Genomic selection in a commercial winter wheat population

Abstract

Key message:
Genomic selection models can be trained using historical data and filtering genotypes based on phenotyping intensity and reliability criterion are able to increase the prediction ability. We implemented genomic selection based on a large commercial population incorporating 2325 European winter wheat lines. Our objectives were (1) to study whether modeling epistasis besides additive genetic effects results in enhancement on prediction ability of genomic selection, (2) to assess prediction ability when training population comprised historical or less-intensively phenotyped lines, and (3) to explore the prediction ability in subpopulations selected based on the reliability criterion. We found a 5 % increase in prediction ability when shifting from additive to additive plus epistatic effects models. In addition, only a marginal loss from 0.65 to 0.50 in accuracy was observed using the data collected from 1 year to predict genotypes of the following year, revealing that stable genomic selection models can be accurately calibrated to predict subsequent breeding stages. Moreover, prediction ability was maximized when the genotypes evaluated in a single location were excluded from the training set but subsequently decreased again when the phenotyping intensity was increased above two locations, suggesting that the update of the training population should be performed considering all the selected genotypes but excluding those evaluated in a single location. The genomic prediction ability was substantially higher in subpopulations selected based on the reliability criterion, indicating that phenotypic selection for highly reliable individuals could be directly replaced by applying genomic selection to them. We empirically conclude that there is a high potential to assist commercial wheat breeding programs employing genomic selection approaches.

Full text

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Theor Appl Genet
DOI 10.1007/s00122-015-2655-1
ORIGINAL ARTICLE
Genomic selection in a commercial winter wheat population
Sang He1 · Albert Wilhelm Schulthess1 · Vilson Mirdita1 · Yusheng Zhao1 ·
Viktor Korzun2 · Reiner Bothe2 · Erhard Ebmeyer2 · Jochen C. Reif1 · Yong Jiang1
Received: 10 August 2015 / Accepted: 11 December 2015
© Springer-Verlag Berlin Heidelberg 2016
a single location were excluded from the training set but
subsequently decreased again when the phenotyping inten-
sity was increased above two locations, suggesting that
the update of the training population should be performed
considering all the selected genotypes but excluding those
evaluated in a single location. The genomic prediction
ability was substantially higher in subpopulations selected
based on the reliability criterion, indicating that phenotypic
selection for highly reliable individuals could be directly
replaced by applying genomic selection to them. We
empirically conclude that there is a high potential to assist
commercial wheat breeding programs employing genomic
selection approaches.
Introduction
Yield growths in wheat are stagnating in several parts of the
world affecting an estimated global acreage of 37 % (Ray
et al. 2015). Genomic selection (Meuwissen et al. 2001)
offers the potential to accelerate selection gain (Burgueño
et al. 2012; Crossa et al. 2010; Poland et al. 2012) espe-
cially by shortening the lengths of breeding cycles (Sallam
et al. 2015). Encouraging prediction accuracies have been
reported for genomic selection for grain yield in wheat
despite the use of populations comprising only 200 (Poland
et al. 2012) to 800 wheat lines (Lopez-Cruz et al. 2015).
Several statistical models have been proposed to imple-
ment genomic selection (Gianola and van Kaam 2008;
Heslot et al. 2012; Meuwissen et al. 2001). The majority
of the genomic selection approaches predict breeding val-
ues solely based on additive effects, which are the primary
target for parental selection (Falconer 1960). The economic
value of inbred varieties, however, is not only influenced
by their additive part but also comprises epistatic effects
Abstract
Key message Genomic selection models can be trained
using historical data and filtering genotypes based on
phenotyping intensity and reliability criterion are able
to increase the prediction ability.
Abstract We implemented genomic selection based on
a large commercial population incorporating 2325 Euro-
pean winter wheat lines. Our objectives were (1) to study
whether modeling epistasis besides additive genetic effects
results in enhancement on prediction ability of genomic
selection, (2) to assess prediction ability when training
population comprised historical or less-intensively phe-
notyped lines, and (3) to explore the prediction ability in
subpopulations selected based on the reliability criterion.
We found a 5 % increase in prediction ability when shifting
from additive to additive plus epistatic effects models. In
addition, only a marginal loss from 0.65 to 0.50 in accuracy
was observed using the data collected from 1 year to pre-
dict genotypes of the following year, revealing that stable
genomic selection models can be accurately calibrated to
predict subsequent breeding stages. Moreover, prediction
ability was maximized when the genotypes evaluated in
Communicated by H. Iwata.
Electronic supplementary material The online version of this
article (doi:10.1007/s00122-015-2655-1) contains supplementary
material, which is available to authorized users.
* Jochen C. Reif
reif@ipk-gatersleben.de
1 Department of Breeding Research, Leibniz Institute of Plant
Genetics and Crop Plant Research (IPK), Corrensstraße 3,
Gatersleben, 06466 Stadt Seeland, Germany
2 KWS Lochow GmbH, Bergen, Germany

