pone.0093017 1..12
Improving the Accuracy of Whole Genome Prediction for
Complex Traits Using the Results of Genome Wide
Association Studies
Zhe Zhang1,2, Ulrike Ober2, Malena Erbe2, Hao Zhang1, Ning Gao1, Jinlong He1, Jiaqi Li1*,
Henner Simianer2*
1 National Engineering Research Center for Breeding Swine Industry, Guangdong Provincial Key Lab of Agro-Animal Genomics and Molecular Breeding, College of Animal
Science, South China Agricultural University, Guangzhou, China, 2 Department for Animal Sciences, Animal Breeding and Genetics Group, Georg-August-Universität
Göttingen, Göttingen, Germany
Abstract
Utilizing the whole genomic variation of complex traits to predict the yet-to-be observed phenotypes or unobserved
genetic values via whole genome prediction (WGP) and to infer the underlying genetic architecture via genome wide
association study (GWAS) is an interesting and fast developing area in the context of human disease studies as well as in
animal and plant breeding. Though thousands of significant loci for several species were detected via GWAS in the past
decade, they were not used directly to improve WGP due to lack of proper models. Here, we propose a generalized way of
building trait-specific genomic relationship matrices which can exploit GWAS results in WGP via a best linear unbiased
prediction (BLUP) model for which we suggest the name BLUP|GA. Results from two illustrative examples show that using
already existing GWAS results from public databases in BLUP|GA improved the accuracy of WGP for two out of the three
model traits in a dairy cattle data set, and for nine out of the 11 traits in a rice diversity data set, compared to the reference
methods GBLUP and BayesB. While BLUP|GA outperforms BayesB, its required computing time is comparable to GBLUP.
Further simulation results suggest that accounting for publicly available GWAS results is potentially more useful for WGP
utilizing smaller data sets and/or traits of low heritability, depending on the genetic architecture of the trait under
consideration. To our knowledge, this is the first study incorporating public GWAS results formally into the standard GBLUP
model and we think that the BLUP|GA approach deserves further investigations in animal breeding, plant breeding as well
as human genetics.
Citation: Zhang Z, Ober U, Erbe M, Zhang H, Gao N, et al. (2014) Improving the Accuracy of Whole Genome Prediction for Complex Traits Using the Results of
Genome Wide Association Studies. PLoS ONE 9(3): e93017. doi:10.1371/journal.pone.0093017
Editor: Xiaodong Cai, University of Miami, United States of America
Received July 16, 2013; Accepted February 27, 2014; Published March 24, 2014
Copyright: � 2014 Zhang et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was supported by the National Natural Science Foundation of China (31200925, 31371258), the earmarked fund for China Agriculture
Research System (CARS-36), the Ph.D. Programs Foundation (the Doctoral Fund) of Ministry of Education of China (20124404120001), the Guangdong Natural
Science Foundation (S2012040007753), the Key Scientific and Technological Projects of Guangzhou (11A62100441). HS, UO and ME acknowledge the funding by
the German Federal Ministry of Education and Research within the AgroClustEr ‘‘Synbreed – Synergistic plant and animal breeding’’ (Funding ID: 0315528C). The
funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: hsimian@gwdg.de (HS); jqli@scau.edu.cn (JL)
Introduction
Predicting the yet-to-be observed phenotypes or unobserved
genetic values for complex traits and inferring the underlying
genetic architecture utilizing genomic data is an interesting and
fast developing area in the context of human disease studies as well
as in animal and plant breeding [1,2,3]. In this context, two
predominant approaches were proposed: (i) whole genome
prediction (WGP) [2,4] and (ii) genome wide association studies
(GWAS) [5,6] or quantitative trait locus (QTL) mapping
studies[7,8,9]. Both concepts use genomic and phenotypic data
in a combined analysis.
GWAS take the road to detect markers significantly associated
with a trait by setting a stringent P-value. Thousands of significant
loci associated with complex traits have recently been found for
model organisms [6,10,11], as well as crops [12,13,14,15,16],
livestock [17,18,19,20,21] and the human population [22,23,24].
However, these loci typically explain only a small fraction of the
total genetic variance. A prominent example is human height, for
which tens of loci explain only ,5% of the genetic variance [25], a
phenomenon also called ‘‘missing heritability’’ in the literature
[26,27].
By fitting all markers in a prediction model simultaneously,
whole genome prediction (WGP) has largely promoted the usage
of whole genome markers, also revolutionizing commercial
breeding systems and showing good results both in simulation
studies [4,28] and analyses of real data [29,30,31]. Furthermore,
WGP is promising with respect to human disease studies [2,32,33].
The genetic architecture of the underlying complex trait together
with the selected statistical prediction approach were found to
have a large effect on the prediction accuracy [34,35,36]. Different
prediction methods assume that the genetic effects of the loci
follow a normal distribution [4], alternative distributions like the t-
distribution [4], the double exponential distribution [37] or other
distributions [38]. Performance of these models depends on how
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http://creativecommons.org/licenses/by/4.0/
closely the model assumptions represent the true underlying
genetic architecture [34,35].
In the context of GWAS, it is not difficult to detect QTLs with
large or moderate effects within large data sets for traits with high
heritability [39], and it is also easier to conduct an accurate WGP
in these cases [1]. However, the power to detect QTLs in a GWAS
and the accuracy of WGP are unfavorable in case of small data
sets and/or traits of low heritability [1,39].
So far, results of GWAS and WGP have mostly been considered
independently from each other, depending on whether the aim
was to decode the genetic architecture (GWAS) or to accurately
predict the unobserved phenotypes or genetic values (WGP).
However, both approaches require the same type of data: a subset
of a population for which phenotypes and genotypes are available.
Since it is well known that the genetic architecture of complex
traits affects the accuracy of genomic prediction [34,35,40,41],
some methods originally developed for WGP were recently used in
a GWAS to detect loci significantly associated with the trait under
consideration [20,42]. Conversely, results from GWAS have
already been pronounced to be useful to improve WGP [20].
However, it is yet to be investigated how to utilize significant
QTLs identified in GWAS to improve WGP and to which extent
existing knowledge of the genetic architecture of complex traits
can help improving WGP.
