Gao et al. Genetics Selection Evolution 2012, 44:8 Ge n e t i c s
Se lec t ion
Evolut ion
http://www.gsejournal.org/content/44/1/8
RESEARCH Open Access
Comparison on genomic predictions using three
GBLUP methods and two single-step blending
methods in the Nordic Holstein population
Hongding Gao1,3, Ole F Christensen1, Per Madsen1, Ulrik S Nielsen2, Yuan Zhang3,
Mogens S Lund1 and Guosheng Su1*
Abstract
Background: A single-step blending approach allows genomic prediction using information of genotyped and
non-genotyped animals simultaneously. However, the combined relationship matrix in a single-step method may
need to be adjusted because marker-based and pedigree-based relationship matrices may not be on the same
scale. The same may apply when a GBLUP model includes both genomic breeding values and residual polygenic
effects. The objective of this study was to compare single-step blending methods and GBLUP methods with and
without adjustment of the genomic relationship matrix for genomic prediction of 16 traits in the Nordic Holstein
population.
Methods: The data consisted of de-regressed proofs (DRP) for 5 214 genotyped and 9 374 non-genotyped bulls.
The bulls were divided into a training and a validation population by birth date, October 1, 2001. Five approaches
for genomic prediction were used: 1) a simple GBLUP method, 2) a GBLUP method with a polygenic effect, 3) an
adjusted GBLUP method with a polygenic effect, 4) a single-step blending method, and 5) an adjusted single-step
blending method. In the adjusted GBLUP and single-step methods, the genomic relationship matrix was adjusted
for the difference of scale between the genomic and the pedigree relationship matrices. A set of weights on the
pedigree relationship matrix (ranging from 0.05 to 0.40) was used to build the combined relationship matrix in the
single-step blending method and the GBLUP method with a polygenetic effect.
Results: Averaged over the 16 traits, reliabilities of genomic breeding values predicted using the GBLUP method
with a polygenic effect (relative weight of 0.20) were 0.3% higher than reliabilities from the simple GBLUP method
(without a polygenic effect). The adjusted single-step blending and original single-step blending methods (relative
weight of 0.20) had average reliabilities that were 2.1% and 1.8% higher than the simple GBLUP method,
respectively. In addition, the GBLUP method with a polygenic effect led to less bias of genomic predictions than
the simple GBLUP method, and both single-step blending methods yielded less bias of predictions than all GBLUP
methods.
Conclusions: The single-step blending method is an appealing approach for practical genomic prediction in dairy
cattle. Genomic prediction from the single-step blending method can be improved by adjusting the scale of the
genomic relationship matrix.
* Correspondence: Guosheng.Su@agrsci.dk
1Department of Molecular Biology and Genetics, Aarhus University, DK-8830,
Tjele, Denmark
Full list of author information is available at the end of the article
© 2012 Gao 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.
mailto:Guosheng.Su@agrsci.dk
Table 1 Heritability (h2) of the traits, number of bulls in
training (Train) and validation datasets (Validgen) for
GBLUP and single-step blending
Trait h2 TrainGBLUP Trainsingle Dif
1 Validgen
2
Milk 0.39 3003 9137 6134 1395
Fat 0.39 3003 9137 6134 1395
Protein 0.39 3003 9137 6134 1395
Growth 0.30 2538 6690 4152 1640
Fertility 0.04 3037 10909 7872 1378
Birth index 0.06 3045 10586 7541 2167
Calving index 0.03 3040 11538 8498 1501
Mastitis 0.04 3006 9174 6168 1461
Health 0.02 3026 9050 6024 1214
Body conf. 0.30 2884 7492 4608 1380
Feet & Leg 0.10 2925 7727 4802 1379
Udder conf. 0.25 2928 7743 4815 1380
Milkingspeed 0.26 2928 7725 4797 1380
Temperament 0.13 2926 7691 4765 1371
Longevity 0.10 2980 8740 5760 916
Yield 0.39 3003 9137 6134 1395
1Number of additional non-genotyped bulls used in single-step blending
compared to GBLUP (Col.4 – Col.3); 2 Only genotyped bulls in the validation
dataset.
