Email updates

Keep up to date with the latest news and content from BMC Proceedings and BioMed Central.

This article is part of the supplement: Proceedings of the 15th European workshop on QTL mapping and marker assisted selection (QTLMAS)

Open Access Highly Accessed Proceedings

Comparison of five methods for genomic breeding value estimation for the common dataset of the 15th QTL-MAS Workshop

Chong-Long Wang12, Pei-Pei Ma1, Zhe Zhang1, Xiang-Dong Ding1, Jian-Feng Liu1, Wei-Xuan Fu1, Zi-Qing Weng1 and Qin Zhang1*

Author Affiliations

1 Key Laboratory of Animal Genetics, Breeding and Reproduction, Ministry of Agriculture of China, College of Animal Science and Technology, China Agricultural University, Beijing 100193, China

2 Institute of Animal Husbandry and Veterinary Medicine, Anhui Academy of Agricultural Sciences, Hefei 230031, China

For all author emails, please log on.

BMC Proceedings 2012, 6(Suppl 2):S13  doi:10.1186/1753-6561-6-S2-S13


The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1753-6561/6/S2/S13


Published:21 May 2012

© 2012 Wang et al.; licensee BioMed Central Ltd.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Background

Genomic breeding value estimation is the key step in genomic selection. Among many approaches, BLUP methods and Bayesian methods are most commonly used for estimating genomic breeding values. Here, we applied two BLUP methods, TABLUP and GBLUP, and three Bayesian methods, BayesA, BayesB and BayesCπ, to the common dataset provided by the 15th QTL-MAS Workshop to evaluate and compare their predictive performances.

Results

For the 1000 progenies without phenotypic values, the correlations between GEBVs by different methods ranged from 0.812 (GBLUP and BayesCπ) to 0.997 (TABLUP and BayesB). The accuracies of GEBVs (measured as correlations between true breeding values (TBVs) and GEBVs) were from 0.774 (GBLUP) to 0.938 (BayesCπ) and the biases of GEBVs (measure as regressions of TBVs on GEBVs) were from 1.033 (TABLUP) to 1.648 (GBLUP). The three Bayesian methods and TABLUP had similar accuracy and bias.

Conclusions

BayesA, BayesB, BayesCπ and TABLUP performed similarly and satisfactorily and remarkably outperformed GBLUP for genomic breeding value estimation in this dataset. TABLUP is a promising method for genomic breeding value estimation because of its easy computation of reliabilities of GEBVs and its easy extension to real life conditions such as multiple traits and consideration of individuals without genotypes.

Background

The goal of genomic selection (GS) [1] is to capture all quantitative trait loci (QTL) influencing a trait by tracing all chromosome segments defined by adjacent markers. With use of highly dense markers, GS is supposed to be able to overcome the problem of traditional maker assisted selection (MAS) that only a limited proportion of the total genetic variance is captured by the markers of QTL. GS has become feasible very recently with the high throughput genotyping technology and the availability of highly dense markers covering whole genome. Genomic breeding value estimation is the key step in GS. A number of approaches have been proposed for estimating genomic breeding values [1-9], among which BLUP methods and Bayesian methods are most commonly used. Here, we applied two BLUP methods (GBLUP [3], TABLUP [4]) and three Bayesian methods (BayesA, BayesB [1], BayesCπ [5]) to the common dataset provided by the 15th QTL-MAS Workshop to evaluate and compare their predictive performances.

Methods

Dataset

The common dataset consisted of an outbred population, which had been simulated using the LDSO software [10], with 1000 generations of 1000 individuals, followed by 30 generations of 150 individuals. 9990 SNP markers were distributed on 5 chromosomes. Each chromosome had a size of 1 Morgan and carried 1998 evenly distributed SNPs (1 SNP every 0.05 cM).

The final dataset used for evaluating genomic selection consisted of 3220 individuals, including 20 sires, 200 dams (each sire mated with 10 dams) and 3000 progenies (15 per dam). All individuals were genotyped for the 9990 SNPs without missing or genotyping error. Of the 15 progenies of each dam, 10 were phenotyped for a continuous trait. The 2000 progenies with phenotypic records and the other 1000 individuals (which had simulated true breeding values) without phenotypic records were treated as reference and validation population, respectively.