In this study, we propose a new approach of utilizing already
existing knowledge of genetic architectures in form of significant
QTL regions obtained in independent association studies to
improve the accuracy of WGP. This includes a new strategy of
building trait-specific genomic relationship matrices used in a best
linear unbiased prediction (BLUP) approach.
Besides the fact that the genetic architecture of a complex trait is
known to affect the accuracy of genomic prediction as well as
model selection [34,35], there is another motivation for incorpo-
rating prior knowledge into the WGP model: WGP has always
been performed within a specific population [4] or with the
combination of raw data sets from several populations [31,43,44].
In these cases, the power of detecting and utilizing the genetic
architecture is limited by the size of the data set used. In contrast
to this, there is a large number of publicly available QTL regions
and top SNPs detected in previous GWAS, which potentially
reveal the genetic architecture of complex traits in a comprehen-
sive way and which might therefore be used to enhance WGP in
such a situation.
We will demonstrate in this study, that the performance of
WGP can be improved by including the publicly available GWAS
results (in case the genetic architecture is important for the
complex trait under consideration) and that WGP accuracy can be
improved especially in situations where the prediction accuracy is
limited by a small sample size of the data set or a small heritability.
The remainder of the paper is organized as follows: We will first
propose a generalized way of building genomic relationship
matrices which are trait-specific. Based on this suggestion, we will
illustrate with a dairy cattle and a rice data set that using already
existing GWAS results from publicly available databases to build
trait-specific genomic relationship matrices improves the accuracy
of WGP compared to two well investigated WGP approaches:
GBLUP [45] and BayesB [4]. We will finally study the impact of
sample size and heritability on the relative performance of our
approach with simulated data and discuss the implications of the
new approach, which we term ‘‘BLUP|GA’’ (‘‘BLUP approach
given the Genetic Architecture’’) in the following.
To our knowledge, this is the first study proposing a formal way
to improve the accuracy of WGP by directly incorporating results
from publicly available GWAS results and which validates the
effectiveness of the new approach using real data sets.
Methodology: A New Approach for Building Trait-Specific
Genetic Variance-Covariance Matrices
Several approaches have already been proposed for building
genomic relationship matrices by estimating the realized genomic
relationship matrix [45,46,47,48]. And various rules were tested to
correct the genotype matrix for allele frequency at single marker
level to centered and standardized marker genotypes [45,46,48].
All of these rules aim at obtaining an unbiased estimate of the
relationship coefficient between pairs of individuals, and all of
them assume that the effects of all loci are drawn from the same
normal distribution.
Following the approach of VanRaden [45], the commonly used
genomic relationship matrix G is defined as
G~
MIMT
2
Xm
i~1
pi(1{pi)
ð1Þ
Here, I is an identity matrix and the matrix M contains the
corrected SNP genotypes, with the number of rows equal to the
number of individuals and the number of columns equal to the
number of markers. Genotypes are coded as 0, 1 and 2,
representing the number of copies of the second allele. For locus
i, the original genotype is corrected for the allele frequency of the
second allele at locus i in the base population by subtracting 2pi.
We used a uniform value of pi = 0.5 for all SNPs to build the
genomic relationship matrix in this study, since the accuracy of
WGP is known to be unaffected by the use of different allele
frequencies for correction [48,49,50]. By using the identity matrix
I in equation (1), it is implicitly assumed that all loci contribute
equally to the variance-covariance structure.
In general, the variance contribution for different loci may be
different [51], since the distribution of effect sizes is variable across
traits. Zhang et al. [51] therefore proposed to use a trait-specific
matrix TA, given by
TA~
MDMT
2
Xm
i~1
pi(1{pi)
ð2Þ
where D is a diagonal matrix with marker weights for each locus
on the diagonal to represent the relative size of variance explained
by the corresponding loci. In the present study, we propose to use
a similar approach, in which only a subset of ‘‘important’’ markers
are weighted accordingly, instead of assigning variable weights to
the full set of available markers. This approach is computationally
less demanding when building the covariance matrix. Since for
most quantitative traits only a very small proportion of loci was
found to have significant effects and a large number of other loci
was found to have very small effects (see e.g. adult height in
humans [25,52] or flowering time in maize [13]), a realistic
weighting strategy is giving individual and large weights to loci
with large effects, and relatively smaller and uniform weights to the
rest of the loci. Based on this, we can divide the m available
markers into two groups, including m1 markers with large and
m2~m{m1 with small effects. In the following, the marker
genotype matrices for these two marker groups will be denoted by
M1, and M2, including m1 and m2 markers, respectively, and M
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will be sorted such that M = [M1, M2]. In this study, classification
of the markers to M1 was based on GWAS results obtained from
public database, and this is described in the section ‘Approach to
infer marker weights from GWAS results’.
We will further use an overall weight v for large effect markers
in M1 and we define c~
Xm
i~1
2pi(1{pi) as well as
c1~
Xm1
i~1
2pi(1{pi).
We finally propose to use the matrix
D~
1
c
diag
c
c1
vh1z(1{v),:::,
c
c1
vhm1z(1{v)|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
m1entries
, (1{v),:::,(1{v)|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}
m2entries
0
BBB@
1
CCCA
in equation (2), where h1, h2, …,hm1 are certain marker weights
which have to be obtained beforehand. This approach is
equivalent to using
T~vSz(1{v)G ð3Þ
with S~
M1diag(h1,:::,hm1 )M
T
1
c1
and G~
MIMT
c
as new trait-
specific variance-covariance matrix. Hereby, S is based on the set
of markers being ‘‘important’’ for the considered trait, whereas G
corresponds to the standard genomic relationship matrix proposed
by VanRaden [45]. Note that when we use equal allele frequencies
(pi = 0.5) in c and c1, then
c1
c
is the proportion of all markers which
are contained in M1, that is
m1
m
. The matrix S is supposed to
capture the genetic architecture part for the trait under
consideration. Further note that T equals G for v~0, and that
it equals TA [51] with D = diag(h1,:::,hm1 )in case v~1and
M~M1.
