Two models that estimated genomic estimated breeding values (EBVs) were applied: one used constructed haplotypes (based on alleles of 20 markers) and IBD matrices, another used single SNP regression. Both models were applied with or without polygenic effect. A fifth model included only polygenic effects and no genomic information. The models needed to estimate 366,959 effects for the haplotype/IBD approach, but only 11,850 effects for the single SNP approach. The four genomic models identified 11 to 14 regions that had a posterior QTL probability >0.1. Accuracies of genomic selection breeding values for animals in generations 4¿6 ranged from 0.84 to 0.87 (haplotype/IBD vs. SNP). It can be concluded that including a polygenic effect in the genomic model had no effect on the accuracy of the total EBVs or prediction of the QTL positions. The SNP model yielded slightly higher accuracies for the total EBVs, while both models were able to detect nearly all QTL that explained at least 0.5% of the total phenotypic varianc

Calus, M.P.L.

Roos, S., de

Veerkamp, R.F.

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Estimating genomic breeding values from the QTL-MAS Workshop 
Data using a single SNP and haplotype/IBD approach
Mario PL Calus*1, Sander PW de Roos2 and Roel F Veerkamp1
Address: 1Animal Breeding and Genomics Centre, Animal Sciences Group, Wageningen University and Research Centre, P. O. Box 65, 8200 AB 
Lelystad, The Netherlands and 2CRV, PO Box 454, 6800 AL Arnhem, The Netherlands
Email: Mario PL Calus* - mario.calus@wur.nl; Sander PW de Roos - roos.s@hg.nl; Roel F Veerkamp - roel.veerkamp@wur.nl
* Corresponding author    
Abstract
Genomic breeding values were estimated using a Gibbs sampler that avoided the use of the
Metropolis-Hastings step as implemented in the BayesB model of Meuwissen et al., Genetics 2001,
157:1819–1829.
Two models that estimated genomic estimated breeding values (EBVs) were applied: one used
constructed haplotypes (based on alleles of 20 markers) and IBD matrices, another used single
SNP regression. Both models were applied with or without polygenic effect. A fifth model
included only polygenic effects and no genomic information.
The models needed to estimate 366,959 effects for the haplotype/IBD approach, but only 11,850
effects for the single SNP approach. The four genomic models identified 11 to 14 regions that
had a posterior QTL probability >0.1. Accuracies of genomic selection breeding values for
animals in generations 4–6 ranged from 0.84 to 0.87 (haplotype/IBD vs. SNP).
It can be concluded that including a polygenic effect in the genomic model had no effect on the
accuracy of the total EBVs or prediction of the QTL positions. The SNP model yielded slightly
higher accuracies for the total EBVs, while both models were able to detect nearly all QTL that
explained at least 0.5% of the total phenotypic variance.
Background
The applied models to estimate genomic breeding values
described in this paper, are derived from a multiple QTL
mapping model described by Meuwissen and Goddard
[1]. The methods are implemented using variable (i.e. in 
this case presence of a QTL or not on a putative QTL posi-
tion) selection via Gibbs sampling [2]. Thus, the applied
Bayesian method avoids the computationally costly
Metropolis-Hastings step that was implemented in the
BayesB model of Meuwissen et al. [3].
from 12th European workshop on QTL mapping and marker assisted selection
Uppsala, Sweden. 15–16 May 2008
Published: 23 February 2009
BMC Proceedings 2009, 3(Suppl 1):S10
<supplement> <title> <p>Proceedings of the 12th European workshop on QTL mapping and marker assisted selection</p> </title> <sponsor> <note>Publication of this supplement was supported by EADGENE (European Animal Disease Genomics Network of Excellence).</note> </sponsor> <note>Proceedings</note> <url>http://www.biomedcentral.com/content/pdf/1753-6561-3-S1-info.pdf</url> </supplement>
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BMC Proceedings 2009, 3(Suppl 1):S10 http://www.biomedcentral.com/1753-6561/3/S1/S10Methods
Parameterization of the model
The data were analyzed with five different models consid-
ering only additive genetic effects. The first model (called
'HAP_POL') was:
where yi is the phenotype of animal i, μ is the overall
mean, si is a fixed effect for sexe, ui is the polygenic effect
of animal i, vj is the direction of the QTL effects of the hap-
lotypes at putative QTL position j, qij1 (qij2) is the size of
the QTL effect for the paternal (maternal) haplotype of
animal i at putative QTL position j, and ei is the residual
term for animal i [1]. Note that the total effect of a haplo-
type is modeled as qij. × vj, and that qij. and vj may have a
positive or negative value. The covariance among poly-
genic effects (u.) was modeled as A × , where A is the
relationship matrix which was based on the full pedigree
and  is the polygenic variance. The second model
(called 'HAP_NOPOL') was the same as HAP_POL, but
omitted the polygenic component. The HAP models
assumed a putative QTL in the midpoint of each marker
bracket. The covariances among haplotypes at bracket j
(q.j.) were modeled as Hj, which is the matrix of estimated
IBD probabilities among the haplotypes at the midpoint
of bracket j. The variance of q.j .was assumed 1, while vj is
a scale parameter that accommodates for a bracket to have
a large (small) effect, if a QTL is (not) present. IBD prob-
abilities between haplotypes were calculated using the