Gao et al. Genetics Selection Evolution 2012, 44:8 Page 2 of 8
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Background
Selection based on dense markers across the genome [1]
has become an important component of dairy cattle breed-
ing programs [2-7]. The accuracy of genomic prediction
relies on the amount of information used to derive the pre-
diction equation. In many genomic selection programs,
thousands of bulls which have been progeny tested over the
last decades have been genotyped and are used as national
reference populations. These have been extended by sharing
data across countries to include much more information,
such as the North American cooperation [8], the Euro-
Genomics project [7], and the joint Brown Swiss project
[9]. Generally, genomic predictions are based on the data of
all genotyped animals. However, in practice, not all indivi-
duals can be genotyped. To make use of as much informa-
tion as possible for genetic evaluation, it is appealing to
blend the genomic predicted breeding value and the trad-
itional estimated breeding values (EBV) into genomically
enhanced breeding values (GEBV) or to perform genomic
prediction using all information available simultaneously.
Many studies have shown that a linear model which
assumes that effects of all single nucleotide polymorph-
isms (SNP) are normally distributed with equal variance
performs as well as variable selection models for most traits
in dairy cattle [2,4]. Because such BLUP models are simple
and have low computational requirements, they have be-
come popular approaches for practical genomic prediction.
De-regressed proofs (DRP) [10,11] are generally used as the
response variable for genomic prediction since they can be
easily derived from the EBV that are usually available.
Several blending strategies, including multi-step and
single-step approaches, have been proposed to estimate
GEBV [4,5,12-18]. The core of a single-step procedure is
the integration of the marker-based relationship matrix
into the pedigree-based relationship matrix such that in-
formation of genotyped and non-genotyped animals is
used simultaneously [13-15]. Previous study by Su et al.
[18] reported that a single-step procedure resulted in
more accurate GEBV than a multi-step procedure.
Some studies [13-15,18] have reported that the com-
bined relationship matrix in a single-step method may
need to be adjusted because the marker- and pedigree-
based relationship matrices may not be on the same
scale, and different methods to adjust for this have been
proposed [19-22]. These adjustments may also benefit
genomic prediction using other models that integrate
marker- and pedigree-based relationship matrices, such
as a GBLUP model with a polygenic effect.
The purpose of this study was to compare single-step
blending and GBLUP methods with and without adjust-
ment of the genomic relationship matrix for genomic
prediction of 16 traits in the Nordic Holstein population.
De-regressed proofs were used as response variables in
both GBLUP and the single-step blending methods.
Methods
Data
Data consisted of 5 214 genotyped bulls born between
1974 and 2008 and 9 374 non-genotyped bulls born be-
tween 1950 and 2008. The bulls were divided into a
training and a validation population by birth date, Octo-
ber 1, 2001. Thus, the training data contained 3 045 gen-
otyped and 8 822 non-genotyped bulls born before this
date, and the validation data contained 2 169 genotyped
bulls born after this date. Non-genotyped bulls born
after October 1, 2001 were not used in training or valid-
ation. For the GBLUP methods described below, the
training data only included the 3 045 genotyped animals.
All 16 traits (sub-indices) in the Nordic Total Merit
index were assessed, including yield, conformation, fer-
tility, and health traits. For each trait, the DRP with reli-
ability less than 0.20 were excluded from the training
and the validation data. This removed 1.3%, 2.8% and
3.2% of DRP for birth index, fertility and health, respect-
ively, and less than 0.5% for the other traits. The num-
bers of individuals in the training and validation datasets
differed between traits (Table 1).
Marker genotypes were obtained using the Illumina Bo-
vine SNP50 BeadChip (Illumina, SanDiego, CA). The final
marker data included 48 073 SNPs for 5 214 bulls after
removing SNP with minor allele frequency (MAF) less
than 0.01 and locus average GenCall score less than 0.60.
Gao et al. Genetics Selection Evolution 2012, 44:8 Page 3 of 8
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De-regressed proofs (DRP) were used as response vari-
ables for genomic prediction in all approaches. Based on
EBV data of 14 588 progeny-tested bulls and pedigree data
of 42 144 animals, the de-regression was carried out by
applying the iterative procedure described in [23,24] using
the MiX99 package [25] and with the heritabilities shown
in Table 1, which were those used in Nordic cattle routine
genetic evaluation. A detailed description of the Nordic cat-
tle genetic evaluation and standardized procedures of EBV
is given in http://www.nordicebv.info/Routine+evaluation/.
