Using eigenvalues as variance priors in the prediction of genomic breeding values by principal component analysis

Macciotta, N.P.P.; Gaspa, Giustino; Steri, Roberto; Nicolazzi, Ezequiel Luís; Dimauro, Corrado; Pieramati, Camillo; Cappio-Borlino, A.

doi:10.3168/jds.2009-3029

Cited by 30 publications

(43 citation statements)

References 39 publications

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“…Despite the generally high reduction in data dimension, the highest accuracies after CV were achieved for a wide range of numbers of PC included in the PCR model, from only one to more than 1000 (Tables 5 and 6). This is a wider range than that reported in previous studies based on simulated data, in which the highest accuracies were achieved when the number of PC ranged from 250 to 350 [19,20]. However, it should be noted that for PCR_eigen, which is the most commonly used approach in the literature, the number of PC in the model was between 28 and 249 after CV and between 1 and 1112 for the “best case scenario”.…”

Section: Discussionmentioning

confidence: 75%

A comparison of principal component regression and genomic REML for genomic prediction across populations

et al. 2014

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BackgroundGenomic prediction faces two main statistical problems: multicollinearity and n ≪ p (many fewer observations than predictor variables). Principal component (PC) analysis is a multivariate statistical method that is often used to address these problems. The objective of this study was to compare the performance of PC regression (PCR) for genomic prediction with that of a commonly used REML model with a genomic relationship matrix (GREML) and to investigate the full potential of PCR for genomic prediction.MethodsThe PCR model used either a common or a semi-supervised approach, where PC were selected based either on their eigenvalues (i.e. proportion of variance explained by SNP (single nucleotide polymorphism) genotypes) or on their association with phenotypic variance in the reference population (i.e. the regression sum of squares contribution). Cross-validation within the reference population was used to select the optimum PCR model that minimizes mean squared error. Pre-corrected average daily milk, fat and protein yields of 1609 first lactation Holstein heifers, from Ireland, UK, the Netherlands and Sweden, which were genotyped with 50 k SNPs, were analysed. Each testing subset included animals from only one country, or from only one selection line for the UK.ResultsIn general, accuracies of GREML and PCR were similar but GREML slightly outperformed PCR. Inclusion of genotyping information of validation animals into model training (semi-supervised PCR), did not result in more accurate genomic predictions. The highest achievable PCR accuracies were obtained across a wide range of numbers of PC fitted in the regression (from one to more than 1000), across test populations and traits. Using cross-validation within the reference population to derive the number of PC, yielded substantially lower accuracies than the highest achievable accuracies obtained across all possible numbers of PC.ConclusionsOn average, PCR performed only slightly less well than GREML. When the optimal number of PC was determined based on realized accuracy in the testing population, PCR showed a higher potential in terms of achievable accuracy that was not capitalized when PC selection was based on cross-validation. A standard approach for selecting the optimal set of PC in PCR remains a challenge.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-014-0060-x) contains supplementary material, which is available to authorized users.

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Section: Discussionmentioning

confidence: 75%

A comparison of principal component regression and genomic REML for genomic prediction across populations

et al. 2014

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“…Thus, the marker (co)variance matrix is not full rank, resulting in a reduction of the maximum number of PC that can be potentially extracted. Previous results obtained on simulated data showed no differences in DGV accuracies between chromosome-wide or genome-wide PC extraction (Macciotta et al, 2010). Differently from the abovementioned papers, where the number of PC was chosen based on the proportion of variance explained, in the present investigation the MINEIGEN criterion was adopted (Kaiser, 1960).…”

Section: Pcamentioning

confidence: 96%

“…In the GS framework, PCA has been used to reduce the number of predictors in the estimation of direct genomic values (DGV) by Solberg et al (2009). Furthermore, eigenvalues of SNP correlation matrix were also used as variance priors to estimate DGV in simulated and real cattle data (Macciotta et al, 2010;Pintus et al, 2012). In this context, PCA was used to reduce the computational demand and the co-linearity among predictors to calculate DGV of pure breed animals.…”

Section: Introductionmentioning

confidence: 99%

Multiple-breed genomic evaluation by principal component analysis in small size populations