Theor Appl Genet
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(Goldringer et al. 1997). Genomic selection models incor-
porating main and epistatic effects have been proposed (Cai
et al. 2011; Wang et al. 2012; Wittenburg et al. 2011; Xu
2007) but the inherently high computation load hampered
their wide application (Jiang and Reif 2015). An attractive
solution to minimize the high computational costs consists
in utilizing extended GBLUP models (EGBLUP) consid-
ering also epistasis (Jiang and Reif 2015). Alternatively,
kernel Hilbert space regression (Gianola and van Kaam
2008) can be applied to accommodate epistasis within the
genomic prediction models (Gianola and van Kaam 2008;
Morota and Gianola 2014; Jiang and Reif 2015).
The prediction ability of genomic selection is influenced
by the genetic composition of the training population, the
relatedness between the training and the test population,
and the heritability of the training population (Isidro et al.
2015). Recent studies examined the potential to reduce
costs by decreasing the training population size and at the
same time keeping the prediction ability constant (Akdemir
et al. 2015; Rincent et al. 2012). Their findings suggested
that using criteria such as the mean prediction error vari-
ance facilitates a resource-efficient establishment of train-
ing populations.
An alternative philosophy is to compile training popu-
lations based on historic data routinely generated in the
course of breeding. Using historic data of breeding popu-
lations, however, entails a sophisticated balance between
population size and heritability: Population sizes are large
at early stages of selection but heritability is for complex
traits often low. In contrast, at late stages, heritability is
high but population sizes small. Despite its relevance for
maximizing the prediction ability, optimal balance between
population size and heritability of the training population
has not yet been examined for wheat.
Once a genomic selection model has been established,
it is of utmost importance to decide whether individuals
of the test population are well represented by the training
population resulting in high prediction abilities. Assessing
prediction accuracy of particular individuals merely based
on genotypic data using the reliability criterion has been
proposed in the context of animal breeding (Hayes et al.
2009a; Henderson 1973; VanRaden et al. 2009). In plant
breeding, Rincent et al. (2012) and Akdemir et al. (2015)
applied this criterion to optimize the training population
according to the genetic constitution of selection candi-
dates. Nevertheless, opposite to animal breeding, the relia-
bility measure has not yet been evaluated as a breeding tool
to measure the prediction accuracy of particular individuals
in plant science.
Here, we draw upon a large-scale diverse population
including 2325 European wheat inbred lines phenotyped
in multiple environmental field trials for grain yield. The
main goal of our study was to investigate the potentials and
limits of whole genome-prediction of grain yield across-
environment performance in wheat. Our specific objec-
tives were (1) to study whether modeling epistasis besides
additive genetic effects results in enhanced prediction abil-
ity of genomic selection, (2) to evaluate prediction ability
when, the training population comprised historical or less-
intensively phenotyped lines, and (3) to explore prediction
ability in subpopulations selected based on the reliability
criterion.
Materials and methods
Phenotypic and genomic data
We used in total 2325 European elite winter wheat lines of
the wheat breeding program of KWS LOCHOW GmbH
(Bergen, Germany). The wheat lines were evaluated in the
years 2012 and 2013 for grain yield in up to nine locations.
In total 154 out of the 2325 wheat lines were tested in both
years. The lines were divided into 13 individual trials con-
nected through five common checks. The experimental
design for each trial was an alpha design with one to three
replications per location with the number of entries per
trial ranging from 32 to 306. Plot size ranged from 6.05 to
17.25 m2 and sowing density varied from 345 to 376 grains
m−2.
Genomic data have been described in detail elsewhere
(Mirdita et al. 2015). Briefly, the wheat lines phenotyped
in the year 2012 were genotyped by Illumina Infinium 9 k
SNP array (Cavanagh et al. 2013) and the lines phenotyped
in 2013 were fingerprinted by Illumina Infinium 90 k SNP
array (Wang et al. 2014) (Illumina, San Diego, CA, USA).
Rate of missing value was 4.81 % for the 9 k SNP array
and 1.69 % for the 90 k SNP array data. We integrated
both data sets imputing missing values with the IMPUTE2
algorithm (Howie et al. 2009). After quality control, SNP
markers with minor allele frequency less than 0.05 were
excluded and 12,642 SNP markers were available for fur-
ther analyses. We estimated Rogers’ distance (Rogers 1972)
for each pair of varieties to study the population structure.
The pairwise Rogers’ distance were used to perform a prin-
cipal coordinate analysis (Gower 1966).
Phenotypic data analysis
We implemented an un-weighted two-stage analysis of
the phenotypic data. This decision is based on previous
findings showing that the difference between weighted
versus unweighted approaches was negligible (Möhring
and Piepho 2009). At the first stage, we analyzed the
data for each environment (location times year com-
bination) separately using a linear mixed model given

