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Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently.

ABSTRACT: BACKGROUND:The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) method, such as single-step genomic BLUP (ssGBLUP), simultaneously analyses phenotypic, pedigree, and genomic information of genotyped and non-genotyped animals. In contrast to ssGBLUP, SNP effects are fitted explicitly as random effects in the ssSNPBLUP model. Similarly, principal components associated with the genomic information can be fitted explicitly as random effects in a single-step principal component BLUP (ssPCBLUP) model to remove noise in genomic information. Single-step genomic BLUP is solved efficiently by using the preconditioned conjugate gradient (PCG) method. Unfortunately, convergence issues have been reported when solving ssSNPBLUP by using PCG. Poor convergence may be linked with poor spectral condition numbers of the preconditioned coefficient matrices of ssSNPBLUP. These condition numbers, and thus convergence, could be improved through the deflated PCG (DPCG) method, which is a two-level PCG method for ill-conditioned linear systems. Therefore, the first aim of this study was to compare the properties of the preconditioned coefficient matrices of ssGBLUP and ssSNPBLUP, and to document convergence patterns that are obtained with the PCG method. The second aim was to implement and test the efficiency of a DPCG method for solving ssSNPBLUP and ssPCBLUP. RESULTS:For two dairy cattle datasets, the smallest eigenvalues obtained for ssSNPBLUP (ssPCBLUP) and ssGBLUP, both solved with the PCG method, were similar. However, the largest eigenvalues obtained for ssSNPBLUP and ssPCBLUP were larger than those for ssGBLUP, which resulted in larger condition numbers and in slow convergence for both systems solved by the PCG method. Different implementations of the DPCG method led to smaller condition numbers, and faster convergence for ssSNPBLUP and for ssPCBLUP, by deflating the largest unfavourable eigenvalues. CONCLUSIONS:Poor convergence of ssSNPBLUP and ssPCBLUP when solved by the PCG method are related to larger eigenvalues and larger condition numbers in comparison to ssGBLUP. These convergence issues were solved with a DPCG method that annihilates the effect of the largest unfavourable eigenvalues of the preconditioned coefficient matrix of ssSNPBLUP and of ssPCBLUP on the convergence of the PCG method. It resulted in a convergence pattern, at least, similar to that of ssGBLUP.

SUBMITTER: Vandenplas J

PROVIDER: S-EPMC6215606 | biostudies-literature | 2018 Nov

REPOSITORIES: biostudies-literature

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Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently.

Vandenplas Jérémie J Eding Herwin H Calus Mario P L MPL Vuik Cornelis C

Genetics, selection, evolution : GSE 20181103 1

<h4>Background</h4>The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) method, such as single-step genomic BLUP (ssGBLUP), simultaneously analyses phenotypic, pedigree, and genomic information of genotyped and non-genotyped animals. In contrast to ssGBLUP, SNP effects are fitted explicitly as random effects in the ssSNPBLUP model. Similarly, principal components associated with the genomic information can be fitted explicitly as random effects in a single-s ...[more]

PMID: 30390656

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Project description:Hanwoo, an important indigenous and popular breed of beef cattle in Korea, shows rapid growth and has high meat quality. Its yearling weight (YW) and carcass traits (backfat thickness, carcass weight- CW, eye muscle area, and marbling score) are economically important for selection of young and proven bulls. However, measuring carcass traits is difficult and expensive, and can only be performed postmortem. Genomic selection has become an appealing procedure for genetic evaluation of these traits (by inclusion of the genomic data) along with the possibility of multi-trait analysis. The aim of this study was to compare conventional best linear unbiased prediction (BLUP) and single-step genomic BLUP (ssGBLUP) methods, using both single-trait (ST-BLUP, ST-ssGBLUP) and multi-trait (MT-BLUP, MT-ssGBLUP) models to investigate the improvement of breeding-value accuracy for carcass traits and YW. The data comprised of 15,279 phenotypic records for YW and 5,824 records for carcass traits, and 1,541 genotyped animals for 34,479 single-nucleotide polymorphisms. Accuracy for each trait and model was estimated only for genotyped animals by five-fold cross-validation. ssGBLUP models (ST-ssGBLUP and MT-ssGBLUP) showed ~19% and ~36% greater accuracy than conventional BLUP models (ST-BLUP and MT-BLUP) for YW and carcass traits, respectively. Within ssGBLUP models, the accuracy of the genomically estimated breeding value for CW increased (19%) when ST-ssGBLUP was replaced with the MT-ssGBLUP model, as the inclusion of YW in the analysis led to a strong genetic correlation with CW (0.76). For backfat thickness, eye muscle area, and marbling score, ST- and MT-ssGBLUP models yielded similar accuracy. Thus, combining pedigree and genomic data via the ssGBLUP model may be a promising way to ensure acceptable accuracy of predictions, especially among young animals, for ongoing Hanwoo cattle breeding programs. MT-ssGBLUP is highly recommended when phenotypic records are limited for one of the two highly correlated genetic traits.