To build the T matrix given in equation (3), three additional
parameters are needed: the subset of m1 markers to build S, the
overall weight v for S, and a vector of marker weights
h~(h1,:::,hm1 )
T
corresponding to each marker used in S. Note
that in the present study the vector of weights h was always
rescaled after choosing its components by multiplying each entry
by
m1Pm1
i~1 hi
to keep the S and G being in the same scale.
In the following, we will consider these three parameters as
variables which have to be specified within a study. The subset of
m1 markers and their corresponding weights can thereby be chosen
very flexible, for example as (i) estimated marker effects or
variances for a proportion of top markers from genomic
prediction; (ii) estimated effects or variances for markers in the
QTL regions detected by GWAS; or (iii) counts of how often a
marker was reported to belong to a (significant) QTL region in the
literature, thus allowing to incorporate prior knowledge of the
underlying genetic architecture of the complex trait under
consideration.
We finally propose to use T (instead of G or TA) as variance-
covariance matrix in a genomic best linear unbiased prediction
(BLUP) model. We will call this approach BLUP|GA (‘‘BLUP
approach conditional on the Genetic Architecture’’).
Results
In the following, we will present WGP results for a real dairy
cattle and a rice data set using the methodology introduced above.
Predictive ability of the WGP was measured via different cross-
validation procedures, applying the BLUP|GA approach with
genetic covariance structure given by the trait-specific variance-
covariance matrix T as proposed in equation (3). The weights h in
T were chosen based on counts of how often a marker was
reported to be within a significant QTL region during association
studies previously carried out in the literature, a knowledge we will
retrieve from publicly available QTL databases. We will compare
the performance of BLUP|GA with the standard GBLUP
approach [45] and with BayesB [4]. Further details can be found
in the ‘Material and Methods’ section.
Dairy Cattle Data
We considered 2,000 bulls of the German Holstein population
which were genotyped with the Illumina Bovine SNP50 Beadchip.
After quality control 45,221 autosomal SNPs were used in the
study. We analyzed the traits milk fat percentage (FP), milk yield
(MY) and somatic cell score (SCS) and used accurately estimated
breeding values (EBVs) from the conventional breeding value
estimation as quasi-phenotypes in the whole genome prediction
models (Table 1).
Marker weights for the BLUP|GA approach were obtained by
using publicly available GWAS results stored in the database
animalQTLdb [17] and based on the number of publications
reporting a significant QTL region including the corresponding
marker. Details on this are given in the ‘Material and Methods’
section. We performed 20 replicates of a five-fold cross-validation
to obtain an average predictive ability for BLUP|GA, GBLUP,
TABLUP and BayesB for three different population sizes.
Results in terms of accuracies are reported in Table 2 and
Figure 1. The BLUP|GA method outperformed the standard
GBLUP approach for all three model traits in terms of accuracy
Table 1. Summary statistics of data sets and corresponding
traits.
Data set Trait N Meana S.D. a r2/h2 b
Cattle Fat percentage 2000 20.027 0.294 0.973
Milk yield 2000 231.7 649.8 0.973
Somatic cell score 2000 103.1 11.6 0.942
Rice Days to flower (Arkansas) 374 87.94 12.63 0.785
Flag leaf length 377 30.63 5.74 0.763
Flag leaf width 377 1.22 0.25 0.717
Panicle number per plant 372 3.25 0.41 0.646
Plant height 383 116.60 21.09 0.832
Panicle length 375 24.37 3.54 0.781
Primary panicle branch
number
375 9.94 1.78 0.621
Seed number per panicle 376 4.85 0.33 0.678
Seed Width 377 3.12 0.39 0.924
Blast resistance 385 5.04 2.94 0.762
Amylose content 401 19.88 5.46 0.900
amean and standard deviation (S.D.) of conventional estimated breeding values
for cattle traits or phenotypes for rice traits;
b
reliability (r
2
) for cattle trait EBV, or heritability (h
2
) for rice trait phenotypes.
doi:10.1371/journal.pone.0093017.t001
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(Table 2). This could be observed for all three population sizes.
The superiority of BLUP|GA increased with the extremity of the
underlying genetic architecture of the complex trait. This
characteristic is similar to that of BayesB, which is also favorable
for traits affected by large-effect QTLs [34,35]. Since the T matrix
used in the BLUP|GA model is a mixture of the G matrix and the
S matrix, we had to choose an overall weight v for the S matrix.
The accuracies of BLUP|GA increased for FP and MY when
increasing v from 0 to 1, with a drop in accuracy for v
approaching 1 (Figure 1). For SCS, the accuracy decreased
continuously with increasing v. Note that accuracies reported for
BLUP|GA in Table 2 correspond to the overall weight v which
led to the highest average accuracy. The BLUP|GA approach
requires far less computing time as BayesB although it enables a
differentiated treatment of the SNPs (Figure S1).
To investigate the performance of WGP in more challenging
situations, we simulated traits with lower heritability based on the
original MY breeding values. For each of the three population
sizes, a random error was added to the original phenotypes (EBV
of MY) to generate a ‘‘new’’ trait with lower heritability. The
average accuracies of BLUP|GA and BayesB for 20 replicates of
five-fold cross-validation for the original phenotypes as well as the
artificial low heritability traits are shown in Figure 2. The accuracy
decreased with the population size and trait heritability (as
expected) for all three approaches. Additionally, it could be
observed that the accuracy of BLUP|GA was higher than that of
GBLUP in all considered scenarios (Figure 2). BLUP|GA showed
no advantage over BayesB for the original phenotype with high
heritability, but outperformed BayesB when the population size
was small or when the trait heritability was low (Figure 2). The
corresponding average values of accuracy and unbiasedness for
GBLUP, BayesB and the best scenario (‘‘best’’ with respect to the
optimal value of v, and the optimal subset of SNP listed in Table 3)
for BLUP|GA are presented in Table S1.
The Rice Diversity Panel
We used 413 inbred accessions of Oryza sativa from the Rice
Diversity Panel data set (cf. Zhao et al. [53]), which were genotyped
for approximately 37,000 SNPs; 11 different traits were considered
in our analyses (Table 1). Marker weights for the BLUP|GA
approach were obtained using GWAS results stored in the
Gramene database [16]. More information is given in the
‘Material and Methods’ section.