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by
y=1rµ+Zg +Wf +e
, where y is the vector of phe-
notypic values of genotypes in the specific environment;
1r is an r-dimensional vector of 1’s and r is the number
of records in the specific environment; μ is the common
intercept; g is the vector of genotypic value of genotypes
tested in the environment regarded as random effect; f is
the vector of other random effects (including replication,
trial and incomplete block); e is the random residual; and
Z along with W are the corresponding design matrices for
g and f, respectively. We assumed that all random effects
follow an independent normal distribution with different
variance components for genotype, replication, trial and
incomplete block effect, respectively. Then the estimated
variance components were used to calculate the repeatabil-
ity for each environment as: σ
2
g
σ
2
g
+σ2
e
R
, where σg
2 is the geno-
typic variance, σe
2 is the residual variance and R indicates
the average number of replications per genotype. Moreo-
ver, we assumed fixed genotype effects to obtain the best
linear unbiased estimation (BLUE) for each genotype.
At the second stage, we combined the BLUEs of all gen-
otypes in each environment and fitted a linear mixed model
across environments given by
y=1mµ+Zg +Eu +e
,
where y is the vector of BLUEs of each genotype in each
environment obtained in the first step; 1m is an m-dimen-
sional vector of 1’s and m is the sum of the number of
genotypes tested in each environment; μ is the common
intercept term; g is the vector of genotypic effects of all
genotypes; u is the vector of environment effects; e is the
vector of residuals; and Z as well as E are the correspond-
ing design matrices for g and u, respectively. We assume
that μ is a fixed parameter,
g
∼N(0, Iσ
2
G)
,
u
∼N(0, Iσ
2
u)
,
and
e
∼N(0, Iσ
2
R)
. Variance components were used to
estimate broad-sense heritability as
h
2=σ
2
G
σ2
G
+
σ2
R
E
, where E
refers to the average number of environments where a gen-
otype has been tested. As our data set is highly unbalanced,
we also estimated the expected h2 across a range of 1–13
environments. In addition, the genotypic effects g were
assumed as fixed to obtain the BLUEs of each genotype
across environments. All linear mixed models were imple-
mented using ASReml-R (Gilmour et al. 2009).
Genomic selection combining data across years
We validated the effect of genomic selection based on data
combined for all the 2325 wheat lines. The prediction accu-
racy of genomic selection was evaluated using four models
including ridge regression best linear unbiased prediction
(RRBLUP; Meuwissen et al. 2001; Whittaker et al. 2000),
BayesCπ (Habier et al. 2011), reproducing kernel Hilbert
space regression (RKHS; Gianola and van Kaam 2008)
and extended genomic best linear unbiased prediction
(EGBLUP; Jiang and Reif 2015). The first two mod-
els exclusively consider additive effects of markers while
the last two exploit both the additive and epistatic effects
among markers.
Let n be the number of genotypes, p be the number of
markers and l be the number of environments. Let
X=(xij)
be the n × p matrix of markers with xij being the number of
a chosen allele at the j-th locus for the i-th genotype. Let y
be the n-dimensional vector of phenotypic records, which
are BLUE of genotypic values obtained in the phenotypic
data analyses. Let 1n be the n-dimensional vector of 1’s. In
the following models, μ always denotes the common inter-
cept term and e denotes the residual term.
The RRBLUP model has the form
y=1nµ+X
α
+e
,
where α is the vector of additive effects of markers. In the
model we assume that
α
∼N

