References of "Faux, Pierre"
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See detailA review of inversion techniques related to the use of relationship matrices in animal breeding
Faux, Pierre ULg; Gengler, Nicolas ULg

in Biotechnologie, Agronomie, Société et Environnement = Biotechnology, Agronomy, Society and Environment [=BASE] (in press)

In animal breeding, prediction of genetic effects is usually obtained through the use of mixed models. For any of these genetic effects, mixed models require the inversion of the covariance matrix ... [more ▼]

In animal breeding, prediction of genetic effects is usually obtained through the use of mixed models. For any of these genetic effects, mixed models require the inversion of the covariance matrix associated to that effect, which is equal to the associated relationship matrix times the associated component of the genetic variance. Given the size of many genetic evaluation systems, computing the inverses of these relationship matrices is not trivial. In this review, we aim to cover computational techniques that ease inversion of relationship matrices used in animal breeding for prediction of the following different types of genetic effects: additive effect, gametic effect, effect due to presence of marked quantitative trait loci, dominance effect and different epistasis effects. Construction rules and inversion algorithms are detailed for each relationship matrix. In the final discussion, we draw up a common theoretical frame to most of the reviewed techniques. Two computational constraints come out of this theoretical frame: setting up the matrix of dependencies between levels of the effect and setting up some parts (diagonal or block-diagonal elements) of the relationship matrix to be inverted. [less ▲]

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See detailComputation and approximation of the inverse of relationship matrices between genotyped animals: Algorithms and Applications
Faux, Pierre ULg

Doctoral thesis (2014)

The recent developments in molecular biology have made available thousands of genetic markers, allowing livestock genotyping at a reasonable cost and the subsequent development of genomic prediction. The ... [more ▼]

The recent developments in molecular biology have made available thousands of genetic markers, allowing livestock genotyping at a reasonable cost and the subsequent development of genomic prediction. The single-step procedure, a unified approach of genomic prediction, requires inversion of two matrices gathering additive relationships between genotyped animals: the genomic relationship matrix (G) and a part of the additive relationship matrix (A22). The inverse of A22 may also be interesting for other applications. Matrix inverse can be constructed successively by, first, computing, for each animal, the vector containing contributions of other animals to its relationship and, secondly, adding the product of each vector of contributions by itself to a zeroed matrix. The objectives of this thesis were (1) to propose algorithms to compute or to approximate the vector of contributions and (2) to test the numerical efficiency of these algorithms (computing speed, memory use and, if needed, approximation accuracy). Computing contributions covered two points: (1) finding or approximating which contributions are different from zero, and (2) computing the value of contributions considered as non-zero. In the first approach, we considered that animals closely related have non-zero contributions and approximated their values by linear regression. This approach was extended in a recursive way. In the second approach, we empirically determined the set of non-zero contributions by a heuristic algorithm of pedigree exploration (only for the case of A22). Values were then computed either by linear regression, or using the already computed inverse. We also tested an approximation strategy: limiting the number of extracted generations of non-genotyped ancestors to reduce pedigree complexity. In a third approach, we followed the same heuristic algorithm as before but restricted the pedigree exploration to find out which animals have a non-zero contribution. Their values were approximated by linear regression. The presentation of the different approaches is followed by a general discussion in which the approaches are compared. It was found that the best compromise between speed, memory and approximation accuracy was achieved by the last approach for the case of A22. Use of this last approach simplified computations and therefore made predictions more feasible. However, for the case of G, no sufficient approximations could be reach in a reasonable time. Perspectives of other uses of algorithms developed and of future researches were drawn, as well as practical perspectives for animal breeding. [less ▲]

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See detailEfficient computation of genomically-enhanced inbreeding coefficients
Faux, Pierre ULg; Gengler, Nicolas ULg

Poster (2014, February 07)

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See detailEstimation of dominance variance for live body weight in a crossbred population of pigs
Dufrasne, Marie ULg; Faux, Pierre ULg; Piedboeuf, Maureen et al

in Journal of Animal Science (2014), 92

The objective of this study was to estimate the dominance variance for repeated live BW records in a crossbred population of pigs. Data were provided by the Walloon Pig Breeding Association and included ... [more ▼]