algorithm of Meuwissen and Goddard [4], which com-
bines linkage disequilibrium with linkage information
and, for each bracket j, considers 20 surrounding markers
and all available pedigree information. The effective pop-
ulation size was assumed 100 and the number of genera-
tions since an arbitrary founder population was also
assumed 100, as in Meuwissen and Goddard [1]. All pairs
of base haplotypes (i.e haplotypes of first generation of
genotyped animals) with an IBD probability above 0.95
were clustered, using a hierarchical clustering algorithm. If
the matrix of IBD probabilities among base haplotypes
was not positive definite after clustering, the matrix was
bended by adding |min_eigenval| + 0.01 to all the diagonal
elements, where |min_eigenval| is the absolute value of the
lowest (negative) eigenvalue. The matrix was subse-
quently inverted by LU denomposition. The elements in
 for the descendant haplotypes were then calculated
using the algorithm of Fernando and Grossman (1989)
[5]. When the IBD probability of descendant haplotypes
with one of their parental haplotypes exceeded 0.95, the
descendant haplotype was clustered with this parental
haplotype.
The third applied model called 'SNP_POL' was:
where yi, si, μ, and ui are as in model 1, vj is the direction of
the effects of the alleles at marker locus j, qij1 and qij2 are
the sizes of the marker effects of animal i at marker locus
j, and ei is the residual term for animal i. The fourth model
(called 'SNP_NOPOL') was the same as SNP_POL, but
omitted the polygenic component.
For reasons of comparison, a fifth model was applied,
which did include the polygenic effects, but omitted the
SNP effects. This model was called 'POL'.
Solving algorithm
For all models, a Markov chain Monte Carlo method
using Gibbs sampling was used to obtain posterior esti-
mates for all the effects in the model [1]. The scale param-
eter of a putative QTL at locus j, vj, was sampled from a
normal distribution N(0, ), if a QTL was present in
γ μi i i ij ij
j
j is u q q v e= + + + +( ) +
=
∑ 1 215994  
σ G
2
σ G
2
H j
−1
γ μi i i ij ij
j
j is u q q v e= + + + +( ) +
=
∑ 1 216000  
σ V
2
Table 1: Correlations (reflecting accuracy) between true and estimated breeding values, and coefficients of regression of true breeding 
values on estimated breeding values (estimated using all five models) for animals without phenotypes in generations 4, 5 and 6.
Method (Group) Gen-4 Gen-5 Gen-6 Gen-4–6
Corr. b r2 Corr. b r2 Corr. b r2 Corr. b r2
HAP_POL (B1) 0.87 0.872 0.75 0.83 0.850 0.70 0.81 0.807 0.66 0.84 0.854 0.70
HAP_NOPOL (B2) 0.87 0.882 0.76 0.84 0.863 0.71 0.81 0.801 0.66 0.84 0.859 0.71
SNP_POL (B3) 0.86 0.893 0.73 0.87 0.969 0.75 0.86 0.942 0.74 0.86 0.943 0.74
SNP_NOPOL (B4) 0.87 0.910 0.76 0.87 0.982 0.76 0.87 0.958 0.76 0.87 0.958 0.75
POL (B5) 0.26 0.435 0.07 0.05 0.104 0.002 0.15 0.452 0.02 0.07 0.143 0.01Page 2 of 4
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BMC Proceedings 2009, 3(Suppl 1):S10 http://www.biomedcentral.com/1753-6561/3/S1/S10bracket j, whereas vj was sampled from N(0, /100) if
no QTL was not present in bracket j. The variance of vj,
, was sampled from an scaled inverse chi-square distri-
bution with a prior variance of 0.058. This prior variance
was calculated as the additive genetic variance, estimated
using model 'POL', divided by 30, i.e. assuming 30 addi-
tive and unrelated QTL affecting the trait, across the 6
chromosomes. The presence of a QTL in bracket j was
sampled from a Bernoulli distribution with probability
equal to , where
P(vj| ) is the probability of sampling vj from N(0, ),
i.e. , and Prj is prior probability of the pres-
ence of a QTL in bracket j. Prj was calculated per bracket as
five times (i.e. assuming five QTL per chromosome) the
length of bracket j, divided by the total length of all the
brackets on the chromosome. More details on the prior
distributions and the fully conditional distributions can
be found in Meuwissen and Goddard [1]. The Gibbs sam-
pler was implemented using residual updating, which was
proven to be an computationally efficient way to solve the
equations [6]. The Gibbs sampler was run for all models
for 30,000 iterations and 3,000 iterations were removed
as burn-in.
Results
Estimates for the mean and both sexes were small in the
SNP and HAP models, i.e. the estimates ranged from 7.3E-
05 to 3.2E-02 (results not shown). Accuracy of estimated
breeding values, i.e. the correlation with the simulated
breeding values, were calculated for all five models for
animals without phenotypic information (Table 1). The
accuracy of estimated breeding values was similar across
the four genomic models. However, the accuracy of the
HAP models decreased across generations, while the accu-
racy of the SNP models appeared to be constant across
generations. Coefficients of the regression of true breeding
values on estimated breeding values were 0.85–0.86 for
the HAP models and 0.94–0.96 for the SNP models, indi-
cating that the bias of the estimated breeding values was
larger for the HAP models than for the SNP models. The
correlations among estimated breeding values (EBVs) of
animals with phenotypes and the correlation with their
phenotypes were calculated (Table 2). The correlation
between phenotypes and EBVs was largest for the POL
model, while both for the SNP and HAP models it was
slightly higher when the polygenic effect was included,
compared to when it was excluded. The correlations
among EBVs of animals without phenotypes were also cal-