0, I
p
σ
2
α
,
e
∼
N(0, Inσ2
e)
,
where Ip and In are identity matrices of order p and n,
respectively, whereas
σ2
α
=σ
2
G
/
p
and σe
2 = σR
2/l. Note that
σG
2 and σR
2 are the estimated genotypic and residual vari-
ances in the phenotypic data analyses. The estimation of α
is given by the mixed model equations (Henderson 1975).
The BayesCπ model has the same basic setting
y=1nµ+X
α
+e
as RRBLUP but with different assump-
tions. Let αj be the jth element of α (j = 1,…, p). Then αj
is assumed to be zero with probability π and
α
j∼N

0, σ
2
α
with probability (1–π), where π is a random variable whose
prior distribution is uniform on the interval [0, 1]. The vari-
ance component σα
2 has a scaled inverse Chi-squared prior
distribution with degree of freedom vα and scale Sα
2. The
prior distribution of the residual is
e
∼N

0, I
n
σ
2
e
and σe
2
also has a scaled inverse Chi-squared prior distribution
with degree of freedom ve and scale Se
2. Parameters vα and
ve were both set to be 4. Se
2 and Sα
2 are derived following
Habier et al. (2011). A Gibbs sampler algorithm was imple-
mented to infer the parameters in the model which was
run for 10,000 iterations with a burn-in of the first 1000
iterations.
We implemented the RKHS model with the kernel-
averaging method (RKHS-KA, de los Campos et al. 2010).
The model has the form
y=1nµ+g1+g2+g3+e
,
where gl (l = 1, 2, 3) is the vector of partial genotypic
values (
g=g1+g2+g3
is the vector of total geno-
typic values). The basic assumption of the model is that
gl
∼N(0, K
l
σ
2
l)
, where
Kl=(kl(xi,xj))
is an n × n semi-
positive definite matrix whose entries are functions of
marker profiles of pairs of genotypes (xi is the i-th row
of the marker matrix X, i = 1,…,n). In this study we use
the Gaussian kernel, i.e.
k
l(xi,xj)=exp[−hl×
xi−x
2
j
p]
,
where hl is a bandwidth parameter. Defining h = (h1,
h2, h3) and following Pérez and de los Campos (2014),
we set
h
=(
1
5M
,
1
M
,
5
M)
, where M is the median squared
Euclidean distance between all lines. The model was