Gaspa

Jorjani²,

Dimauro

et al. 2015

Animal

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In this study, the effects of breed composition and predictor dimensionality on the accuracy of direct genomic values (DGV) in a multiple breed (MB) cattle population were investigated. A total of 3559 bulls of three breeds were genotyped at 54 001 single nucleotide polymorphisms: 2093 Holstein (H), 749 Brown Swiss (B) and 717 Simmental (S). DGV were calculated using a principal component (PC) approach for either single (SB) or MB scenarios. Moreover, DGV were computed using all SNP genotypes simultaneously with SNPBLUP model as comparison. A total of seven data sets were used: three with a SB each, three with different pairs of breeds (HB, HS and BS), and one with all the three breeds together (HBS), respectively. Editing was performed separately for each scenario. Reference populations differed in breed composition, whereas the validation bulls were the same for all scenarios. The number of SNPs retained after data editing ranged from 36 521 to 41 360. PCs were extracted from actual genotypes. The total number of retained PCs ranged from 4029 to 7284 in Brown Swiss and HBS respectively, reducing the number of predictors by about 85% (from 82% to 89%). In all, three traits were considered: milk, fat and protein yield. Correlations between deregressed proofs and DGV were used to assess prediction accuracy in validation animals. In the SB scenarios, average DGV accuracy did not substantially change when either SNPBLUP or PC were used. Improvement of DGV accuracy were observed for some traits in Brown Swiss, only when MB reference populations and PC approach were used instead of SB-SNPBLUP (+10% HBS, +16%HB for milk yield and +3% HBS and +7% HB for protein yield, respectively). With the exclusion of the abovementioned cases, similar accuracies were observed using MB reference population, under the PC or SNPBLUP models. Random variation owing to sampling effect or size and composition of the reference population may explain the difficulty in finding a defined pattern in the results.

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“…Using simulation data they demonstrated that when the number of markers greatly exceeds the number of observations 'preconditioned' or specialized PCA can successfully identify almost all SNPs with true genetic effects. Other studies have also used PCR and PLS for genome-assisted prediction of breeding values (Solberg et al, 2009;Macciotta et al, 2010). However, these methods are very challenging to use and require extensive computing technology and time.…”

Section: Introductionmentioning

confidence: 99%

Selective Genotyping for Marker Assisted Selection Strategies for Soybean Yield Improvement

Fallen

Allen

Kopsell

et al. 2015

PGGB

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IntroductionCultivar improvements in yield have allowed the soybean [Glycine max (L.) Merr.] to become the most important source of vegetable protein and oil in the world and the second most important crop in the U.S. In 2012, the estimated seed yield of soybean in the U.S. was 82 million metric tons harvested from 31.2 million hectares of land (Soy Stats, 2013). However, the genetic gain is still only about 1% a year in soybean (Hao et al., 95 Abstract Using molecular markers in soybean [Glycine max (L.) Merr.] has lead to the identification of major loci controlling quantitative and qualitative traits that include: disease resistance, insect resistance and tolerance to abiotic stresses. Yield has been considered as one of the most important quantitative traits in soybean breeding. Unfortunately, yield is a very complex trait and most yield quantitative trait loci (QTL) that have been identified have had only limited success for marker assisted selection (MAS). The objective of this study was to identify QTL associated with soybean seed yield in preliminary yield trials grown in different environments and to evaluate their effective use for MAS using a yield prediction model (YPM), which included epistasis. To achieve this objective, 875 F 5:9 recombinant inbred lines (RIL) from a population developed from a cross between two prominent ancestors of the North American soybean (Essex and Williams 82) were used. The 875 RIL and check cultivars were divided into four groups based on maturity and each group was grown in Knoxville, TN and one other location that had an environment in which the maturity group (MG) was adapted to be grown. Each RIL was genotyped with >50,000 single nucleotide polymorphic markers (SNPs) of which 17,232 were This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.polymorphic across the population. Yield QTL were detected using a single factor (SF) analysis of variance (ANOVA) and composite interval mapping (CIM). Based on CIM, 23 yield QTL were identified. Twenty-one additional QTL were detected using SF ANOVA. Individually, these QTL explained from 4.5% to 11.9% of the phenotypic variation for yield. QTL were identified on all 20 chromosomes and five of the 46 QTL have not been previously reported. This study provides new information concerning yield QTL in soybean and may offer important insights into MAS strategies for soybean.Keywords: Genomic selection, epistasis, predictive breeding, QTL analysis.2012; Rincker et al., 2014). Sebastian (2010) and Hyten et al. (2006) showed that current selection procedures are not efficient in exploiting the available genetic diversity. Using MAS for yield could not only increase breeding efficiency, but also would improve our understanding of the genetic mechanisms of seed yield. Although there has been an increased interest in MA...

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Using eigenvalues as variance priors in the prediction of genomic breeding values by principal component analysis

Cited by 30 publications

References 39 publications

A comparison of principal component regression and genomic REML for genomic prediction across populations

A comparison of principal component regression and genomic REML for genomic prediction across populations

Multiple-breed genomic evaluation by principal component analysis in small size populations

Selective Genotyping for Marker Assisted Selection Strategies for Soybean Yield Improvement

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