We found that BLUP|GA yielded the highest average accuracy
across all the 11 traits (Table 4). It outperformed GBLUP for nine
out of the 11 traits, either in terms of accuracy or in terms of
unbiasedness. On average, BLUP|GA showed an advantage over
GBLUP and BayesB by 0.01 in accuracy, while GBLUP and
TABLUP performed equally well (Table 4). BayesB performed
slightly better than BLUP|GA for two out of the 11 traits, and
worse than GBLUP on five traits. Compared to GBLUP,
BLUP|GA had the highest increase in accuracy for the traits
‘‘days to flower’’ (0.036, 5.4%), ‘‘amylase content’’ (0.020, 2.5%),
and ‘‘blast resistance’’ (0.014, 2.0%), which indicates that the
existing knowledge on the genetic architectures underlying these
traits can indeed enhance WGP. The BLUP|GA approach
improved the unbiasedness of prediction for nine out of the 11
traits compared to GBLUP (Table 4).
BayesB outperformed BLUP|GA only for ‘‘seed width’’ and
‘‘blast resistance’’ (Table 4). This suggests that the existing
knowledge from the QTL list [54] for these two traits is not more
promising than the one extracted from the rice diversity panel
itself. To validate this assumption, we ran BLUP|GA using an S
matrix build from the top SNPs selected by the size of estimated
marker effects from the equivalent model of GBLUP [55] obtained
within each fold of the 20 replicates of five-fold cross-validation.
The average accuracies of BLUP|GA from this scenario were
0.861 (60.001) and 0.704 (60.003) for ‘‘seed width’’ and ‘‘blast
resistance’’, respectively. The increased accuracy in this additional
scenario and the small number of known QTL (31, Table 3) for
‘‘seed width’’ suggest that the underlying genetic architecture for
this trait within the rice diversity panel might be different from that
obtained from the GWAS list and that the QTL list might be too
short to reflect the complete genetic architecture for this trait. The
TABLUP result (0.852, Table 4) also confirmed our assumption.
Table 2. Accuracy and unbiasedness of WGP for dairy cattle.
Fat percentage Milk yield Somatic cell score
N Method r(EBV, GEBV) b(EBV,GEBV) r(EBV, GEBV) b(EBV,GEBV) r(EBV, GEBV) b(EBV,GEBV)
2000 BLUP|GA 0.82460.001 0.97560.001 0.75160.001 1.02560.002 0.64660.001 1.02960.002
BayesB 0.84260.000 0.98560.001 0.74960.001 1.02760.002 0.64160.001 1.06960.003
GBLUP 0.72660.001 1.02860.002 0.72060.001 1.04260.002 0.64460.001 1.02660.002
TABLUP 0.80660.001 1.02160.001 0.73860.001 0.97360.002 0.646±0.001 0.93260.002
500 BLUP|GA 0.78560.001 1.01760.003 0.67360.003 1.13360.005 0.41260.004 0.95260.011
BayesB 0.78160.001 1.00760.002 0.67060.002 1.13760.006 0.39860.005 1.07560.014
GBLUP 0.50160.003 0.98660.007 0.59360.004 1.16960.007 0.40360.005 0.95460.012
TABLUP 0.68460.002 1.17460.004 0.62660.004 1.11560.007 0.40560.005 0.85660.010
125 BLUP|GA 0.77660.003 1.04260.008 0.50660.007 1.20360.020 0.24560.013 0.95460.057
BayesB 0.78260.004 1.10960.010 0.45060.009 1.77460.039 0.24860.012 1.12460.060
GBLUP 0.40160.011 1.21460.035 0.43260.010 1.37960.034 0.24360.013 0.96660.058
TABLUP 0.53260.009 1.44360.026 0.43460.009 1.23360.032 0.24660.012 0.83160.041
Mean (6 standard error of means) of accuracy (r) and unbiasedness (b) were calculated from 20 replicates of five-fold cross-validation for each of the three traits. The
best result in each block is printed in boldface.
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Discussion
We proposed a new WGP approach called BLUP|GA. One
plausible feature of BLUP|GA is the fact that any existing
knowledge of the genetic architecture of the complex trait under
consideration can be fitted into this prediction model by choosing
the corresponding marker weights in equation (3), which can
potentially improve the predictive ability of WGP. In this study,
we used publicly available QTL lists as the prior knowledge of the
underlying genetic architecture (‘‘GA’’) in an application of a dairy
cattle and a rice data set. Results indicated that the publicly
available QTLs identified from hundreds of association studies can
help to improve the accuracies of WGP via the BLUP|GA model
and that the BLUP|GA approach dominates two influential WGP
methods, GBLUP and BayesB, for the data sets considered in this
study. The BLUP|GA approach therefore provides a flexible
connection between WGP and the existing knowledge of the
genetic architecture of complex traits as given by association
studies.
BLUP|GA incorporates prior knowledge of the underlying
genetic architecture
The most important difference between BLUP|GA and any
other WGP approach is that BLUP|GA can enhance the accuracy
of WGP by modeling any ‘‘existing knowledge’’ of the GA,
including publicly available GWAS results. This can be achieved
in three steps: (i) building the S matrix based on a list of important
markers and their corresponding weights which are obtained from
‘‘existing knowledge’’, (ii) forming the T matrix as the weighted
sum of S and G using equation (3), and (iii) predicting the genetic
Figure 1. Accuracies of WGP in dairy cattle data set. The solid lines show the change of BLUP|GA accuracy with the overall weight (v) for fat
percentage (red), milk yield (blue), and somatic cell score (green). SNP weights in the BLUP|GA approach were based on the number of QTL reports as
described in the ‘Material and Methods’ section. GBLUP corresponds to the scenarios with overall weight v= 0, and the accuracies of BayesB are
presented by horizontal colored dash lines. Accuracies were calculated as the mean of 20 replicates of five-fold cross-validation with variable
population size (N = 125, 500 and 2000).
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merit of all individuals by solving the mixed model equations, in
which the covariance structure is given by the T matrix. SNPs
used to build S should lie in trait associated chromosomal regions
and their corresponding marker weights should represent their
relative contributions. In this study, we obtained the list of
important SNPs and their corresponding marker weights for
different traits within a dairy cattle and a rice data set from QTL
databases which are publicly available (Table 3, Figure 3).