Estimation of variance components and EBVs

The variance components and the traditional BLUP EBVs were estimated using phenotypes and pedigree and the software DMUv6 [11] based on the following model:

<a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M1">View MathML</a>

where y is the vector of phenotypes of individuals in the reference population, μ is the overall mean, a is the vector of additive genetic effects of the phenotyped individuals and their parents, Z is the incidence matrix of a, and e is the vector of residual errors. The variance-covariance matrices of a and e are <a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M2">View MathML</a> and <a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M3">View MathML</a>, respectively, where A is the additive genetic relationship matrix, <a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M4">View MathML</a> is the additive genetic variance, and <a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M5">View MathML</a> is the residual variance.

The reliabilities of the traditional EBVs were obtained from DMU directly and calculated as the square of the correlation between EBVs and the true unknown breeding values.

Estimation of SNP effects

BayesA, BayesB and BayesCπ were used to estimate SNP effects in the reference population based on the following model:

<a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M6">View MathML</a>

where g is the vector of random SNP effects, X is the matrix of genotype indicators (with values 0, 1, or 2 for genotypes 11, 12, and 22, respectively).

The differences between the three Bayesian methods lay in the assumptions for the prior distribution of SNP effects. BayesA assumes that all SNPs have an effect, but each has a different variance. BayesB and BayesCπ assume that each SNP has either an effect of zero or non-zero with probabilities π and 1-π, respectively, and for those having non-zero effects it is assumed that each SNP has a different variance in BayesB and a common variance in BayesCπ. In addition, in BayesB π is treated as a known parameter, while in BayesCπ it is treated as an unknown parameter with a uniform (0, 1) prior distribution. In this study, we set π = 0.99 for BayesB, and adopted the same prior distributions of g and e for the three Bayesian methods as those in [1,5].

The Markov chain was run for 50,000 cycles of Gibbs sampling (for BayesB, 100 additional cycles of Metropolis-Hastings sampling were performed for the SNP effect variance in each Gibbs sampling cycle), and the first 5000 cycles were discarded as burn-in. All the samples of SNP effects after burn-in were averaged to obtain the SNP effect estimate.

Calculation of GEBVs

The genomic estimated breeding values (GEBVs) of all genotyped individuals were obtained using five methods: BayesA, BayesB, BayesCπ, GBLUP and TABLUP.

For BayesA, BayesB and BayesCπ, the GEBV of a genotyped individual was calculated as the sum of all marker effects according to its marker genotypes [1].

For GBLUP and TABLUP, the GEBVs were estimated based on the following model:

<a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M10','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M10">View MathML</a>

where u is the vector of genomic breeding values of all genotyped individuals with the variance-covariance matrix equal to <a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M7">View MathML</a> for GBLUP or <a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M8">View MathML</a> for TABLUP. <a onClick="popup('http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1753-6561/6/S2/S13/mathml/M9">View MathML</a> is the additive genetic variance estimated from the reference population.

The G matrix (realized relationship matrix) was constructed by using genotypes of all markers [3]. The TA matrix (trait-specific marker-derived relationship matrix), was constructed by using genotypes of all markers with each marker being weighted with its estimated effect obtained from BayesB following the rules proposed by Zhang et al. [4].

The accuracies of GEBVs were calculated as the correlation between GEBVs and the simulated true breeding values.

Results and discussion

Variance components

The estimated additive genetic variance and residual variance were 24.82 and 58.65, respectively. Therefore, the estimated heritability was 0.30. These estimates were used for the subsequent estimation of SNP effects and GEBVs.