The objective of this study was to estimate the dominance variance for repeated live BW records in a crossbred population of pigs. Data were provided by the Walloon Pig Breeding Association and included 22,197 BW records of 2,999 crossbred Piétrain × Landrace K+ pigs from 50 to 210 d of age. The BW records were standardized and adjusted to 210 d of age for analysis. Three single-trait random regression animal models were used: Model 1 without parental subclass effect, Model 2 with parental subclasses considered unrelated, and Model 3 with the complete parental dominance relationship matrix. Each model included sex, contemporary group, and heterosis as fixed effects as well as additive genetic, permanent environment, and residual as random effects. Variance components and their SE were estimated using a Gibbs sampling algorithm. Heritability tended to increase with age: from 0.50 to 0.64 for Model 1, from 0.19 to 0.42 for Model 2, and from 0.31 to 0.53 for Model 3. Permanent environmental variance tended to decrease with age and accounted for 29 to 44% of total variance with Model 1, 29 to 37% of total variance with Model 2, and 34 to 51% of total variance with Model 3. Residual variance explained <10% of total variance for the 3 models. Dominance variance was computed as 4 times the estimated parental subclass variance. Dominance variance accounted for 22 to 40% of total variance for Model 2 and 5 to 11% of total variance for Model 3, with a decrease with age for both models. Results showed that dominance effects exist for growth traits in pigs and may be reasonably large. The use of the complete dominance relationship matrix may improve the estimation of additive genetic variances and breeding values. Moreover, a dominance effect could be especially useful in selection programs for individual matings through the use of specific combining ability to maximize growth potential of crossbred progeny. [less ▲]

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See detailEstimation of dominance variance for growth traits with sire-dam subclass effects in a crossbred population of pigs
Dufrasne, Marie ULg; Faux, Pierre ULg; Piedboeuf, Maureen et al

Poster (2014)

Nonadditive genetic effects may be not negligible but are often ignored in genetic evaluations. The most important nonadditive effect is probably dominance. Prediction of dominance effects should allow a ... [more ▼]

Nonadditive genetic effects may be not negligible but are often ignored in genetic evaluations. The most important nonadditive effect is probably dominance. Prediction of dominance effects should allow a more precise estimation of the total genetic merit, particularly in populations that use specialized sire and dam lines, and with large number of full-sibs, like pigs. Computation of the inverted dominance relationship matrix, D-1, is difficult with large datasets. But, D-1 can be replaced by the inverted sire-dam subclass relationship matrix F-1, which represents the average dominance effect of full-sibs. The aim of this study was to estimate dominance variance for longitudinal measurements of body weight (BW) in a crossbred population of pigs The dataset consisted of 20,120 BW measurements recorded between 50 and 210 d of age on 2,341 crossbred pigs (Piétrain X Landrace). A random regression model was used to estimate variance components. Fixed effects were sex and date of recording. Random effects were additive genetic, permanent environment, parental dominance and residual. Dominance variance represented 7 to 9% of the total variance and 11 to 30% of additive variance. Those results showed that dominance variance exists for growth traits in pigs and may be relatively large. The estimation of dominance effects may be useful for mate selection program to maximize genetic merit of progeny. [less ▲]

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See detailInversion of a part of the numerator relationship matrix using pedigree information
Faux, Pierre ULg; Gengler, Nicolas ULg

in Genetics, Selection, Evolution (2013), 45

Background. In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals ... [more ▼]

Background. In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on A22i might be minor. This hypothesis was also tested. Methods. The inverse of A22 can be computed from the inverse of the triangular factor (T-1 ) obtained by Cholesky root-free decomposition of A22 . We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of A22i is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting A22i to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results. The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions. Depending on the size and structure of the selected sub-population, gains in time to compute A22 are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. [less ▲]

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See detailEstimation of dominance variance with sire-dam subclass effects in a crossbred population of pigs
Dufrasne, Marie ULg; Faux, Pierre ULg; Piedboeuf, Maureen et al

Poster (2013, August 26)

Nonadditive genetic effects may be not negligible but are often ignored in genetic evaluations. The most important nonadditive effect is probably dominance. Prediction of dominance effects should allow a ... [more ▼]

Nonadditive genetic effects may be not negligible but are often ignored in genetic evaluations. The most important nonadditive effect is probably dominance. Prediction of dominance effects should allow a more precise estimation of the total genetic merit, particularly in populations that use specialized sire and dam lines, and with large number of full-sibs, like pigs. Computation of the inverted dominance relationship matrix, D-1, is difficult with large datasets. But, D-1 can be replaced by the inverted sire-dam subclass relationship matrix F-1, which represents the average dominance effect of full-sibs. The aim of this study was to estimate dominance variance for longitudinal measurements of body weight (BW) in a crossbred population of pigs, assuming unrelated sire-dam subclass effects. The edited dataset consisted of 20,120 BW measurements recorded between 50 and 210 d of age on 2,341 crossbred pigs from 89 Piétrain sires and 169 Landrace dams. A random regression model was used to estimate variance components. Fixed effects were sex and date of recording. Random effects were additive genetic, permanent environment, sire-dam subclass and residual. Random effects, except residual, were modeled with linear splines. Only full-sib contributions were considered by using uncorrelated sire-dam classes. Estimated heritability of BW increased with age from 0.40 to 0.60. Inversely, estimated dominance decreased with age, from 0.28 to 0.01. Ratio of dominance relative to additive variance was high at early age (58.3% at 50 d) and decreased with age (2.6% at 200 d). Those results showed that dominance effects might be important for early growth traits in pigs. However, this need to be confirmed and dominance relationships will be included in the next steps. [less ▲]