Statistical models
Three GBLUP and two single-step blending methods
were used. All analyses were performed with the DMU
package [26,27], for estimating both the variance compo-
nents and breeding values.
Simple GBLUP
The basic GBLUP method [28,29] used to predict direct
genomic breeding values (DGV) was:
y ¼ 1μþ Zgþ e
where y is the data vector of DRP of genotyped bulls, μ
is the overall mean, 1 is a vector of ones, Z is a design
matrix that allocates records to breeding values, g is a
vector of DGV to be estimated, and e is a vector of resi-
duals. It was assumed that g � N 0;Gσ2g
� �
where σ2g is
the additive genetic variance, and G is the marker-based
genomic relationship matrix [28,29]. Allele frequencies
used to construct G were estimated from the observed
genotype data. Random residuals were assumed such
that e � N 0;Dσ2e
� �
where σ2e is the residual variance
and D is a diagonal matrix with elements dii ¼ 1=wi. The
weights wi account for heterogeneous residual variances
due to differences in reliabilities of DRP. They were defined
as wi¼ r2i =ð1� r2i Þ , where r2i is the reliability of DRP. The
reliability was calculated as r2i ¼ EDC=ðEDCþ kÞ , where
EDC is effective daughter contribution, and
k ¼ ð4� h2Þ=h2. To avoid possible problems caused by ex-
treme weight values, reliabilities larger than 0.98 were set to
0.98.
GBLUP with a polygenic effect
y ¼ 1μþ Zuþ Zgþ e
where u is the vector of residual polygenic effects that
are not captured by the SNP.
Here, we used an equivalent approach. Let gω ¼
uþ g , Var gωð Þ ¼ Aσ2u þ Gσ2g , where A is the pedigree-
based relationship matrix. Define σ2gω ¼ σ2u þ σ2g and
w ¼ σ2u= σ2uþσ2g
� �
, then w ¼ σ2u= σ2u þσ2g
� �
¼ ω σ2gω and
σ2g ¼ 1�ωð Þσ2gω , such that Var gωð Þ ¼ ωAþ 1�ωð ÞG½ �σ2gω
where ω is the ratio of residual polygenic to total additive
genetic variance. Thus, the above model is equivalent to
y¼1μþZgωþe:
It was assumed that gωeN 0; Gωσ2gω
� �
, where Gω is a
combined relationship matrix, Gω ¼ ωAþ 1�ωð ÞG . The
estimates of gω were defined as DGVω to distinguish from
the simple GBLUP and the single-step blending methods.
Adjusted GBLUP with a polygenic effect
The model was the same as the above GBLUP method
with a polygenic effect but G was adjusted to be on the
same scale as A. Then, the combined relationship matrix
was G�ω ¼ ωAþ 1�ωð ÞG� , where G� is the adjusted gen-
omic relationship matrix. The adjustment of G is
described below.
Original single-step blending
The original single-step blending method [15,17,18] uses
information from genotyped and non-genotyped indivi-
duals simultaneously by combining the genomic rela-
tionship matrix G with the pedigree-based numerator
relationship matrix A, using the following model:
y ¼ 1μþ Zaþ e
where y is the vector of DRP for both genotyped and non-
genotyped bulls, 1 is a vector of ones, Z is a design matrix,
and a is the vector of additive genetic effects, which are
the sum of the genomic and the residual polygenic effects.