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implemented using the Bayesian approach (de los Cam-
pos et al. 2010), which was run for 10,000 iterations with
a burn-in of the first 1000 iterations.
The EGBLUP model has the form
y=1nµ+g1+g2+e
, where the total genotypic value
is split into additive genotypic value (
g1
) and additive ×
additive epistatic genotypic values (
g2
). We assume that
g
1∼N(0, Gσ
2
g1)
and g2∼N(0, Hσ
2
g2)
, where
G
is the
n × n genomic relationship matrix (VanRaden 2008) and
H
is the epistatic relationship matrix defined as
G#G
follow-
ing Henderson (1985). Note that # denotes the Hadamard
(element-wise) product of matrices. Parameters were esti-
mated using the Bayesian approach with the multi-kernel
method (Pérez and de los Campos 2014), which was run
for 10,000 iterations with a burn-in of 1000 iterations as
well.
In the above model we assumed a homogeneous resid-
ual variance. This assumption is justified by findings of a
recent study reporting that genomic predictions based on
homo- or heterogeneous residual variances were corre-
lated with coefficients above 0.99 (Schulz-Streeck et al.
2013). The prediction abilities of the four models for each
trait were evaluated in a fivefold cross-validation scheme
using the full data set combining all lines across 2 years.
In each run of cross-validation, the lines were randomly
divided into five subsets. Four of the five subsets were
used as the training set and the remaining one was the test
set. The ability of prediction was defined as the correla-
tion between BLUEs and predicted genotypic values of the
lines in the test set:
rGS
=cor

y
pred
,y
obs
. We used BLUEs
as response variable for genomic selection and not de-
regressed BLUPs as often used in animal breeding (Gar-
rick et al. 2009; Ostersen et al. 2011; Weber et al. 2012).
In wheat breeding, the main target of selection is the geno-
typic but not the breeding value. Therefore, BLUEs seems
to be more appropriate as they reflect an estimate of the
whole genotypic value and not solely the breeding value.
The procedure was repeated 20 times, yielding in total 100
different combinations of training and test sets. The final
prediction ability was the mean value of rGS obtained in
100 runs. In addition, we fitted the models also using the
full data to inspect the posterior mean of parameters of
models utilizing Bayesian approach. The posterior mean
of residual variance could be regarded as another criterion
aside from prediction ability assessing goodness-of-fit of
models (Crossa et al. 2010). The RRBLUP and the Bayes
Cπ model were implemented using R (R Core Team,
2014). The RKHS and EGBLUP model were implemented
using the R package BGLR (Pérez and de los Campos
2014). We checked convergence issues for Bayes Cπ,
RKHS and EGBLUP by inspecting the trace plots of vari-
ance components.
Evaluating the prediction ability from 1 year to the next
We implemented genomic prediction based on data col-
lected in the year 2012 to predict the performance of the
genotypes evaluated in the year 2013. We used all four
above outlined genomic selection models. Prediction abil-
ity was estimated as the correlation between predicted and
observed genotypic values of all genotypes in year 2013.
Influence of the composition of training population
on prediction ability
With the aim of studying the impact of the quality of phe-
notypic data on the prediction ability, we constructed 100
different training populations (sampling randomly 120
individuals out of the total tested during 2012) but with var-
ying number of phenotyping intensity (ranging from 1 to 5
locations). We used genotypes evaluated in year 2013 in at
least seven locations as test population. We contrasted this
scenario with a one not standardizing the population size of
the test set varying the minimum levels for the number of
locations from 1 to 5.
Detecting genotypes outside the calibration space
with the reliability criterion
We evaluated the potential to use the concept of reliability
in the genomic best linear unbiased prediction (GBLUP;
VanRaden 2008) model to detect genotypes which are
outside of the calibration space. The GBLUP model is of
the form
y=1nµ+g+e
, where g is the vector of geno-
typic values and
e
is the vector of residuals. We assume
that
g
∼N(0, Gσ
2
g)
, where
G
is the n × n genomic rela-
tionship matrix (VanRaden 2008), and
e
∼
N(0, Iσ2
e)
.
The reliability of the estimated genotypic value of the
ith genotype was defined as the correlation between the
true and estimated genotypic value:
ri=cor(gi,ˆgi)
. Let
C
=

C11 C12
C21 C22

=

1
′
n1n1
′
n
1nIn+Gσ2
e
/σ 2
g
be the coef-
ficient matrix of the mixed model equations (MME,
Henderson 1975). Let

C
11
C
12
C21 C22

be a generalized
inverse matrix of
C
. Then, the reliability can be calcu-
lated as
r
i=

