Volume 5 Supplement 3
Proceedings of the 14th European workshop on QTL mapping and marker assisted selection (QTLMAS)
Genomic selection for QTLMAS data using a traitspecific relationship matrix
 Zhe Zhang^{1, 2},
 XiangDong Ding^{1},
 JianFeng Liu^{1},
 DirkJan de Koning^{3}Email author and
 Qin Zhang^{1}Email author
DOI: 10.1186/175365615S3S15
© Zhang et al; licensee BioMed Central Ltd. 2011
Published: 27 May 2011
Abstract
Background
The genomic estimated breeding values (GEBV) of the young individuals in the XIV QTLMAS workshop dataset were predicted by three methods: best linear unbiased prediction with a traitspecific markerderived relationship matrix (TABLUP), ridge regression best linear unbiased prediction (RRBLUP), and BayesB.
Methods
The TABLUP method is identical to the conventional BLUP except that the numeric relationship matrix is replaced with a traitspecific markerderived relationship matrix (TA). The TA matrix was constructed based on both marker genotypes and their estimated effects on the trait of interest. The marker effects were estimated in a reference population consisting of 2 326 individuals using RRBLUP and BayesB. The GEBV of individuals in the reference population as well as 900 young individuals were estimated using the three methods. Subsets of markers were selected to perform lowdensity marker genomic selection for TABLUP method.
Results
The correlations between GEBVs from different methods are over 0.95 in most scenarios. The correlations between BayesB using all markers and TABLUP using 200 or more selected markers to construct the TA matrix are higher than 0.98 in the candidate population. The accuracy of TABLUP is higher than 0.67 with 100 or more selected markers, which is nearly equal to the accuracy of BayesB with all markers.
Conclusions
TABLUP method performed nearly equally to BayesB method with the common dataset. It also provides an alternative method to predict GEBV with lowdensity markers. TABLUP is therefore a promising method for genomic selection deserving further exploration.
Background
With the availability of whole genome highdensity single nucleotide polymorphism (SNP) chips in many livestock and plant species, methods using the genomic information to detect the underling architecture of complex traits have become popular. In breeding programmes, the method to predict genomic estimated breeding values (GEBV) with wholegenome markers was termed genomic selection, as proposed by Meuwissen et al. [1]. The general idea of genomic selection is to estimate the effects of dense markers that are distributed across the wholegenome and then sum up the estimated marker effects to obtain the GEBV for genotyped individuals. Many methods have been proposed in the framework of genomic selection [1, 2]. In this study, a BLUP method using a trait specific relationship matrix (TA) in the mixed model equations was employed to estimate GEBVs. This method is coined TABLUP [3].
The aim of this study is to validate the TABLUP method and compare it with the ridge regression BLUP (RRBLUP) and the BayesB method using the simulated common dataset provided in the XIV QTLMAS workshop. We tried to assess the performance of different methods and explain the results either with or without knowing the simulated true breeding values (TBV).
Methods
Dataset
The common dataset consists of 3 226 individuals from five consecutive generations (F0  F4). Each of the 2 326 individuals in generation F0 to F3 has phenotypic records on two traits: a quantitative trait Q and a binary trait B. In this study, we only deal with trait Q. Individuals with phenotypic records (F0  F3) and without phenotypic records (F4) were treated as reference and candidate population, respectively. A genome consisting of 10 031 biallelic SNPs on 5 chromosomes with 100 million bps length each were simulated without any missing data and genotyping error. All SNPs were included in our analyses.
Estimation of SNP effects
where y is the vector of phenotypic values or estimated breeding values; b is a vector of fixed effects (including an overall mean); g_{ i } is the random effect of marker i; m is the total number of markers; e is a vector of residual errors; and X and Z_{i} are design matrices corresponding to b and g_{ i }. We assumed that residuals e are independent and follow a normal distribution, . All marker effects g_{ i } were also assumed to be normally distributed, for RRBLUP or a scaled inverse chisquare distribution with a proportion of π for BayesB.
In RRBLUP, the variance of marker effect was assumed to be identical for all markers and was calculated as , where is the total additive genetic variance which was estimated from the simulated data. In BayesB, the prior of the proportion of loci without effect, π, was estimated from a preanalysis of the simulated data. The Markov chain was run for 10 000 cycles with 100 cycles of MetropolisHastings sampling in each Gibbs sampling, and the first 2 000 cycles were discarded as burnin. All the samples of marker effects after burnin were averaged to obtain the marker effect.
Estimation of GEBVs
The GEBVs of all genotyped individuals were estimated using three methods: TABLUP, RRBLUP and BayesB. For RRBLUP and BayesB, the GEBV of a genotyped individual was calculated as the sum of all marker effects according to its marker genotypes as proposed by Meuwissen et al. [1].
where y is the vector of phenotypes of individuals in the reference population and u is the vector of breeding values of all genotyped individuals (F0  F4) with the variancecovariance matrix equal to , where TA is a trait specific relationship matrix, and the was estimated from the reference population via AIREML and the DMU software [4].
The TA matrix was constructed by using genotypes of all markers and their estimated effects obtained from either RRBLUP or BayesB (denoted as TAP and TAB, respectively), as proposed in our previous study [3]. As an alternative to using all markers, the top 5000, 2000, 1000, 500, 200 and 100 markers were selected from the whole dataset according to the sizes of their effects estimated from the whole dataset to construct the TA matrix.
Results and discussion
Variance components
The pedigree and phenotype data of generations F0  F3 were used to estimate the variance components. The estimated variances are 56.6 for additive genetic effect and 47.7 for residual effect. Therefore, the estimated heritability of trait Q is 0.54.
Estimates of marker effects
Correlation between GEBVs from different methods
Correlations between GEBVs from different methods.
RRBLUP  BayesB  TAP  TAB  