Project description:The objective of this study was to investigate the application of BLUP and single step genomic BLUP (ssGBLUP) models in different scenarios of paternity uncertainty with different strategies of scaling the G matrix to match the A22 matrix, using simulated data for beef cattle. Genotypes, pedigree, and phenotypes for age at first calving (AFC) and weight at 550 days (W550) were simulated using heritabilities based on real data (0.12 for AFC and 0.34 for W550). Paternity uncertainty scenarios using 0, 25, 50, 75, and 100% of multiple sires (MS) were studied. The simulated genome had a total length of 2,333 cM, containing 735,293 biallelic markers and 7,000 QTLs randomly distributed over the 29 BTA. It was assumed that QTLs explained 100% of the genetic variance. For QTL, the amount of alleles per loci randomly ranged from two to four. The BLUP model that considers phenotypic and pedigree data, and the ssGBLUP model that combines phenotypic, pedigree and genomic information were used for genetic evaluations. Four ways of scaling the mean of the genomic matrix (G) to match to the mean of the pedigree relationship matrix among genotyped animals (A22) were tested. Accuracy, bias, and inflation were investigated for five groups of animals: ALL = all animals; BULL = only bulls; GEN = genotyped animals; FEM = females; and YOUNG = young males. With the BLUP model, the accuracies of genetic evaluations decreased for both traits as the proportion of unknown sires in the population increased. The EBV accuracy reduction was higher for GEN and YOUNG groups. By analyzing the scenarios for YOUNG (from 0 to 100% of MS), the decrease was 87.8 and 86% for AFC and W550, respectively. When applying the ssGBLUP model, the accuracies of genetic evaluation also decreased as the MS in the pedigree for both traits increased. However, the accuracy reduction was less than those observed for BLUP model. Using the same comparison (scenario 0 to 100% of MS), the accuracies reductions were 38 and 44.6% for AFC and W550, respectively. There were no differences between the strategies for scaling the G matrix for ALL, BULL, and FEM groups under the different scenarios with missing pedigree. These results pointed out that the uninformative part of the A22 matrix and genotyped animals with paternity uncertainty did not influence the scaling of G matrix. On the basis of the results, it is important to have a G matrix in the same scale of the A22 matrix, especially for the evaluation of young animals in situations with missing pedigree information. In these situations, the ssGBLUP model is an appropriate alternative to obtain a more reliable and less biased estimate of breeding values, especially for young animals with few or no phenotypic records. For accurate and unbiased genomic predictions with ssGBLUP, it is necessary to assure that the G matrix is compatible with the A22 matrix, even in situations with paternity uncertainty.

Project description:BackgroundPreselection of candidates, hereafter referred to as preselection, is a common practice in breeding programs. Preselection can cause bias and accuracy loss in subsequent pedigree-based best linear unbiased prediction (PBLUP). However, the impact of preselection on subsequent single-step genomic BLUP (ssGBLUP) is not completely clear yet. Therefore, in this study, we investigated, across different heritabilities, the impact of intensity and type of preselection on subsequent ssGBLUP evaluation of preselected animals.MethodsWe simulated a nucleus of a breeding programme, in which a recent population of 15 generations was produced with PBLUP-based selection. In generation 15 of this recent population, the parents of the next generation were preselected using several preselection scenarios. These scenarios were combinations of three intensities of preselection (no, high or very high preselection) and three types of preselection (genomic, parental average or random), across three heritabilities (0.5, 0.3 or 0.1). Following each preselection scenario, a subsequent evaluation was performed using ssGBLUP by excluding all the information from the preculled animals, and these genetic evaluations were compared in terms of accuracy and bias for the preselected animals, and in terms of realized genetic gain.ResultsType of preselection affected selection accuracy at both preselection and subsequent evaluation stages. While preselection accuracy decreased, accuracy in the subsequent ssGBLUP evaluation increased, from genomic to parent average to random preselection scenarios. Bias was always negligible. Genetic gain decreased from genomic to parent average to random preselection scenarios. Genetic gain also decreased with increasing intensity of preselection, but only by a maximum of 0.1 additive genetic standard deviation from no to very high genomic preselection scenarios.ConclusionsUsing ssGBLUP in subsequent evaluations prevents preselection bias, irrespective of intensity and type of preselection, and heritability. With GPS, in addition to reducing the phenotyping effort considerably, the use of ssGBLUP in subsequent evaluations realizes only a slightly lower genetic gain than that realized without preselection. This is especially the case for traits that are expensive to measure (e.g. feed intake of individual broiler chickens), and traits for which phenotypes can only be measured at advanced stages of life (e.g. litter size in pigs).

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Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently.

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Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently.

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