1−
diσ2
e
σ2
g
, where di is the diagonal ele-
ment in
C22
corresponding to the ith genotype. Note that
di
σ
2
e
=SE (ˆg
i
)
2
=var (g
i−ˆ
g
i)
. is the squared stand-
ard error or the prediction error variance (PEV) of
ˆgi
(Hen-
derson 1975).
In principle, the reliability measures the bias of the esti-
mated genotypic value
ˆgi
, compared with the true genotypic
value gi. However, the true genotypic value is unknown in

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reality. Instead, we have the observed genotypic values,
denoted by
˜gi
, from phenotypic data analysis. We expect
that the reliability can also be used to approximately meas-
ure the difference between
ˆgi
and
ˆgi
in the sense that the
prediction ability for genotypes having high reliabilities is
higher than for genotypes having low reliabilities.
To test our hypothesis, we randomly sampled 50 % out
of 2325 genotypes as a training population and the remain-
ing 50 % formed the test population. The GBLUP model
was applied to obtain the predicted genotypic values and
the reliabilities for the genotypes in the test population.
Then, the prediction ability for different subsets of geno-
types in the test population was calculated, where the dif-
ferent subsets consisted of the first N % (N runs from 10 to
60 with a step of 10) of genotypes with highest reliabilities.
The above procedure was repeated 1000 times.
Results
Population structure
After marker imputation and quality control, 12,642 SNP
markers for 2325 genotypes (with 38.45 % of this data
being imputed) were available for further analyses. The
molecular diversity among the 2325 European elite wheat
lines was examined applying principal coordinate analysis
based on the pairwise Rogers’ distances previously esti-
mated based on the SNP markers (Supplementary Fig. S1).
We observed no apparent subpopulation structure. This was
further confirmed by inspecting the distribution of pair-
wise Rogers’ distances approximating a normal distribution
(Supplementary Fig. S2).
Quality of phenotypic data
The phenotypic data was non-orthogonal (Supplementary
Table S1) depicting the typical structure of grain yield trials
performed in multi-stage selection programs. The repeat-
ability estimated for the individual environments were
high and ranged from 0.78 to 0.93 (Fig. 1a). The genotypic
variance estimated for the 2325 wheat lines across environ-
ments was significantly (P < 0.01) larger than zero. The
heritability amounted to 0.66 but it is important to note
that number of environments and, hence, also the expected
heritability varied widely between wheat lines tested at a
different number of environments (Fig. 1b). We observed
a wide variation in BLUEs of the genotypes with the 1st
and 3rd quantiles of 9.10 and 9.78 Mg ha−1, respectively
(Fig. 1c). Out of the 2325 wheat lines, 154 have been tested
in both years. The BLUEs estimated for the 154 lines sepa-
rately for years 2012 and 2013 were significantly (P < 0.01)
correlated with a Pearson moment correlation coefficient
amounting to 0.57 (Fig. 2).
Performance of genomic selection models
We contrasted the prediction ability of two genomic selec-
tion models considering main and epistatic effects (EGB-
LUP and RKHS) with two genomic selection approaches
exploiting only main effects (RRBLUP and BayesCπ).
The EGBLUP and RKHS models performed similarly
and statistically significantly outperformed the RRBLUP
and BayesCπ models with an increased prediction ability
of approximately 5 % (P < 0.001) (Fig. 3). Moreover, the
Fig. 1 a Repeatability for grain yield estimated in each environment
using the 2325 wheat lines. b The number of environments in which
they have been tested and the relationship between heritability esti-
mates and the number of testing environments. c Distribution of their
best linear unbiased estimates (BLUEs) for grain yield