It was assumed that aeN 0;Hσ2a� � , where matrix H is
the modified genetic relationship matrix that combines
pedigree-based relationship information [13,15]:
H ¼ Gω
A21A
�1
11 Gω
GωA
�1
11 A12
A21A
�1
11 GωA
�1
11 A12 þ A22 � A21A�111 A12
� �
where A11 is the sub-matrix of the pedigree-based rela-
tionship matrix (A) for genotyped animals, A22 is the sub-
matrix of A for non-genotyped animals, A12 (or A21) is
the sub-matrix of A for relationships between genotyped
and non-genotyped animals, and Gω ¼ 1� ωð ÞGþ ωA11,
where ω is a weight (within the range from 0.05 to 0.40 in
this study). The G matrix used in the single-step blending
was the same as in the GBLUP method. The inverse of H
[15,17] is
H�1¼ G
�1
ω � A�111
0
0
0
� �
þ A�1
Adjusted single-step blending
In the adjusted single-step blending method, the G matrix
was adjusted for the difference between the original
http://www.nordicebv.info/Routine+evaluation/
Table 2 Reliabilities of genomic predictions using
different methods
Trait GBLUP GBLUPAG GBLUPAG*
Milk 0.431 0.428 0.428
Fat 0.455 0.457 0.457
Protein 0.429 0.435 0.435
Growth 0.468 0.481 0.481
Fertility 0.411 0.419 0.419
Birth index 0.258 0.263 0.263
Calving index 0.301 0.303 0.303
Mastitis 0.362 0.359 0.359
Health 0.435 0.435 0.435
Body conf. 0.313 0.316 0.316
Feet & Leg 0.311 0.307 0.306
Udder conf. 0.366 0.357 0.357
Milkingspeed 0.292 0.295 0.295
Temperament 0.184 0.183 0.183
Longevity 0.320 0.334 0.334
Yield 0.431 0.437 0.438
Mean 0.360 0.363 0.363
GBLUP without a polygenic effect (GBLUP), GBLUP with a polygenic effect and
a weight of 0.2 (GBLUPAG), and adjusted GBLUP (i.e., using adjusted G matrix)
with a polygenic effect and a weight of 0.2 (GBLUPAG*).
Table 3 Intercept (INT) and regression coefficient (REG) of
DRP on genomic predictions from different methods
Trait GBLUP GBLUPAG GBLUPAG*
INT REG INT REG INT REG
Milk 2.028 0.920 1.455 0.960 1.445 0.961
Fat 2.837 0.877 2.385 0.912 2.377 0.913
Protein 3.906 0.847 3.182 0.883 3.169 0.884
Growth −0.240 1.045 −0.246 1.083 −0.246 1.084
Fertility 1.439 0.980 1.583 1.032 1.586 1.034
Birth index 0.846 0.865 0.707 0.926 0.705 0.927
Calving index 1.002 1.016 0.822 1.060 0.819 1.061
Mastitis 0.365 0.937 0.283 0.947 0.281 0.947
Health 0.585 1.156 0.579 1.175 0.579 1.176
Body conf. 1.172 0.864 0.965 0.895 0.961 0.896
Feet & Leg 1.389 1.009 1.284 1.055 1.283 1.056
Udder conf. 2.973 0.899 2.705 0.926 2.701 0.926
Milkingspeed 1.751 0.836 1.575 0.886 1.572 0.887
Temperament 2.665 0.727 2.579 0.751 2.578 0.752
Longevity 2.537 0.905 2.171 0.939 2.164 0.940
Yield 3.975 0.853 3.286 0.887 3.273 0.887
Mean Dev.1 1.857 0.107 1.613 0.093 1.609 0.093
GBLUP without a polygenic effect (GBLUP), GBLUP with a polygenic effect with
a weight of 0.2 (GBLUPAG) and adjusted GBLUP with a polygenic effect with a
weight of 0.2 (GBLUPAG*);
1Mean of absolute deviation from 1 for regression
coefficient and from 0 for intercept.
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genomic relationship matrix and pedigree relationship
matrix (A11), as proposed by previous studies [19,20]. The
G matrix was adjusted using two parameters α and β [21],
i.e.,
G
� ¼ Gβþ α;
which were derived from the following equations:
Avg:diagðGÞβþ α ¼ Avg:diagðA11Þ
Avg:offdiagðGÞβþ α ¼ Avg:offdiagðA11Þ
Matrix G* was then used to replace G to construct the
combined relationship matrix in the single-step blending
method.
The weights ω ranging from 0.05 to 0.40 were used to
construct Gω and G
�
ω for the single-step blending meth-
ods and for the GBLUP methods with a polygenic effect.
Validation
The reliabilities of genomic predictions were measured
as squared correlations between the predicted breeding
values and DRP for bulls in the validation data, divided
by the average reliability of the DRP in validation data. A
Hotelling-Williams t-test was used to test the difference
between the validation correlations obtained from these
five prediction methods [30,31]. Bias of genomic predic-
tions was measured as the regression of DRP on the
genomic predictions [32].
