Bayesian integration of external information into the single step approach for genomically enhanced prediction of breeding values

Conference (2012, July 17)

An assumption to compute unbiased estimated breeding values (EBV) is that all information, i.e. genomic, pedigree and phenotypic information, has to be considered simultaneously. However, current ... [more ▼]

An assumption to compute unbiased estimated breeding values (EBV) is that all information, i.e. genomic, pedigree and phenotypic information, has to be considered simultaneously. However, current developments of genomic selection will bias evaluations because only records related to selected animals will be available. The single step genomic evaluation (ssGBLUP) could reduce pre-selection bias by the combination of genomic, pedigree and phenotypic information which are internal for the ssGBLUP. But, in opposition to multi-step methods, external information, i.e. information from outside ssGBLUP, like EBV and associated reliabilities from Multiple Across Country Evaluation which represent a priori known phenotypic information, are not yet integrated into the ssGBLUP. To avoid multi-step methods, the aim of the study was to assess the potential of a Bayesian procedure to integrate a priori known external information into a ssGBLUP by considering simplifications of computational burden, a correct propagation of external information and no multiple considerations of contributions due to relationships. To test the procedure, 2 dairy cattle populations (referenced by “internal” and “external”) were simulated as well as milk production for the first lactation of each female in both populations. Internal females were randomly mated with internal and 50 external males. Genotypes of 3000 single-nucleotide polymorphisms for the 50 males were simulated. A ssGBLUP was applied as the internal evaluation. The external evaluation was based on phenotypic and pedigree external information. External information integrated into the ssGBLUP consisted to external EBV and associated reliabilities of the 50 males. Results showed that rank correlations among Bayesian EBV and EBV based on the joint use of external and internal data and genomic information were higher than 0.99 for the 50 males and internal animals. The respective correlations for the internal evaluation were equal to 0.50 and 0.90. Thereby, the Bayesian procedure can integrate external information into ssGBLUP. [less ▲]

Rapport d'activités final du premier mandat (du 1er janvier 2010 au 31 décembre 2011) : DairySNP, Etude de la variabilité génomique des bovins laitiers et mixtes en vue de mieux connaître leur biodiversité et d'initier une sélection génomique au sein de ces races

Report (2012)

A recursive algorithm for decomposition and creation of the inverse of the genomic relationship matrix

in Journal of Dairy Science (2012), 95(10), 6093-6102

As the number of genotyped animals increases, some genomic prediction models have issues related to inversion of the genomic relationship and related matrices. We developed a recursive algorithm to ... [more ▼]

As the number of genotyped animals increases, some genomic prediction models have issues related to inversion of the genomic relationship and related matrices. We developed a recursive algorithm to approximate the inverses of those matrices. The algorithm converges after a few rounds of recursion, but additional work is needed to reduce computing costs further. [less ▲]

Is It Possible to Define a European Total Merit Index?

in Interbull Bulletin (2012), 44

Developing a common European bull list is an objective of the PROTEJE (PROduction Traits European Joint Evaluation) workgroup started in 2001 as an initiative of the European Holstein herdbooks. Six Total ... [more ▼]

Developing a common European bull list is an objective of the PROTEJE (PROduction Traits European Joint Evaluation) workgroup started in 2001 as an initiative of the European Holstein herdbooks. Six Total Merit Indexes were compared to define a common breeding goal across Europe. A principal component analysis was used to observe the direction of the largest common variation among the studied Total Merit Indexes. Results showed that the considered indexes had a lot in common. The first principal component explained 86% of the total variation. Based on previous researches establishing combined proofs on a European phantom scale for most traits and trait groups and using a multiple regression for this European Total Merit Index, relative emphases on production and functionality of 37% and on conformation of 26% could be established. [less ▲]

A recursive method of approximation of the inverse of genomic relationships matrix

Conference (2011, July 11)

Genomic evaluations by some procedures such as genomic BLUP (GBLUP) or single-step GBLUP (ssGBLUP) use the inverse of the genomic relationship matrix (G). The cost to create such an inverse is cubic and ... [more ▼]

Genomic evaluations by some procedures such as genomic BLUP (GBLUP) or single-step GBLUP (ssGBLUP) use the inverse of the genomic relationship matrix (G). The cost to create such an inverse is cubic and becomes prohibitively expensive after 30–100k genotypes. The purpose of this study was to develop methodologies, which eventually could compute a good approximation of G−1 at reduced cost. A recursive approximation of the inverse is based on a decomposition similar to that for the pedigree-based relationship: G−1 = (T−1)’D−1T−1, where T is a triangular and D a diagonal matrix. In the first step, animals are processed from the oldest to the youngest. For each animal, a subset of ancestors is selected with coefficients of genomic relationship to that animal greater than a threshold. A system of equations is created where the coefficients of G for the selected ancestors are in the left hand side and the coefficients of G for the given animal corresponding to the ancestors are the right hand side. The solution to that system of equation is stored in one line of T. Then, D is computed as diagonal elements of T−1G(T−1)’. If off-diagonals of D are too large, the approximation to G can be improved by repeated applications of G−1 = (T−1)’D−1T−1 and D = T−1G(T−1)’. After n rounds, the approximation of G inverse is a product of 2n triangular matrices and one diagonal matrix. This recursive method has been assessed on a sample of 1,718 genotyped dairy bulls. The correlation between GEBV using the complete or approximated G were 0.54 in the first round, 0.96 in the second, and 0.99 in the third. The cost of the proposed method depends on the population structure. It is likely to be high for closely related animals but lower for populations where few animals are strongly related. Additional research is needed to identify near-sparsity in T and D to eliminate unimportant operations. [less ▲]

European TMI estimation

Conference given outside the academic context (2011)

Total Merit Indexes (TMI) of 6 national evaluations (France, Germany, Walloon Region of Belgium, Italy, Netherlands and Nordic countries) were available. A principal component analysis was performed on ... [more ▼]

Total Merit Indexes (TMI) of 6 national evaluations (France, Germany, Walloon Region of Belgium, Italy, Netherlands and Nordic countries) were available. A principal component analysis was performed on this data in order to assess the common direction of selection between those 6 countries. Results showed that this methodology was a good basis to define a common european TMI. [less ▲]

Working on a Method to Compute Inverse of Genomic Relationship Matrix from Sparse Matrices

Conference (2010, July 12)

Genomic relationships matrix (G) are dense matrices used in genomic prediction of dairy cattle. As the number of genotyped animals will increase, an approximation of the inverse of genomic relationships ... [more ▼]

Genomic relationships matrix (G) are dense matrices used in genomic prediction of dairy cattle. As the number of genotyped animals will increase, an approximation of the inverse of genomic relationships matrix is needed. We have developed a method based on a decomposition of G similar to decomposition of additive relationships matrix A. The method of inversion is tested on a set of simulated data. [less ▲]