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standard deviations of the prediction accuracies were also
around 17 % smaller for EGBLUP and RKHS as compared
to RRBLUP and BayesCπ. Next, we studied the stability of
the genomic selection models developed in the year 2012
and evaluated the predicting ability using lines tested in
the year 2013. The prediction ability in average for all the
methods decreased from 0.65 to 0.5 compared to the sce-
nario when combining the data across both years (Fig. 3).
Genomic models based on Bayesian approach (EGB-
LUP, RKHS and BayesCπ) simultaneously could be com-
pared according to posterior mean of residual variance. The
EGBLUP and RKHS models performed similarly and both
outperformed BayesCπ in term of posterior mean of resid-
ual variance (P < 0.001), which is in accordance to their
performances in terms of prediction ability (Table 1). All
models converged promptly which could be evidenced by
inspecting the trace plot of residual variance (Supplemen-
tary Fig. S3).
Influence of composition of training population
on prediction abilities
The prediction ability was substantially impacted by the
phenotyping intensity of the training population assuming
a standardized population size of 120 individuals (Fig. 4a).
The prediction ability based on a training population evalu-
ated at only 1 location was only approximately half of that
of a population evaluated at 5 locations. Additionally, pre-
diction ability was maximized when the genotypes evalu-
ated in a single location were excluded from the training
set but subsequently decreased again when the phenotyping
intensity was increased above two locations (Fig. 4b).
Association between prediction ability and reliability
of particular individuals
The prediction ability was considerably influenced by the
constitution of the test population differentiated by the reli-
ability criterion. The top 10 % of the individuals in test
population with highest reliability estimates showed an
Fig. 2 Association between best linear unbiased estimates (BLUEs)
for grain yield of 154 wheat lines evaluated during the years 2012–
2013
Fig. 3 Prediction abilities of genomic selection using grain yield data
of both years 2012 and 2013 evaluated via fivefold cross-validation
using the four genomic selection models RR-BLUP, EG-BLUP,
RKHS, and BayesCπ. Prediction abilities of genomic selection cali-
brated using grain yield data of year 2012 to predict the performance
of genotypes tested in the year 2013. Standard deviations of cross
validations are presented as vertical lines
Table 1 Estimates of posterior mean of parameters within each
model from the full-data analysis for grain yield
Model Parameter Posterior mean (standard deviation)
EGBLUP
σe
20.049 (0.005)
σ2
g1
0.060 (0.007)
σ2
g2
0.026 (0.003)
RKHS
σe
20.039 (0.005)
σ2
g1
0.139 (0.096)
σ2
g2
0.259 (0.035)
σ2
g3
0.029 (0.007)
BayesCπ
σe
20.107 (0.005)
σα
21.65 × 10−4 (7.10 × 10−5)
π0.184 (0.087)

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advantage of 0.2 in the prediction ability in contrast to the
top 60 % of lines (Fig. 5).
Discussion
We studied relevant factors with potential implications on
the implementation of genomic selection for grain yield
using data from a commercial winter wheat breeding pro-
gram with more than 2000 genotypes. Theoretically, the
upper limit of the prediction ability for genomic selection
corresponds to the selection accuracy (square root of the
heritability, h) (Crossa et al. 2010). In our study, the esti-
mation of h based on the 2 year data was 0.81 and in par-
allel the prediction ability achieved by genomic selection
amounted to 0.65. In this sense, the general results of our
study are promising for the implementation of genomic
selection into wheat plant breeding programs and their the-
oretical and practical implications are deeply discussed in
the following sections.
Subpopulation structure and genotype‑by‑year
interaction are of minor relevance for the prediction
abilities observed within the 2 year winter wheat
dataset
Several studies have reviewed factors influencing the pre-
diction ability of genomic selection (Guo et al. 2014;
Habier et al. 2007; Heffner et al. 2009; Jannink et al.
2010; Liu et al. 2011; Zhao et al. 2012; Zhong et al.
2009). Among these factors, subpopulation structure could
severely impact the ability of genomic predictions in crop
plants (Guo et al. 2014; Isidro et al. 2015; Windhausen
et al. 2012). In our study, we did not find a pronounced sub-
population structure (Supplementary Fig. S1), suggesting
that the bias in prediction abilities for grain yield based on
fivefold cross-validation (randomly dividing the data into
training and test sets) would be inconspicuous.
Before the release of a new commercial variety, wheat
breeders in Germany often focus on the breeding line per-
formance across test environments, because genotype-
by-location interaction have only a small influence on
the grain yield performance in Germany (Utz and Laidig
1989). Hence, the main focus of our study was the predic-
tion of grain yield performance across environments for
the selection candidates. Furthermore, genotype-by-year
and genotype-by-location-by-year interactions are the main
forces determining genotype-by-environment interaction
on grain yield performance in Germany (Utz and Laidig
1989) but unfortunately, these sources of variation are not
predictable or exploitable by plant breeders. One of the
Fig. 4 Grain yield prediction
abilities of the four genomic
selection models RR-BLUP,
EG-BLUP, RKHS, and
BayesCπ using subsets of geno-
types during the year 2012 clas-
sified by the number of testing
locations being (a) equal or (b)
more or equal than 1, 2, 3, and
5, to predict genotypes tested
in seven locations in the year
2013. Number in brackets refers
to the number of genotypes used
in the training populations
Fig. 5 Prediction abilities of genomic selection for grain yield using
data combining 2012 and 2013 years considering different subsets of
test populations constituted by the 10–60 % most reliable individuals