Estimates of SNP effects

Figure 1 includes the profiles of SNP effects estimated by BayesA (Figure 1A), BayesB (Figure 1B) and BayesCπ (Figure 1C). These estimated effects, which are obviously not evenly distributed, reflect the underlying architecture of the trait. The estimated value of π in BayesCπ is 0.9986. In general, the SNP effect profiles from the three Bayesian methods are quite similar. In particular, all of the three methods show a big peak on chromosome 1, two peaks on chromosome 2, and a peak on chromosome 3. In addition, BayesCπ shows another peak on chromosome 3 and a peak on chromosome 4. No peaks appear on chromosome 5 for all of the three methods. The peak positions and the corresponding SNP effect estimates are given in Table 1. For chromosomes 1, 2 and 3, where one, two and two additive QTL were simulated, respectively, these peak positions match all the simulated QTL positions quite well, except that BayesA and BayesB missed one QTL on chromosome 3. For chromosomes 4 and 5, where an imprinted QTL and two epistatic QTL were simulated, respectively, either no peak was detected or the detected peak is far away from the simulated position. From these results, it seems that these methods could also serve as tools for QTL mapping and BayesCπ performed better in this respect. The drawback of BayesA and BayesB regarding the impact of prior hyperparameters and treating the prior probability π as known has been addressed by Gianola et al. [12] and Habier et al. [5]. Our results partially confirmed their arguments.

thumbnailFigure 1. Absolute values of estimated SNP effects by BayesA (A), BayesB (B) and BayesCπ (C).

Table 1. Peak positions of profiles of the estimated SNP effects and the corresponding estimated SNP effects

Correlations between GEBVs by different methods and between EBVs and GEBVs for the 20 sires

For the 20 sires, the reliability of traditional EBVs was 0.95. Table 2 shows the correlations between GEBVs by different methods and between EBVs and GEBVs of the 20 sires. The correlations between EBVs and GEBVs by different methods ranged from 0.933 to 0.966, and the highest correlation was given by GBLUP and the lowest by BayesCπ. In general, the GEBVs by different methods were highly correlated with the correlation coefficients over 0.95, indicating that the GEBVs for the 20 sires by different methods were quite consistent.

Table 2. Correlations between GEBVs by different methods (the first 4 columns) and between traditional EBVs and GEBVs (the last column) for the 20 sires

Correlations between GEBVs by different methods for the 1000 progenies without phenotypic values

Table 3 shows the correlations between GEBVs by different methods for the 1000 progenies without phenotypic values. The correlations ranged from 0.812 to 0.997, and the highest correlation was between TABLUP and BayesB, and the lowest between GBLUP and BayesCπ. The correlations among the three Bayesian methods and TABLUP are all very high (over 0.97), indicating high similarity in GEBVs from these methods, while the correlations between them and GBLUP are all less than 0.9, indicating some differences in GEBVs exist herein.

Table 3. Correlations between GEBVs by different methods for the 1000 progenies without phenotypic values.

Accuracies and biases of GEBVs

The availability of true breeding values (TBVs) of the 1000 progenies without phenotypic values allowed a more efficient assessment for methods. Table 4 shows the correlations of TBVs and GEBVs, which measure the accuracies of GEBVs, and regressions of TBVs on GEBVs, which measure the biases of GEBVs, by different methods. In terms of both accuracy and bias, the three Bayesian methods and TABLUP performed similarly with correlations over 0.92 and slightly downward bias. BayesB and BayesCπ were slightly more accurate than BayesA and TABLUP, while TABLUP yielded smallest bias. GBLUP gave the lowest accuracy and the highest downward bias.

Table 4. Accuracies and biases of GEBVs for the 1000 progenies without phenotypic values.

TABLUP is an improvement of GBLUP in the way that the G matrix is replaced with TA matrix. In construction of the TA matrix, not only the marker genotypes, but also the marker effects are taken into account. The advantage of the TA matrix over the G matrix is that it not only accounts for the Mendelian sampling term, but also puts greater weight on loci explaining more of genetic variance for the trait of interest. This makes TABLUP more accurate than GBLUP. On the other hand, although TABLUP and the Bayesian methods gave similar accuracies, TABLUP has two important features that Bayesian methods lack. The first is that the reliability of an individual's GEBV can be calculated by TABLUP through the method outlined for GBLUP by VanRaden [3] and Strandén et al. [13]. The second is that TABLUP can be extended to estimate GEBVs for individuals without genotypes by constructing a joint pedigree-genomic relationship matrix according to the rule proposed by Legarra et al. [14].

Conclusions

BayesA, BayesB, BayesCπ and TABLUP performed similarly and satisfactorily and remarkably outperformed GBLUP for genomic breeding value estimation in this dataset. TABLUP is a promising method for genomic breeding value estimation because of its easy computation of reliabilities of GEBVs and its easy extension to real life conditions such as multiple traits and consideration of individuals without genotypes.