RRBLUP  0.989  0.971  0.973  
BayesB  0.938  0.982  0.957  
TAP  0.985  0.959  1.000  
TAB  0.942  0.999  0.963 
TABLUP with lowdensity markers
The correlations between TAB and BayesB are always the highest for all numbers of markers. Generally, the correlations increase with the increase of number of markers, but become almost constant when the numbers of markers are over 1 000. Even though only 500 markers (5 percent of all markers) were selected, the correlations of GEBVs between TABLUP and BayesB or RRBLUP are 0.92. In particular, the correlation between TAB and BayesB is close to 1.0 when the numbers of markers are over 500. This implies that TABLUP with only a proportion of selected markers might be recommendable for genomic selection in candidate populations because of the remarkably reduced cost for genotyping, even though there might be a little loss of accuracy.
Comparison with true breeding values
Comparsion with true breeding values
Method  No. marker  r  b  MSD 

BayesB  10031  0.676  0.957  41.9 
RRBLUP  10031  0.608  0.943  48.7 
TAB  10031  0.675  0.971  42.1 
5000  0.675  0.964  42.1  
2000  0.675  0.950  42.0  
1000  0.677  0.945  41.9  
500  0.678  0.945  41.8  
200  0.675  0.938  42.1  
100  0.672  0.927  43.5  
TAP  10031  0.626  1.074  46.9 
5000  0.632  1.045  46.4  
2000  0.640  0.990  45.5  
1000  0.643  0.951  45.3  
500  0.647  0.952  44.9  
200  0.647  0.930  45.0  
100  0.626  0.951  46.9 
Conclusions
TheTABLUP method performed comparably to the currently widely used BayesB and RRBLUP methods. It provides the possibility to use lowdensity markers for estimating GEBV with a relatively high accuracy. It is therefore a promising method for genomic selection and deserves further exploration.
List of abbreviations used
 QTL:

quantitative trait locus
 MAS:

marker assisted selection
 SNP:

single nucleotide polymorphism
 GEBV(s):

genomic estimated breeding value(s)
 TBV(s):

true breeding value(s)
 RRBLUP:

ridge regression best linear unbiased prediction
 TABLUP:

best linear unbiased prediction with trait specific relationship matrix
 TAB:

TABLUP with weights from BayesB
 TAP:

TABLUP with weights from RRBLUP.
Declarations
Acknowledgements
This work was supported by the State HighTech Development Plan of China (Grant No. 2008AA101002), the National Natural Science Foundation of China (Grant No. 30800776), the National Key Basic Research Program of China (Grant No.2006CB102104). DJK acknowledges support from the Biotechnology and Biological Sciences Research Council (BBSRC) through an Institute Strategic Program Grant to the Roslin Institute.
This article has been published as part of BMC Proceedings Volume 5 Supplement 3, 2011: Proceedings of the 14th QTLMAS Workshop. The full contents of the supplement are available online at http://www.biomedcentral.com/17536561/5?issue=S3.
Authors’ Affiliations
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