Department of Animal Science and Center for Integrated Animal Genomics, Iowa State University, Ames, USA
Department of Genetics and Animal Breeding, Poznan University of Life Sciences, Poznan, Poland
Animal Breeding and Genomics Centre, Wageningen UR Livestock Research, Lelystad, The Netherlands
Abstract
Background
The goal of this study was to apply Bayesian and GBLUP methods to predict genomic breeding values (GEBV), map QTL positions and explore the genetic architecture of the trait simulated for the 15^{th }QTLMAS workshop.
Methods
Three methods with models considering dominance and epistasis inheritances were used to fit the data: (i) BayesB with a proportion π = 0.995 of SNPs assumed to have no effect, (ii) BayesCπ, where π is considered as unknown, and (iii) GBLUP, which directly fits animal genetic effects using a genomic relationship matrix.
Results
BayesB, BayesCπ and GBLUP with various fitted models detected 6, 5, and 4 out of 8 simulated QTL, respectively. All five additive QTL were detected by Bayesian methods. When two QTL were in either coupling or repulsion phase, GBLUP only detected one of them and missed the other. In addition, GBLUP yielded more false positives. One imprinted QTL was detected by BayesB and GBLUP despite that only additive gene action was assumed. This QTL was missed by BayesCπ. None of the methods found two simulated additivebyadditive epistatic QTL. Variance components estimation correctly detected no evidence for dominance geneaction. Bayesian methods predicted additive genetic merit more accurately than GBLUP, and similar accuracies were observed between BayesB and BayesCπ.
Conclusions
Bayesian methods and GBLUP mapped QTL to similar chromosome regions but Bayesian methods gave fewer false positives. Bayesian methods can be superior to GBLUP in GEBV prediction when genomic architecture is unknown.
Background
Bayesian methods and the genomic BLUP procedure (GBLUP) can be used for prediction of genomic estimated breeding values (GEBV) and quantitative trait loci (QTL) detection. BayesB generally performs slightly better than GBLUP, especially when nonadditive gene actions are involved
Methods
Data
The simulated population included 20 sires, 10 dams per sire and 15 fullsib progeny per dam. The genome consisted of 5 chromosomes of 1 Morgan and 1,998 evenly spaced SNPs. Sources of information for analysis included 2 generations of pedigree, genotypes for all individuals and phenotypic records for 10 progeny per family. More detailed description of the dataset is available at
Methods to predict GEBV
For additive geneaction, the statistical models BayesB
where
In GBLUP the presence of dominance was investigated using a model with an additional random dominance effect (G2) for each animal. The variancecovariance matrix for this effect was created similar to the genomic relationship matrix G, except genotypes were coded as 1 for heterozygotes and 0 for both homozygotes. The third model (G3) had an additional random additivebyadditive epistatic effect for each animal, with G^{2 }as the variancecovariance matrix. GEBV were estimated using models G1 to G3 with variance components estimated using
Methods to map QTL
In the Bayesian methods, QTL positions were identified based on the absolute value of estimated SNP effects, the posterior inclusion probability (or model frequency) for each SNP, and the variance of GEBV (or window variance) for any 10 consecutive SNP standardized by dividing by the total variance of GEBV in the population. The QTL were mapped to the SNP that explained the largest proportion of the total variance of GEBV within the significant overlapping windows, whose variances were in top
where α is the vector of allele substitution effects,
Results
Estimated variance components
Table
Estimated variance components and heritability (h^{2})
Methods
Genetic Variance Components
Residual
Total
h^{2}
Additive
Epistasis
Dominance
True Value
26.35
61.49
87.84
0.3
BayesB
24.61


60.17
84.78
0.29
BayesCπ
AM
24.19


60.29
84.48
0.286
DM
24.27

0.12
60.16
84.55
0.287
GBLUP
G1
22.09


59.8
81.89
0.269
G2
22.19

0.51
59.34
82.03
0.27
G3
22.09
6.20E06

59.8
81.89
0.269
Obtained by BayesB (π = 0.995), BayesCπ using an additive model (AM) and dominance model (DM), GBLUP using additive model (G1), with additional random dominance effects (G2) and epistatic effects (G3).
QTL mapping
Figure
Single SNP association signals across the genome
Single SNP association signals across the genome. Absolute value of estimated SNP effects and model frequencies obtained by BayesCπ using an additive model.
Model frequencies of SNPs across the genome
Model frequencies of SNPs across the genome. For additive and dominance effects obtained by BayesCπ using a dominance model.
10SNP window variances across the genome obtained by BayesCπ
10SNP window variances across the genome obtained by BayesCπ. Colours differentiate chromosomes and vertical lines indicate true simulated QTL locations along with their gene actions.
Estimated marker effects (absolute values) across the genome obtained by GBLUP
Estimated marker effects (absolute values) across the genome obtained by GBLUP. Colours differentiate chromosomes.
Predictive accuracy of GEBV
Table
Correlations among GEBV
Method
BayesB
BayesCπ
GBLUP
BayesCπ
0.997
GBLUP
0.918
0.897
TBV
0.934
0.939
0.825
Obtained by Bayesian methods and GBLUP, and with simulated true breeding values (TBV) for validation individuals.
Discussion
The simulated trait was affected by one QTL with major and seven with minor effects. Two QTL were interacting with each other (epistasis) and one was imprinted. All approaches detected the major QTL and three to six QTL with smaller effects. The Bayesian methods detected more simulated QTL regions and gave fewer false positives than GBLUP. GBLUP failed to find one of the two QTL that were close to each other. This confirms the finding of
The failure to detect the imprinted QTL for BayesCπ and the epistatic QTL for BayesB and BayesCπ reveals some drawbacks of basing QTL mapping solely on window variances. A 10SNP window may include too much noise, which results in shrinkage of the signals towards zero. Thus, the variance of the causative region may be underestimated. As shown in Figures
GEBV obtained using Bayesian and GBLUP analyses were highly correlated among each other, which agrees with
Conclusions
Bayesian methods and GBLUP revealed the additive genetic attributes of the simulated trait. The number of indicated regions and their positions were in good agreement with the truth. Bayesian methods were superior to GBLUP in QTL mapping, with fewer false positives. The window variance is a plausible criterion to identify QTL using Bayesian methods, although some drawbacks exist. The mutual correlations among alternative methods were close to one but Bayesian methods yielded higher accuracy for GEBV than GBLUP.
List of abbreviations used
QTL: quantitative trait locus; BLUP: best linear unbiased prediction; GBLUP: BLUP with a realized relationship matrix; TABLUP: BLUP with a trait specific relationship matrix; GEBV(s): genomic estimated breeding value(s); TBV(s): true breeding value(s); SNP: single nucleotide polymorphism.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
MP and JZ drafted the paper. JZ, MP and AW performed the analyses. TS, AW, RF, DG, JD critically revised the manuscript and mentored the analyses. All authors read and approved the manuscript.
Acknowledgements
Mario Calus provided software to calculate G. MP acknowledges financial support of GreenHouseMilk project and the Koepon Stichting (Arnhem, the Netherlands). The GreenHouseMilk project is financially supported by the European Commission under the Seventh Research Framework Programme, Grant Agreement KBBE238562. This publication represents the views of the authors, not the European Commission, and the Commission is not liable for any use that may be made of the information. Contribution in initial analysis of the simulated dataset of Maciej Szydłowski, Sebastian Mucha, Marek A. Wietrzykowski and Alicja Borowska (Department of Genetics and Animal Breeding, Poznan University of Life Science) is greatly appreciated.
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