Results
Genomic predictions using the GBLUP method were
improved when a polygenic effect was included (Tables 2
and 3). With a relative weight of 0.2 on the residual poly-
genic variance, the average reliability of genomic predic-
tions for the 16 traits was 0.363, which was 0.3% points
higher than the average reliability from the simple
GBLUP. Moreover, the GBLUP method with a polygenic
effect reduced bias of genomic predictions. Averaged over
the 16 traits, the absolute deviation of the regression coef-
ficient (DRP on genomic prediction) from 1 was 0.093
when using the GBLUP methods with a polygenic effect
and 0.107 when using the simple GBLUP method. The
GBLUP methods with a polygenic effect slightly reduced
also bias in mean, as the intercept in the regression ana-
lysis was closer to 0, compared with the simple GBLUP.
For the two GBLUP methods with a polygenic effect, ad-
justment of the genomic relationship matrix had no effect
on predictive ability and bias.
Table 4 reports validation reliabilities of GEBV from the
two single-step blending methods and DGVω from the
GBLUP method with a polygenic effect (the adjusted
GBLUP method is shown as an example) for the 16 traits,
Table 4 Reliabilities of genomic predictions using different methods
Traits GBLUPAG* Singleori Singleadj Singleori
-GBLUPAG*
Singleadj
-GBLUPAG*
Singleadj
-Singleori
Milk 0.428 0.450 0.456 0.022* 0.028** 0.006*
Fat 0.457 0.458 0.466 0.001 0.009* 0.008**
Protein 0.435 0.437 0.446 0.002 0.011 0.009**
Growth 0.481 0.503 0.503 0.022** 0.022** 0.000
Fertility 0.419 0.425 0.431 0.006 0.012 0.005
Birth index 0.263 0.274 0.274 0.011 0.011 −0.001*
Calving index 0.303 0.328 0.329 0.025** 0.026** 0.002
Mastitis 0.359 0.383 0.384 0.024** 0.025** 0.000
Health 0.435 0.467 0.469 0.032 0.034* 0.003
Body conf. 0.316 0.317 0.317 0.001 0.001 0.000
Feet & Leg 0.306 0.296 0.296 −0.01 −0.01 0.000
Udder conf. 0.357 0.358 0.358 0.001 0.001 −0.001
Milkingspeed 0.295 0.312 0.312 0.017* 0.017* 0.000
Temperament 0.183 0.206 0.206 0.023* 0.023* 0.000
Longevity 0.334 0.415 0.415 0.081** 0.081** 0.000
Yield 0.438 0.436 0.446 −0.002 0.008 0.010**
Mean 0.363 0.379 0.382 0.016 0.019 0.003
Adjusted GBLUP with a polygenic effect with a weight of 0.2 (GBLUPAG*), original single-step blending (Singleori) and adjusted single-step blending (Singleadj) with
a weight of 0.2; *significant difference at p< 0.05; **significant difference at p< 0.01.
Table 5 Intercept (INT) and regression coefficient (REG) of
DRP on genomic predictions using different methods
Trait GBLUPAG* Singleori Singleadj
INT REG INT REG INT REG
Milk 1.445 0.961 1.225 0.963 0.843 0.975
Fat 2.377 0.913 2.136 0.910 1.752 0.932
Protein 3.169 0.884 2.967 0.877 2.441 0.898
Growth −0.246 1.084 −0.133 1.093 −0.103 1.095
Fertility 1.586 1.034 1.633 1.023 1.917 1.044
Birth index 0.705 0.927 0.608 1.054 0.583 1.057
Calving index 0.819 1.061 0.439 1.009 0.520 1.019
Mastitis 0.281 0.947 0.206 0.954 0.246 0.958
Health 0.579 1.176 0.677 1.138 0.793 1.148
Body conf. 0.961 0.896 0.652 0.913 0.605 0.918
Feet & Leg 1.283 1.056 1.058 1.028 1.051 1.030
Udder conf. 2.701 0.926 2.144 0.934 2.114 0.935
Milkingspeed 1.572 0.887 1.371 0.858 1.355 0.861
Temperament 2.578 0.752 1.816 0.757 1.795 0.760
Longevity 2.164 0.940 1.531 0.963 1.384 0.969
Yield 3.273 0.887 3.079 0.878 2.524 0.902
Mean Dev.1 1.609 0.093 1.355 0.084 1.252 0.080
Adjusted GBLUP with a polygenic effect with a weight of 0.2 (GBLUPAG*),
original single-step blending (Singleori) and adjusted single-step blending
(Singleadj) with weight a weight of 0.2;
1Mean of absolute deviation from 1 for
regression coefficient and from 0 for intercept.