We showed that GWAS results are not only useful for follow-up
studies in the context of association studies, but also for WGP. For
two out of the three dairy cattle model traits, the accuracies of the
BLUP|GA approach showed an ‘‘n’’ type curve (Figure 1), which
suggests that neither the G matrix (v= 0) nor the S matrix (v= 1)
alone, but rather the T matrix as a mixture of both, is the most
appropriate variance-covariance matrix with respect to the
predictive ability in the standard GBLUP approach.
Our study also gives an answer to the question raised by human
genetics ‘‘to what extent GWAS have identified genetic variants
likely to be of clinical or public health importance’’ [23]. Our
results show that GWAS results are useful for the prediction of
genetic merits in animal and plant breeding, and this might also be
valid for the prediction of disease risk in humans and therefore
deserves more exploration in the future.
Computational efficiency
With the fast increase of the data volume available, the
computational efficiency of a whole genome approach becomes a
critical issue in the post-genomic era. The BLUP|GA approach
Figure 2. Accuracy of WGP for simulated traits with different heritabilities and sample sizes. The curves show the change of the accuracy
obtained with BLUP|GA for varying overall weight v for milk yield. Different curves represent the accuracies obtained from traits with original
phenotype (solid line), or simulated phenotypes with heritability of 0.5 (short-dashed line), 0.3 (point line) and 0.1 (long-dashed line), respectively. The
numbers of QTL counts were used to infer the marker weights for the BLUP|GA approach. The GBLUP approach corresponds to scenarios in which
v= 0 (starting points for each curve), and the accuracies of BayesB are presented by horizontal lines. Accuracies were calculated as the mean of 20
replicates of five-fold cross-validation with different population sizes (N = 125, 500, and 2000).
doi:10.1371/journal.pone.0093017.g002
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PLOS ONE | www.plosone.org 6 March 2014 | Volume 9 | Issue 3 | e93017
shares similar computational characteristics with the GBLUP
approach, which is time and memory efficient, especially when the
G matrix has been built and stored before running a job (Figure
S1). On the contrary, Bayesian modeling is computationally
intensive, and it usually takes hours to run analyses of data sets
based on high density SNP chips (Figure S1, [33]), and days to run
analyses of data sets based on whole genome sequences [56]. With
the decrease of sequencing costs, the p.n problem will become
even more serious for WGP approaches. The relationship matrix
based approach gains attractiveness in this situation, since it can
manage the same prediction problem in the dimension of number
of individuals rather than the number of markers.
QTL lists from GWAS results
Our results demonstrated that the comprehensive QTL list
collected from GWAS and QTL mapping studies can be used to
improve the performance of WGP via the BLUP|GA model. In
the past decade, the genetics community conducted thousands of
phenotype-genotype association studies to dissect the genetic
architecture of complex traits in animals [17,18,19,20,57], plants
[12,13,14,15] and humans [22,23,58]. Finally, hundreds of QTLs
were detected to be associated with each of the traits of interest,
such as MY in dairy cattle (Table 3) [17], plant height in rice
(Table 3) [54] or adult human height [52,59]. One usual strategy
to utilize these results is to sift out most promising SNPs for follow-
Table 3. SNP list summary.
Data set Trait Total QTL
a
Number of SNPs with QTL count
b
. =
1 2 3 5 10
Cattle Fat percentage 279 1325 257 135 57 1
Milk yield 247 1622 250 107 85 0
Somatic cell score 169 993 184 66 1 0
Rice Days to flower (Arkansas) 38 6488 2196 292 204 0
Flag leaf length 110 13652 3467 1551 1019 0
Flag leaf width 106 13689 7658 3237 560 58
Panicle number per plant 197 19968 11031 6605 3765 672
Plant height 979 34240 31030 26430 14029 6791
Panicle length 240 23942 16521 10865 4164 477
Primary panicle branch number 52 7207 2769 465 0 0
Seed number per panicle 58 17487 9722 1424 48 0
Seed Width 31 4998 840 88 0 0
Blast resistance 169 18628 13194 6631 2076 190
Amylose content 50 6059 1916 1037 165 0
a
Total QTL: Total number of QTL regions for each trait obtained from animalQTLdb (Release 18) [17] and Gramene (Release 36) [16].
b
QTL Counts were obtained as described in the ‘Material and Methods’ section. The exact number of top SNPs used in final analysis were showed in bold face.
doi:10.1371/journal.pone.0093017.t003
Table 4. Accuracy and unbiasedness of WGP for rice.
Trait r(PHE, GEBV) b(PHE,GEBV)
BLUP|GA BayesB GBLUP TABLUP BLUP|GA BayesB GBLUP TABLUP
Days to flower (Arkansas) 0.70060.003 0.67560.011 0.66460.003 0.66360.003 1.00160.004 1.01360.010 1.05160.005 0.95260.006
Flag leaf length 0.51660.003 0.51360.003 0.50560.003 0.51460.003 0.94260.008 0.97060.009 0.99960.008 0.86060.007
Flag leaf width 0.76660.002 0.76560.002 0.75760.002 0.75960.002 1.04160.003 1.02960.003 1.05760.003 0.98460.003
Panicle number per plant 0.82260.001 0.82060.001 0.82160.001 0.81460.002 1.01660.002 1.01460.002 1.02160.002 0.97660.003
Plant height 0.76060.002 0.75160.002 0.75360.002 0.75360.002 1.06160.003 1.04360.003 1.05660.003 1.01160.003
Panicle length 0.66160.004 0.65760.004 0.65960.004 0.65160.004 0.99460.006 0.98460.007 0.99160.006 0.90560.006
Primary panicle branch number 0.62660.003 0.62560.003 0.62560.003 0.62560.003 1.02460.006 1.03060.006 1.04460.006 0.91360.006
Seed number per panicle 0.57960.004 0.57260.004 0.57560.004 0.56860.004 1.12160.007 1.05360.006 1.11860.007 0.91460.005
Seed Width 0.83760.001 0.84260.005 0.83760.001 0.85260.001 1.02760.003 0.96760.008 1.02660.003 1.01560.003
Blast resistance 0.70360.003 0.70460.003 0.68960.003 0.69060.003 1.04360.004 1.03160.005 0.99860.005 0.96460.005
Amylose content 0.82560.004 0.80160.005 0.80560.005 0.80560.005 1.01360.004 0.93460.010 1.03160.006 0.98060.005
AVERAGE 0.709 0.702 0.699 0.699 1.026 1.006 1.036 0.952
Mean (6 standard error of means) of accuracy (r) and unbiasedness (b) were calculated from 20 replicates of five-fold cross-validation for each trait. The best result in
each block is printed in boldface. Average accuracy (r) and unbiasedness (b) were calculated for each method across all 11 traits.