culated (Table 3). Correlations among EBVs from the SNP
and HAP models were all > 0.94, indicating small differ-
ences in predictive ability between those models. The cor-
relation between the POL and the other models were
much lower for animals without phenotypes (0.21–0.23;
Table 3), compared to animals with phenotypes (0.76–
0.78; Table 2).
Posterior QTL probabilities > 0.1 were plotted along the
genome for all genomic models (Figure 1). All models
were able to detect nearly all QTL that explained at least
0.5% of the total phenotypic variance.
σ V
2
σ V
2
P V
2
j
P V
2
j P V
2
( | ) Pr
( | ) Pr ( | / ) ( Pr )
v j
v j v j j
σ
σ σ
×
× + × −100 1
σ V
2 σ V
2
1
2
2
2
πσ
σ
V
2
V
2
e
−
v j
Table 3: Correlations between estimated breeding values for animals without phenotypes, estimated using all five models.
Model HAP_NOPOL SNP_POL SNP_NOPOL POL
HAP_POL 0.993 0.941 0.942 0.209
HAP_NOPOL 0.946 0.949 0.205
SNP_POL 0.994 0.230
SNP_NOPOL 0.228
Table 2: Correlations between phenotypes and estimated breeding values for animals with phenotypes, estimated using all five 
models.
Model HAP_POL HAP_NOPOL SNP_POL SNP_NOPOL POL
Phenotype 0.639 0.627 0.625 0.615 0.799
HAP_POL 0.998 0.989 0.988 0.782
HAP_NOPOL 0.991 0.990 0.771
SNP_POL 0.997 0.770
SNP_NOPOL 0.762Page 3 of 4
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Discussion
The presented methods have been applied in multiple
studies, where they proved to be able to detect QTL [1,7]
as well as estimate genomic breeding values accurately [7-
9]. In the present study, differences in accuracies of the
EBVs of the HAP and SNP models were small, which is in
agreement with the finding that for r2 values between
adjacent markers of ~0.2 the differences in accuracies of
the HAP and SNP models are negligible [8]. Apparently,
including linkage analysis information next to linkage dis-
equilibrium information in the model (i.e. going from the
SNP to the HAP model), does not yield additional infor-
mation to estimate effects more accurately.
Interestingly, the POL model yielded a higher correlation
between EBV and phenotype than the genomic models.
However, the accuracy of the EBVs for animals with the
genomic models were 0.93–0.94, while the accuracy for
the same animals were only 0.70 for the POL model
(results not shown).
Conclusion
For the provided data set, including a polygenic effect in
the genomic model had no effect on the accuracy of the
total EBVs or prediction of the QTL positions. The SNP
model yielded slightly higher accuracies for the total EBVs,
while both models were able to detect nearly all QTL that
explained at least 0.5% of the total phenotypic variance.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
MPLC carried out the analyses and drafted the manu-
script. APWR helped to draft the manuscript and to inter-
pret the results. RFV helped to interpret the results and
present them in the manuscript. All authors read and
approved the final manuscript.
Acknowledgements
Hendrix Genetics, CRV B.V., and NWO-Casimir (The Netherlands Organ-
ization for Scientific Research) are acknowledged for financial support. The 
authors thank John Bastiaansen for suggestions and comments on the 
results of this study.
This article has been published as part of BMC Proceedings Volume 3 Sup-
plement 1, 2009: Proceedings of the 12th European workshop on QTL 
mapping and marker assisted selection. The full contents of the supplement 
are available online at http://www.biomedcentral.com/1753-6561/
3?issue=S1.
References
1. Meuwissen THE, Goddard ME: Mapping multiple QTL using link-
age disequilibrium and linkage analysis information and mul-
titrait data.  Genetics Selection Evolution 2004, 363:261-279.
2. George EI, McCulloch RE: Variable selection via gibbs sampling.
Journal of the American Statistical Association 1993, 88:881-889.
3. Meuwissen THE, Hayes BJ, Goddard ME: Prediction of total
genetic value using genome-wide dense marker maps.  Genet-
ics 2001, 157(4):1819-1829.
4. Meuwissen THE, Goddard ME: Prediction of identity by descent
probabilities from marker-haplotypes.  Genet Sel Evol 2001,
336:605-634.
5. Fernando RL, Grossman M: Marker assisted selection using best
linear unbiased prediction.  Genet Sel Evol 1989, 214:467-477.
6. Legarra A, Misztal I: Computing strategies in genome-wide
selection.  J Dairy Sci 2008, 911:360-366.
7. De Roos APW, Schrooten C, Mullaart E, Calus MPL, Veerkamp RF:
Breeding value estimation for fat percentage using dense
marker maps on Bos taurus autosome 14.  J Dairy Sci 2007,
90:4821-4829.
8. Calus MPL, Meuwissen THE, De Roos APW, Veerkamp RF: Accu-
racy of genomic selection using different methods to define
haplotypes.  Genetics 2008, 178:553-561.
9. Calus MPL, Veerkamp RF: Accuracy of breeding values when
using and ignoring the polygenic effect in genomic breeding
value estimation with a marker density of one SNP per cM.
J Anim Breed Genet 2007, 124(6):362-368.
Posterior QTL probabilities along the genome, estimated using HAP_POL, HAP_NOPOL, SNP_POL, and SNP_NO OL, and the position of QTL that xplained > 0.5% van de phe typic varianceFigure 1
Posterior QTL probabilities along the genome, esti-
mated using HAP_POL, HAP_NOPOL, SNP_POL, 
and SNP_NOPOL, and the position of QTL that 
explained > 0.5% van de phenotypic variance.
0
0.1
0.2
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0.5
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1 SNP_POL
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True QTL positionsPage 4 of 4
(page number not for citation purposes)


