X X' R Z X' R y L L L L D L L = L M M + + + 1 1 1 1 * L 1 1 1 * L 1 * L u u Z' R X Z' R Z G D Z' R y D D u L L L L L L M L Inverse of (combined genomic -) pedigree based (co)variances matrix
Special case: MACE Integration of MACE-EBV 1 1 1 X' R X X' R Z X' R y L L L L D L L = L M M + + + 1 1 1 1 * L 1 1 1 * L 1 * L u u Z' R X Z' R Z G D Z' R y D D u L L L L L L M 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 1 1 1 X' R X X' R Z X' R y L L L L D L L = L M M + + + 1 1 1 1 * L 1 1 1 * L 1 * L u u Z' R X Z' R Z G D Z' R y D D u L L L L L L M 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 1 1 1 X' R X X' R Z X' R y L L L L D L L = L M M + + + 1 1 1 1 * L 1 1 1 * L 1 * L u u Z' R X Z' R Z G D Z' R y D D u L L L L L L M L Inverse of (combined genomic -) pedigree based (co)variances matrix RHS of an hypothetical BLUP of MACE-EBV 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 1 1 1 X' R X X' R Z X' R y L L L L D L L = L M M + + + 1 1 1 1 * L 1 1 1 * L 1 * L u u Z' R X Z' R Z G D Z' R y D D u L L L L L L M L Inverse of (combined genomic -) pedigree based (co)variances matrix RHS of an hypothetical BLUP of MACE-EBV Inverse of prediction error (co)variances matrix of MACE-EBV RHS of an hypothetical BLUP of local EBV Inverse of prediction error (co)variances matrix 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 Li ge (ULg GxABT), Belgium National Fund for Scientific Research (FNRS), Belgium