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with a relative weight ω=0.20. The adjusted single-step
blending led to the highest reliability of genomic predic-
tions, followed by the original single-step blending, and the
GBLUP method resulted in the lowest reliability. Reliabil-
ities ranged from 0.206 to 0.503 (average 0.379) for the ori-
ginal single-step blending, from 0.206 to 0.503 (average
0.382) for the adjusted single-step blending, and from 0.183
to 0.481 (average 0.363) for the GBLUP method. In general,
single-step blending was better than the GBLUP method
and adjusted single-step blending was better than the ori-
ginal single-step blending, especially for production traits.
On average, reliabilities of genomic breeding values pre-
dicted using the original single-step blending were 1.6 %
higher than reliabilities from the adjusted GBLUP method,
but 0.3% lower than reliabilities from the adjusted single-
step blending.
The regression coefficients (Table 5) ranged from 0.757
to 1.138 (average absolute deviation from 1 equal to 0.084)
for the original single-step blending, from 0.760 to 1.148
(average absolute deviation 0.080) for the adjusted single-
step blending, and from 0.752 to 1.176 (average absolute
deviation 0.093) for the adjusted GBLUP method. Predic-
tions from the single-step blending methods appeared to
have less bias than predictions from GBLUP, and predic-
tions from the adjusted single-step blending has slightly less
bias than predictions from the original single-step blending
method. In addition, the two single-step blending methods
led to smaller absolute deviation of the intercept from 0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
0
.3
5
5
0
.3
6
0
0
.3
6
5
0
.3
7
0
0
.3
7
5
0
.3
8
0
0
.3
8
5
0
.3
9
0
Weights
R
e
lia
b
ili
tie
s
Single−ori
Single−adj
GBLUP−AG
GBLUP−AG*
Figure 1 The impact of different weights on reliability of
genomic predictions using different methods. GBLUP with a
polygenic effect (GBLUP-AG), adjusted GBLUP with a polygenic
effect (GBLUP-AG*), original single-step blending (Single-ori), and
adjusted single-step blending (Single-adj).
Gao et al. Genetics Selection Evolution 2012, 44:8 Page 6 of 8
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than the adjusted GBLUP method, indicating less bias in
mean.
Table 6 presents differences between groups of the top
300 bulls based on predictions from the different meth-
ods. For all 16 traits, more than 9% of the top 300 bulls
based on the adjusted GBLUP method differed from the
top 300 bulls based on the two single-step blending
methods. Differences between the two single-step blend-
ing methods were small, except for production traits,
which was in agreement with the small differences in
reliabilities of GEBV from the two single-step blending
methods.
In order to test the effect of different weighting factors
ω in forming Gω and H, eight values of ω between 0.05
and 0.40 were used for the two single-step blending meth-
ods and the two GBLUP methods with a polygenic effect.
On average, reliabilities varied from 0.356 to 0.363 over
the eight scenarios for the two GBLUP methods, from
0.372 to 0.379 for the original single-step blending, and
from 0.374 to 0.382 for the adjusted single-step blending
(Figure 1). The highest mean reliability was obtained when
using a weight of 0.15 or 0.20 for the four methods. The
mean absolute deviation of the regression coefficient from
1 varied from 0.080 to 0.104 for the two GBLUP methods,
from 0.074 to 0.098 for original single-step blending
and from 0.072 to 0.091 for adjusted single-step blending
Table 6 Differences between groups of the top 300 bulls
based on genomic prediction using different methods
Trait GBLUPAG* Vs.
Singleadj
GBLUPAG* Vs.
Singleori
Singleori Vs.