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See detailGenetic evaluation of calving ease for Walloon Holstein dairy cattle
Vanderick, Sylvie ULg; Troch, Thibault ULg; Gillon, Alain et al

Conference (2013, August 25)

Calving complications have an incidence on the economic profitability of dairy herds. In the Walloon Region of Belgium, calving ease data recording is being done on voluntary basis since 2000. This allows ... [more ▼]

Calving complications have an incidence on the economic profitability of dairy herds. In the Walloon Region of Belgium, calving ease data recording is being done on voluntary basis since 2000. This allows now the implementation of a genetic evaluation of Holstein dairy cattle addressing the need of dairy breeders to select bulls in order to reduce frequency of calving problems. Calving ease scores were analyzed using univariate animal linear models, which were fitted with the genetic correlation between direct and maternal additive genetic effects either estimated or constrained to zero. Variance components and related genetic parameters were estimated from a dataset including 33,155 calving records. Included in the models were fixed season effects, fixed herd effects and fixed sex of calf*age of dam classes*group of calvings interaction effects, random herd*year of calving effects, random maternal permanent environment effects, and random animal direct and maternal additive genetic effects. For both models, direct and maternal heritabilities for calving ease were about 8% and about 2%, respectively. Genetic correlation between direct and maternal additive effects was found to be non-significantly different from zero. So, an animal linear model with genetic correlation between direct and maternal effects constrained to zero was adopted for the routine genetic evaluation of calving ease for Walloon Holstein dairy cattle. This model was validated by Interbull in January 2013 and, since April 2013, the Walloon Region of Belgium has officially participated to the international MACE evaluation for calving traits. [less ▲]

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See detailGenetic evaluation of calving ease for Walloon Holstein dairy cattle.
Vanderick, Sylvie ULg; Troch, Thibault ULg; Gillon, Alain et al

in Interbull Bulletin (2013), 47

Calving complications have an incidence on the economic profitability of dairy herds. In the Walloon Region of Belgium, calving ease data recording is being done on voluntary basis since 2000. This allows ... [more ▼]

Calving complications have an incidence on the economic profitability of dairy herds. In the Walloon Region of Belgium, calving ease data recording is being done on voluntary basis since 2000. This allows now the implementation of a genetic evaluation of Holstein dairy cattle addressing the need of dairy breeders to select bulls in order to reduce frequency of calving problems. Calving ease scores were analyzed using univariate animal linear models, which were fitted with the genetic correlation between direct and maternal additive genetic effects either estimated or constrained to zero. Variance components and related genetic parameters were estimated from a dataset including 33,155 calving records. Included in the models were fixed season effects, fixed herd effects and fixed sex of calf*age of dam classes*group of calvings interaction effects, random herd*year of calving effects, random maternal permanent environment effects, and random animal direct and maternal additive genetic effects. For both models, direct and maternal heritabilities for calving ease were about 8% and about 2%, respectively. Genetic correlation between direct and maternal additive effects was found to be non-significantly different from zero. So, an animal linear model with genetic correlation between direct and maternal effects constrained to zero was adopted for the routine genetic evaluation of calving ease for Walloon Holstein dairy cattle. This model was validated by Interbull in January 2013 and, since April 2013, the Walloon Region of Belgium has officially participated to the international MACE evaluation for calving traits. [less ▲]

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See detailDevelopment of a genomic evaluation for milk production for a local bovine breed
Colinet, Frédéric ULg; Vandenplas, Jérémie ULg; Faux, Pierre ULg et al

in Book of Abstracts of the 64th Annual Meeting of the European Federation of Animal Science (2013, August)

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See detailStrategies for computation and inversion of the additive relationship matrix among genotyped animals
Faux, Pierre ULg; Gengler, Nicolas ULg

in Book of Abstracts of the 64th Annual Meeting of the European Federation of Animal Science (2013, August)

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See detailDirect use of MACE EBV in the Walloon single-step Bayesian genomic evaluation system
Vandenplas, Jérémie ULg; Colinet, Frédéric ULg; Faux, Pierre ULg et al

in Journal of Dairy Science (2013, July), 96(E-Supplement),

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See detailRelationship matrices and Iterative construction of their inverses
Faux, Pierre ULg; Gengler, Nicolas ULg

Diverse speeche and writing (2012)

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See detailBayesian integration of external information into the single step approach for genomically enhanced prediction of breeding values
Vandenplas, Jérémie ULg; Misztal, Ignacy; Faux, Pierre ULg et al

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 ▲]

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