doi:10.1371/journal.pone.0093017.t004
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up replication studies to determine true association findings in
previous GWAS [60,61], although it usually takes years or longer
from a QTL to a validated gene [62]. Alternatively, our results
have shown that utilizing the QTL list via the BLUP|GA
approach, one can benefit from more accurate GEBVs in animal
and plant breeding programs or from more accurate predictions of
individual genetic risk of complex disease in humans, although the
exact functions and relationships of all genes underlying the
complex trait under consideration are not known yet.
The QTL list used for BLUP|GA may come from hundreds of
studies and hence is the most comprehensive profile of the
underlying genetic architecture that is available. This is evidenced
by the similar shape of profiles obtained by our analyses of the
cattle QTL list (Figure 3) and the estimated marker effects for MY
in the cattle data set (Figure S2). By counting the significant QTLs
and inferring the corresponding weights for each marker for a
trait, we can account for relatively more important regions across
the whole genome, which is the kind of model selection we are
interested in.
Genetic architecture and accuracy of WGP
The genetic architecture of a complex trait is one of the most
influential factors for WGP [34,35]. Generally, if a trait is
controlled by only a few major genes, methods with an explicit
model selection are known to work best in WGP and these major
genes should easily be detected in a GWAS. In case no major
genes exist, it is hard to detect moderate or small effect QTLs in
GWAS [25,63], and the GBLUP method usually performs better.
From a WGP perspective, our results for the three model traits
in the dairy cattle data set (Figure 1, Table 2), as well as several
studies using simulations [34,41] or real data [35,40], have clearly
Figure 3. Distribution of reported QTLs positions and marker weights obtained from QTL list. Reported QTLs associated with fat
percentage (red), milk yield (blue) and somatic cell score (green) retrieved from animalQTLdb (http://www.animalgenome.org/animlQTLdb) [17].
Marker weights were calculated as the number of times that each marker was reported to be within a significant QTL region (QTL counts). The
colored bar under each plot shows the distribution of QTL positions across the whole genome for the three traits with color keys defined in the first
plot (top-right).
doi:10.1371/journal.pone.0093017.g003
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http://www.animalgenome.org/animlQTLdb
confirmed this hypothesis. Considering the dairy cattle data set,
using the BLUP|GA method improved the accuracy of WGP for
traits with a characteristic genetic architecture, such as FP and
MY, but not for a trait without evidence of a characteristic trait
genetic architecture, such as SCS. For the rice traits, more
significant QTL regions were identified for the plant height than
panicle length (Table 3, Figure S3), and we obtained more gain in
accuracy for plant height (Table 4). It would be interesting to
explore the performance of the BLUP|GA approach with other
species as well. This is left for future work.
As the effect size of detectable QTL decreases with the increase
of population size, a training population with sufficient size (Ns),
suitable population structure and accurate phenotypes is usually
needed to detect the genetic architecture of a complex trait [39].
The required sample size Ns to achieve a certain accuracy will be
different for different species and populations according to their
effective population size (Ne) and genome length [34,47]. In this
study, the Germany Holstein dairy cattle population was taken as
an example (Ne = ,100 [64]), and the training population sizes
used in the study were approximately 1 Ne (100), 4 Ne (400) and 16
Ne (1,600), respectively. These training population sizes are large
relative to the small value of Ne (compared to other common
species such as humans (,10,000) [65,66], mice (.20,000)[67]
and swine (,100 for one breed) [68,69]. The decreased accuracies
(Figure 1, Figure 2) and the shrunk estimated marker effects
(Figure S2) indicate that the power of detecting genetic architec-
ture and the predictive ability of WGP is seriously affected by the
training population size as well as the accuracy of phenotype
(heritability). Incorporating existing knowledge of the underlying
genetic architecture into the WGP model (such as QTL lists from
previous publications) therefore appears to be even more
reasonable when the population size is small and the heritability
is low. The new approach is more potent in case the combining of
raw data sets are less possible, which was confirmed by our
simulation results from the cattle data set (Figure 2, Table S1).
The new approach presented in this study still offers room for
further improvements, such as refining the SNP list and marker
weights obtained from QTL lists or modifying the T matrix while
combining the information from G and S. We have tried to base
weights in h on accumulated P-values rather than the number of
citations, which basically led to very similar findings (results not
shown). Other concepts like including e.g. pathway information
might be promising as well and are left for further studies.
Conclusions
The BLUP|GA method provides a new tool to incorporate
existing knowledge of the genetic architecture of complex traits
explicitly into a genomic prediction model. Using the BLUP|GA
model, we illustrated that the publicly available QTL lists detected
by hundreds of GWAS and QTL mapping studies improved the
performance of WGP compared to standard WGP methods within
a dairy cattle and a rice data set, respectively. The accuracy of
WGP could be improved for two out of the three model traits in
dairy cattle and for nine out of 11 traits in the rice diversity panel.
The publicly available GWAS results were shown to be potentially
more useful for WGP utilizing smaller data sets and/or traits of
low heritability, depending on the genetic architecture of the trait
under consideration. BLUP|GA also improved the prediction
accuracies compared to the traditional methods GBLUP and
BayesB. To our knowledge, this is the first study incorporating
public GWAS results into the standard BLUP model and we think
that the BLUP|GA approach deserves further investigations in
animal breeding, plant breeding as well as human genetics.
Materials and Methods
A dairy cattle and a rice data set were analyzed in this study.