Singleadj
Milk 39 38 18
Fat 33 33 11
Protein 36 38 17
Growth 42 44 3
Fertility 29 33 8
Birth index 32 32 2
Calving index 38 39 4
Mastitis 32 33 1
Health 33 35 6
Body conf. 32 31 3
Feet & Leg 36 37 2
Udder conf. 38 40 3
Milkingspeed 35 35 1
Temperament 48 46 2
Longevity 41 44 8
Yield 27 31 16
Adjusted GBLUP with a polygenic effect with a weight of 0.2 (GBLUPAG*),
original single-step blending (Singleori), and adjusted single-step blending
(Singleadj) with a weight of 0.20, measured as the number of bulls that are not
among the top 300 based on the second method.
(Figure 2). Mean of absolute deviations tended to decrease
with increasing weights.
Discussion
This study applied three GBLUP and two single-step
blending methods for genomic prediction in Nordic
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
0
.0
6
0
.0
8
0
.1
0
0
.1
2
0
.1
4
Weights
M
e
a
n
D
e
v.
Single−ori
Single−adj
GBLUP−AG
GBLUP−AG*
Figure 2 The impact of different weights on the mean absolute
deviation from 1 of the regression coefficient of DPR on
prediction using different methods. GBLUP with a polygenic
effect (GBLUP-AG), adjusted GBLUP with a polygenic effect (GBLUP-AG*),
original single-step blending (Single-ori), and adjusted single-step
blending (Single-adj).
Gao et al. Genetics Selection Evolution 2012, 44:8 Page 7 of 8
http://www.gsejournal.org/content/44/1/8
Holsteins. Predictive abilities of the five methods were
compared in terms of reliability and bias. Results indi-
cated that both the original single-step blending and the
adjusted single-step blending were more accurate than
the three GBLUP methods because the two single-step
blending approaches used much more information to
predict breeding values. Similar results were reported by
Su et al. [18] for the Nordic Red population. In the current
study, the size of the training dataset for the single-step
blending methods was almost three times as large as
that for the three GBLUP methods (Table 1) since DRP of
the non-genotyped animals also provided information
through a combined relationship matrix. Including pedi-
gree information may also improve genomic predictions
because the SNP may not account for all additive genetic
variance. As shown in this study, including a residual poly-
genic effect in the GBLUP methods led to slightly higher
reliability of genomic predictions.
A regression coefficient of DRP on genomic predic-
tions less than 1 indicates overestimation of the variance
of genomic predictions (inflation), while a coefficient
larger than 1 indicates underestimation (deflation). The
two single-step blending methods led to less bias than
the three GBLUP methods, and the two GBLUP meth-
ods with a polygenic effect resulted in less bias than the
simple GBLUP method without a polygenic effect. The
problem of inflation of genomic predictions is critical
in practice [33-35] as it can give an unfair advantage to
juvenile over older progeny test bulls [17]. Aguilar et al.
[17] showed that this bias was reduced by weighting the
G and A matrices, and Liu et al. [36] found that includ-
ing a polygenic effect in a GBLUP model (random
regressions on SNP genotypes) led to less bias in gen-
omic predictions. The present study showed that the
weighting factor had an effect on the bias of genomic
predictions for all traits in the single-step blending
approaches and the GBLUP methods with a polygenic
effect. A weight of 0.40 resulted in the smallest mini-
mum absolute deviation from 1 for the regression of
GEBV or DGVω on DRP, averaged over the 16 traits, but
a loss of reliability around 0.8%, compared to a weight of
0.20, which led to highest average reliability and an ac-
ceptable average absolute deviation of regression coeffi-
cient from 1 (Figure 1, 2).
The adjusted single-step blending method resulted in
less bias than the original single-step blending for all set-
tings of the weight factor. In a simulation study, Vitezica
et al. [19] also found that the single-step method was
less biased and more accurate when the genomic rela-
tionship matrix was adjusted by a constant. Using
chicken data, Chen et al. [20] showed that unbiased eva-
luations can be obtained by adding a constant to the G
matrix that is based on current allele frequencies and
suggested that the optimal G has average of diagonal and
off-diagonal elements close to those of A11. Forni et al.
[22] also showed that re-scaling the G matrix is a reason-
able solution to avoid inflation in pig data. However, in
the present study, the adjusted G matrix did not improve
genomic predictions in the GBLUP methods with a poly-
genic effect. This suggests that, based on the present data,
adjustment of G has little effect on genomic prediction
when only genotyped animals are used, but may be im-
portant in other data where there is a large difference in
scale between G and A.