List of abbreviations used

QTL: quantitative trait locus; MAS: marker assisted selection; GS: genomic selection; BLUP: best linear unbiased prediction; GBLUP: BLUP with a realized relationship matrix; TABLUP: BLUP with a trait specific relationship matrix; EBV(s): estimated breeding value(s); 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

CLW, PPM and ZZ contributed the data analyses and the manuscript. XDD and JFL contributed the modification of manuscript. WXF and ZQW carried out the data analyses. QZ coordinated the analyses and revised the manuscript. All authors have read and contributed to the final text of the manuscript.

Acknowledgements

This work was supported by the State High-Tech Development Plan of China (Grant No. 2008AA101002, 2011AA100302), the National Natural Science Foundation of China (Grant No. 30800776, 30972092, 31171200), Beijing Municipal Natural Science Foundation (Grant No. 6102016), and the Modern Pig Industry Technology System Program of Anhui Province.

This article has been published as part of BMC Proceedings Volume 6 Supplement 2, 2012: Proceedings of the 15th European workshop on QTL mapping and marker assisted selection (QTL-MAS). The full contents of the supplement are available online at http://www.biomedcentral.com/bmcproc/supplements/6/S2.

References

  1. Meuwissen THE, Hayes BJ, Goddard ME: Prediction of total genetic value using genome-wide dense marker maps.

    Genetics 2001, 157:1819-1829. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  2. Solberg TR, Sonesson AK, Woolliams JA, Meuwissen THE: Reducing dimensionality for prediction of genome-wide breeding values.

    Genetics Selection Evolution 2009, 41:29. BioMed Central Full Text OpenURL

  3. VanRaden PM: Efficient methods to compute genomic predictions.

    J Dairy Sci 2008, 91:4414-4423. PubMed Abstract | Publisher Full Text OpenURL

  4. Zhang Z, Liu J, Ding X, Bijma P, de Koning D-J, Qin Z: Best linear unbiased prediction of genomic breeding values using a trait-specific marker-derived relationship matrix.

    PLoS ONE 2010, 5(9):e12648. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  5. Habier D, Fernando RL, Kizilkaya K, Garrick DJ: Extension of the Bayesian alphabet for genomic selection.

    BMC Bioinformatics 2011, 12:186. PubMed Abstract | BioMed Central Full Text | PubMed Central Full Text OpenURL

  6. Yi N, Xu S: Bayesian LASSO for quantitative trait loci mapping.

    Genetics 2008, 179:1045-1055. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  7. Zou H, Hastie T: Regularization and variable selection via the elastic net.

    Journal of the Royal Statistical Society B 2005, 67:301-320. Publisher Full Text OpenURL

  8. Gianola D, Fernando RL, Stella A: Genomic-assisted prediction of genetic value with semiparametric procedures.

    Genetics 2006, 173:1761-1776. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  9. Long N, Gianola D, Rosa GJM, Weigel KA, Avendano S: Machine learning classification procedure for selecting SNPs in genomic selection: application to early mortality in broilers.

    J Anim Breed Genet 2007, 124:377-389. PubMed Abstract | Publisher Full Text OpenURL

  10. Ytournel F: Linkage disequilibrium and QTL fine mapping in a selected population. PhD thesis. Station de Génétique Quantitative et Appliquée, INRA; 2008. OpenURL

  11. Madsen P, Jensen J: DMU: A user's Guide. A Package for Analysing Multivariate Mixed Models.

    University of Aarhus, Faculty of Agricultural Sciences, Department of Animal Breeding and Genetics 2007. OpenURL

  12. Gianola D, de los Campos G, Hill WG, Manfredi E, Fernando RL: Additive Genetic Variability and the Bayesian Alphabet.

    Genetics 2009, 183:347-363. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  13. Strandén I, Garrick DJ: Technical note: derivation of equivalent computing algorithms for genomic predictions and reliabilities of animal merit.

    J Dairy Sci 2009, 92:2971-2975. PubMed Abstract | Publisher Full Text OpenURL

  14. Legarra A, Aguilar I, Misztal I: A relationship matrix including full pedigree and genomic information.

    J Dairy Sci 2009, 92:4656-4663. PubMed Abstract | Publisher Full Text OpenURL