Summary statistics for these sets and the considered traits are given
in Table 1.
The German Holstein Population
Genotypic data from the Illumina Bovine SNP50 Beadchip [70]
was available for 5,024 German Holstein bulls. SNPs with a minor
allele frequency lower than 1%, with missing position or a call rate
lower than 95% were excluded. After filtering, there were 42,551
SNPs remaining for further analyses. Imputation of missing
genotypes at these SNP positions was done using Beagle 3.2
[71]. For all bulls, conventional estimated breeding values for milk
fat percentage (FP), milk yield (MY) and somatic cell score (SCS)
with reliabilities greater than 70% were available.
The three traits, FP, MY and SCS, were considered due to their
well-established distinct genetic architectures. For FP, a single
mutation in the diacylglycerol acyltransferase 1 (DGAT1) gene
explains approximately 30% of the genetic variance in Holstein
Friesian cattle [60,72]. For MY, several moderate effect loci have
been detected, whereas for SCS, which is a health index counting
the number of somatic cells in milk, only loci with small effects
have been reported so far, so that it can be considered as a trait
exhibiting a quasi-infinitesimal mode of inheritance. These three
traits therefore represent three different possible genetic architec-
tures of complex traits.
For our further studies, we chose to use the 2,000 bulls with the
highest reliabilities in the trait MY to decrease the time
demanding. In order to consider two additional scenarios with
even smaller population size, we randomly selected a subset of 500
and 125 individuals out of these 2,000 individuals. To investigate
the effect of different heritabilities, we also created new phenotypes
for the bulls by adding random error terms to the conventional
estimated breeding values such that the heritability of the new
phenotypes was 0.5, 0.3 and 0.1, respectively.
The Rice Diversity Panel
The rice diversity panel consists of 413 inbred accessions of
Oryza sativa collected from 82 countries [53]. They were
systematically phenotyped for 34 traits and genotyped with a
custom-designed 44,100 oligonucleotide genotyping array. In
total, we used 36,901 SNPs in the present study. We considered
a subset of 11 (listed in Table 1) out of the 34 traits, which have
more than 30 QTL reports respectively. Phenotypes and
genotypes are publicly available from http://www.nature.com/
ncomms/journal/v2/n9/full/ncomms1467.html [53] and http://
www.ricediversity.org/data/sets/44 kgwas/. For more details
about the rice diversity panel we refer to Zhao et al.[53].
Approach to infer marker weights from GWAS results
For a given trait of interest, we first extracted a full list including
the ‘‘most important SNPs’’ with respect to this trait, for which the
according weights have to be chosen in a second step. These are
the SNPs which are finally used to build the S matrix in the
BLUP|GA approach.
We first retrieved regions of QTLs associated with the trait
under consideration from the literature. For each reported QTL,
we picked the SNPs from the genotype data set located in the
corresponding QTL region. If a reported QTL region did not
contain any SNP, we extended the QTL region by 300 kb at both
sides to track the SNPs nearby. If a reported QTL region
contained more than 1,000 SNPs, the corresponding QTL report
was excluded from our analysis, since this QTL would not be
GWAS Results Improves Whole Genome Prediction
PLOS ONE | www.plosone.org 9 March 2014 | Volume 9 | Issue 3 | e93017
http://www.nature.com/ncomms/journal/v2/n9/full/ncomms1467.html
http://www.nature.com/ncomms/journal/v2/n9/full/ncomms1467.html
http://www.ricediversity.org/data/sets/44
http://www.ricediversity.org/data/sets/44
informative with respect to the marker weights obtained in the
next step. We thereby obtain a list of the most important SNPs as
well as a list of corresponding QTL regions. For each SNP in this
list, we then calculated its marker weight for the trait specific
matrix S used in the BLUP|GA approach by counting the number
of publications which report a significant QTL region which is
included in the QTL list and which contains the considered SNP.
Finally, we removed a marker from the SNP list, if its
corresponding QTL count did not exceed 1 in order to minimize
the effect of potential false positive QTL(s) to the marker weights.
Marker weights for the dairy cattle data set
A list of significant QTLs for the dairy cattle data set was
obtained from animalQTLdb [17] (http://www.animalgenome.
org/QTLdb, Release 18, October 2, 2012), which is a compre-
hensive QTL database for domestic animals. This list included
5,920 QTLs on 407 traits from 331 publications. For each QTL,
the estimated QTL intervals in base-pairs (bp), the associated trait,
the significant P-value and other related information were given.
For more details, we refer to Hu [17] and http://www.
animalgenome.org/QTLdb. There were 279, 247 and 169 QTLs
reported for FP, MY and SCS, respectively (cf. Table 3). Applying
the approach described above to obtain a list of QTL regions, 194,
210 and 124 QTLs were finally included in our further analyses.
The number of SNPs from the genotype data which were located
in these QTL regions and the number of QTL reports for these
SNPs are summarized in Table 3. The reported QTLs for FP are
clustered on chromosomes 6, 14 and 20, while the positional
distributions for QTLs associated with SCS trend to be evenly
spaced across the whole genome (Figure 3). The final marker
weights (QTL counts, obtained by the procedure described in the
previous section) are also plotted in Figure 3. The annotation
information for the SNPs and the corresponding marker weights
are provided in Table S2.
Marker weights for rice data set
The QTL list for Oryza sativa (rice) was obtained from the
Gramene database (ftp://ftp.gramene.org/pub/gramene/
release36/data/qtl/Release 36, January 26, 2013) [54]. It
included 8,216 QTLs on 236 traits. For the 34 traits available in
the panel, we excluded traits with less than 30 QTL reports, and
only kept the first (Days to flower at Arkansas) from the 5 flowering
time traits in our further analyses, so that 11 out of the 34 traits
were finally used to validate the new approach. The numbers of
SNPs from the rice diversity panel which were located in
corresponding QTL regions for each trait are summarized in
Table 3. Marker weights were again inferred by counting the
number of publications reporting a significant QTL region as
described above, and the marker weights for plant height and
panicle length were plotted in Figure S3. The annotation
information for these SNPs and their marker weights are provided
in Table S3.