The results from the present study indicate that in-
creasing the weighting factor (0.40) reduces bias and
that weighting factors around 0.15 to 0.20 give the high-
est reliability but the optimal weighting factors differed
between traits. Similarly, Liu et al. [36] observed that the
optimal residual polygenic variance in a GBLUP model
(random regressions on SNP genotypes) with a polygenic
effect appears to differ among traits. Therefore, trait-
specific weighting factors should be used in the single-
step blending methods and the GBLUP methods with a
polygenic effect. In the near future, both bulls and hei-
fers may be pre-selected based on genomic EBV. This
will lead to biased predictions of breeding values in both
conventional and genomic evaluation procedures. In
such situations, appropriate methods to correct the bias
of predictions are required [37].
Christensen et al. [21] compared the adjusted and ori-
ginal single-step blending methods on pig data. In their
study, the improvement of prediction reliabilities by ad-
justment of G matrix is much larger, compared with the
results from the current study. This may be because there
was more inbreeding in the pig data, which resulted in
average values of the diagonal and off-diagonal elements
of A11 equal to 1.145 and 0.298, and estimates of β and α
equal to 0.895 and 0.298, respectively. In the present
study, the averages of the diagonal and off-diagonal ele-
ments of A11were 1.060 and 0.085, and estimates of β and
α were 0.976 and 0.085, i.e. closer to one and zero, re-
spectively. This means that the original G matrix was less
adjusted in this study compared to the study on pig data
by Christensen et al. [21].
Conclusions
The single-step blending methods can increase reliability
and reduce bias of genomic predictions. The adjusted
single-step blending method performed slightly better
than the original single-step blending method, both with
respect to reliability and bias of genomic predictions.
The weighting factor used in these single-step blending
methods had a small effect on reliability of genomic pre-
diction but an important effect on bias.
Competing interests
The authors declare that they have no competing interests.
Gao et al. Genetics Selection Evolution 2012, 44:8 Page 8 of 8
http://www.gsejournal.org/content/44/1/8
Acknowledgements
The authors thank Danish Cattle Federation, Faba co-op, Swedish Dairy
Association and Nordic Cattle Genetic Evaluation for providing data. This
work was performed in the project “Genomic Selection – from function to
efficient utilization in cattle breeding (grant no. 3405-10-0137)”, funded
under GUDP by the Danish Directorate for Food, Fisheries and Agri Business,
the Milk Levy Fund, VikingGenetics, Nordic Cattle Genetic Evaluation, and
Aarhus University.
Author details
1Department of Molecular Biology and Genetics, Aarhus University, DK-8830,
Tjele, Denmark. 2Danish Agricultural Advisory Service, DK-8200, Aarhus N,
Denmark. 3College of Animal Science and Technology, China Agricultural
University, 100193, Beijing, People Republic of China.
Authors’ contributions
HG performed statistical analysis and wrote the manuscript. OFC derived the
single-step methods and improved the manuscript. PM provided the
software, helped to the analysis and added valuable comments. USN
prepared the data. GS and MSL conceived the study, made substantial
contribution for the results interpretation and revised the manuscript. MSL,
GS and YZ coordinated the project. All authors read and approved the
manuscript.
Received: 28 October 2011 Accepted: 28 March 2012
Published: 28 March 2012
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doi:10.1186/1297-9686-44-8
Cite this article as: Gao et al.: Comparison on genomic predictions using
three GBLUP methods and two single-step blending methods in the
Nordic Holstein population. Genetics Selection Evolution 2012 44:8.
http://dmu.agrsci.dk/dmuv6_guide.5.0.pdf
http://dmu.agrsci.dk/dmuv6_guide.5.0.pdf
Abstract
Background
Methods
Results
Conclusions
Background
Methods
Data
link_Tab1
Statistical models
Simple GBLUP
GBLUP with a polygenic effect
Adjusted GBLUP with a polygenic effect
Original single-step blending
Adjusted single-step blending
Validation
Results
link_Tab2
link_Tab3
link_Tab4
link_Tab5
Discussion
link_Tab6
link_Fig1
link_Fig2
Conclusions
Competing interests
Author details
sectionArt9550672906260293
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