Pierre Faux

Inversion of a part of the numerator relationship matrix using pedigree information.

BackgroundIn 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 A22-1might be minor. This hypothesis was also tested.MethodsThe 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 A22-1 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 A22-1 to the inverse computed using the fully extracted pedigree was measured by an appropriate norm.ResultsThe 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.ConclusionsDepending on the size and structure of the selected sub-population, gains in time to compute A22-1 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.

Estimation of dominance variance for live body weight in a crossbred population of pigs

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 for Model 1, 29 to 37% of total variance for Model 2, and 34 to 51% of total variance for 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.

A strategy to improve phasing of whole-genome sequenced individuals through integration of familial information from dense genotype panels

BackgroundHaplotype reconstruction (phasing) is an essential step in many applications, including imputation and genomic selection. The best phasing methods rely on both familial and linkage disequilibrium (LD) information. With whole-genome sequence (WGS) data, relatively small samples of reference individuals are generally sequenced due to prohibitive sequencing costs, thus only a limited amount of familial information is available. However, reference individuals have many relatives that have been genotyped (at lower density). The goal of our study was to improve phasing of WGS data by integrating familial information from haplotypes that were obtained from a larger genotyped dataset and to quantify its impact on imputation accuracy.ResultsAligning a pre-phased WGS panel [~5 million single nucleotide polymorphisms (SNPs)], which is based on LD information only, to a 50k SNP array that is phased with both LD and familial information (called scaffold) resulted in correctly assigning parental origin for 99.62% of the WGS SNPs, their phase being determined unambiguously based on parental genotypes. Without using the 50k haplotypes as scaffold, that value dropped as expected to 50%. Correctly phased segments were on average longer after alignment to the genotype phase while the number of switches decreased slightly. Most of the incorrectly assigned segments, and subsequent switches, were due to singleton errors. Imputation from 50k SNP array to WGS data with improved phasing had a marginal impact on imputation accuracy (measured as r2), i.e. on average, 90.47% with traditional techniques versus 90.65% with pre-phasing integrating familial information. Differences were larger for SNPs located in chromosome ends and rare variants. Using a denser WGS panel (~13 millions SNPs) that was obtained with traditional variant filtering rules, we found similar results although performances of both phasing and imputation accuracy were lower.ConclusionsWe present a phasing strategy for WGS data, which indirectly integrates familial information by aligning WGS haplotypes that are pre-phased with LD information only on haplotypes obtained with genotyping data, with both LD and familial information and on a much larger population. This strategy results in very few mismatches with the phase obtained by Mendelian segregation rules. Finally, we propose a strategy to further improve phasing accuracy based on haplotype clusters obtained with genotyping data.