Genomic Prediction with BLUP (Best Linear Unbiased
Prediction)
The statistical model for the genomic BLUP approach is
y~XmzZgze, ðModel1Þ
in which y is a vector of phenotypic values; m is the overall mean; g
is a multivariate normally distributed vector of genetic values for
all individuals in the model; e*N(0,s2eI) is the residual term; X
and Z are incidence matrices relating the overall mean and the
genetic values to the phenotypic record. We assume g*N(0,s2gG)
in the GBLUP approach and g*N(0,s2gT) in BLUP|GA,
respectively, where T is the matrix from equation (3) and the
‘‘GA’’ stands for ‘‘genetic architecture’’. For TABLUP, the TA
matrix were built according to equation (2) that proposed by
Zhang et al. [51]. Estimated genetic values were obtained by
solving the mixed model equations [73,74] corresponding to
Model 1, which are given by
XTX XTZ
ZTX ZTZz
s2e
s2g
G{1
2
64
3
75: m̂m
ĝg
� �
~
XTY
ZTY
” #
:
A combined AI-EM restricted maximum likelihood algorithm
(AI-average information, EM-expectation maximization) was used
to estimate the variance components of the model via the DMU
software package [75] from the complete data and these variance
components were used in the cross-validations later on.
Genomic Prediction with BayesB
The model for BayesB [4] is given by
y~XmzMsze, ðModel2Þ
where y, X, m, M and e are as defined in Model 1 and s is a vector
of normally distributed and independent SNP effects. The
variance of the ith marker effect,s2si
was assumed a priori to be
0 with probability of p or to follow a scaled inverse chi-squared
distribution with probability of (1 – p) [4]. In our research, we
chose p~0:95 for all scenarios such that on average 5% markers
were contributing to the additive genetic variance in each cycle.
The MCMC chain was run for 10,000 cycles with 100 cycles of
Metropolis-Hastings sampling in each Gibbs sampling, and the
first 2,000 cycles were discarded as burn-in. All the samples of
marker effects from later cycles were averaged to obtain the
estimates of marker effects. For more details on the BayesB
approach we refer to the original article [4].
Cross-validation
A five-fold cross-validation (CV) procedure [76] was used to
assess the predictive ability of the different prediction methods. In
each replicate of a five-fold CV, individuals were randomly
divided into five groups (folds) with equal size (in case the
population size was not divisible by five, some groups included
slightly more individuals than the other groups). The genetic
values of all individuals in each of the five folds were predicted
using records of the other four folds. Hence, in each replicate, we
performed genomic prediction five times. Each individual
therefore belonged once to the validation set and four times to
the training set. For all scenarios, the five-fold CV was replicated
20 times, resulting in 20 average accuracies.
Accuracy and unbiasedness
Both accuracy and predictive ability in this study were defined
as the Pearson correlation coefficient between observed pheno-
typic values (PHE) and predicted genetic values (PGV):
r~cor(PHE,PGV ). For the dairy cattle data set, the mean
reliabilities for the EBVs, which were treated as phenotypes in our
genomic prediction model, are 0.97, 0.97 and 0.94 for FP, MY,
and SCS, respectively (Table 1). The reported results for dairy
GWAS Results Improves Whole Genome Prediction
PLOS ONE | www.plosone.org 10 March 2014 | Volume 9 | Issue 3 | e93017
http://www.animalgenome.org/QTLdb
http://www.animalgenome.org/QTLdb
http://www.animalgenome.org/QTLdb
http://www.animalgenome.org/QTLdb
ftp://ftp.gramene.org/pub/gramene/release36/data/qtl/Release
ftp://ftp.gramene.org/pub/gramene/release36/data/qtl/Release
cattle can therefore be a good indicator of ‘‘accuracy’’ defined as
the correlation between true breeding values (TBV) and genomic
estimated breeding valuescor(TBV ,PGV ). The unbiasedness was
calculated as the regression coefficient of PHE on PGV,
b~reg(PHE,PGV ). For the scenarios with low heritability traits
in the dairy cattle data set, we used the original phenotypes (EBVs)
rather than the simulated new phenotypes to validate different
methods.
Supporting Information
Figure S1 Computing times for GBLUP, BLUP|GA and
BayesB. Computing times for GBLUP, BLUP|GA and BayesB
(10,000 iterations) for population size N = 2,000 and m = 42,551
markers on an Intel Core i5-3470 CPU 3.2 GHz64 with 16 GB
RAM. For GBLUP and BLUP|GA, the computing time includes
building the G matrix and solving the mixed model equations. For
BayesB, the average time demanding for 10,000 iterations is
shown.
(TIF)
Figure S2 Estimated marker effects for milk yield in
dairy cattle. Estimated marker effects obtained with different
population sizes (N). Dark blue dots represent the top 1% SNPs
with the largest estimated marker effects.
(TIF)
Figure S3 Distribution of reported QTLs positions and
marker weights obtained from rice QTL list. Reported
QTLs associated with plant height (red), and panicle lenght (blue)
retrieved from Gramene database (ftp://ftp.gramene.org/pub/
gramene/release36/data/qtl/Release 36, January 26, 2013) [54].
Marker weights were calculated as the number of times that each
marker was reported to be within a significant QTL region (QTL
counts). The colored bar under each plot shows the distribution of
QTL positions across the whole genome for the three traits with
color keys defined in the first plot (top-right).
(TIF)
Table S1 Accuracy and unbiasedness for traits with low
heritability and small population sizes (based on the
dairy cattle data set). The best result in each block is printed in
boldface.
(DOC)
Table S2 SNP lists for the dairy cattle data set. This table
(excel format) includes the name, chromosome, physical position,
trait associated, number of QTL reports, and other important
information for each SNP used in this study.
(XLS)
Table S3 SNP lists for rice diversity panel. This table
(excel format) includes the name, chromosome, physical position,
trait associated, QTL report, and other information for each SNP
used in this study.
(RAR)
Author Contributions
Conceived and designed the experiments: HS JQL ZZ. Performed the
experiments: ZZ UO ME NG JLH HZ. Analyzed the data: ZZ UO ME
NG JLH HZ. Contributed reagents/materials/analysis tools: UO ME.
Wrote the paper: ZZ UO ME HZ JQL HS.
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