Mapping multiple QTL using linkage disequilibrium and linkage analysis information and multitrait data. Genetics Selection Evolution

Marker assisted selection using best linear unbiased prediction. Genet Sel Evol

ME: Prediction of identity by descent probabilities from marker-haplotypes. Genet Sel Evol

Misztal I: Computing strategies in genome-wide selection.

Prediction of total genetic value using genome-wide dense marker maps. Genetics

RF: Breeding value estimation for fat percentage using dense marker maps on Bos taurus autosome 14. J Dairy Sci

Estimating genomic breeding values from the QTL-MAS Workshop Data using a single SNP and haplotype/IBD approach

Two models that estimated genomic estimated breeding values (EBVs) were applied: one used constructed haplotypes (based on alleles of 20 markers) and IBD matrices, another used single SNP regression. Both models were applied with or without polygenic effect. A fifth model included only polygenic effects and no genomic information. The models needed to estimate 366,959 effects for the haplotype/IBD approach, but only 11,850 effects for the single SNP approach. The four genomic models identified 11 to 14 regions that had a posterior QTL probability &gt;0.1. Accuracies of genomic selection breeding values for animals in generations 4¿6 ranged from 0.84 to 0.87 (haplotype/IBD vs. SNP). It can be concluded that including a polygenic effect in the genomic model had no effect on the accuracy of the total EBVs or prediction of the QTL positions. The SNP model yielded slightly higher accuracies for the total EBVs, while both models were able to detect nearly all QTL that explained at least 0.5% of the total phenotypic varianc

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Estimating genomic breeding values from the QTL-MAS Workshop Data using a single SNP and haplotype/IBD approach

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