Theor Appl Genet
1 3
main advantages of genomic selection is the acceleration of
the breeding process by reaching more cycles of selection
per unit of time (Longin et al. 2015; Rutkoski et al. 2012),
therefore, any kind of genomic selection approach using
historical plant breeding data should be ultimately imple-
mented to predict the performance of untested genotypes
in untested years. Previous studies suggested that even
though genotype-by-year interaction has potentially a nega-
tive influence on the prediction ability of genomic selection
using historical data (Dawson et al. 2013; Rutkoski et al.
2015), its negative effect could be neglected (Dawson et al.
2013). The phenotypic correlation of common genotypes
between years 2012 and 2013 was 0.57 (Fig. 2), which sug-
gests the presence of genotype-by-year interaction within
our 2 year dataset. Interestingly, we observed that predic-
tion ability of genomic selection using the pooled data of
the years 2012 and 2013 averaged 0.65, and it only dropped
to an average of 0.5 when genomic selection models were
calibrated using solely the data collected during 2012 to
perform predictions for the following year (Fig. 3). Taken
together, these results plus the observations made by Daw-
son et al. (2013) using CIMMYT’s 17 years historical data,
indicate that models to perform forward genomic predic-
tions in wheat could be accurately calibrated using plant
breeding historical data from adjacent past years and that
prediction models can be built upon 1 year phenotypic data
without a drastic loss in prediction ability. The latter is
pivotal, because historic data of wheat breeding programs
often comprises genotypes tested in a single year.
Modeling epistasis improved the prediction ability
of genomic selection
It has been mentioned in the past that the presence of di-
genic interactions or epistasis could bias predictions based
solely on additive effects (Crossa et al. 2010; Gianola et al.
2006; González-Camacho et al. 2012; Heslot et al. 2012).
When shifting from additive (e.g. RRBLUP) to additive
plus epistatic effects (RKHS) models in wheat, Heslot
et al. (2012); Crossa et al. (2010) found a 4 and 25 % of
improvement in prediction abilities for grain yield, respec-
tively, which agrees with the 5 % of improvement found in
our study (Fig. 3). Consequently, including epistatic effects
within the genomic prediction models holds the promise
to increase the prediction ability of the genotypic value
(Crossa et al. 2010; Heslot et al. 2012).
Prediction ability of genomic selection increased
by filtering based on quality of the phenotypic data
We observed that keeping the population size constant but
increasing their phenotyping intensity led to higher pre-
diction ability levels (Fig. 4a). Hence, training genomic
selection models using high-quality phenotypic data poten-
tially provide more precise genomic predictions. However,
since phenotyping resources are limited in applied wheat
breeding programs, there is always a trade-off between fil-
tering based on phenotypic data quality and the number of
genotypes used to calibrate genomic selection models. It is
well known that a reduction in the training population size
would lead to a decreased prediction ability (Asoro et al.
2011; Lorenzana and Bernardo 2009), and in consequence
this loss in prediction ability is expected to weaken or can-
cel out the gain in prediction ability reached by a model
trained exclusively with intensively phenotyped geno-
types. Our results properly illustrates this trade-off between
phenotyping intensity and the training population size
(Fig. 4b): Genomic prediction ability was maximized when
the genotypes evaluated in a single location were excluded
from the training set but subsequently decreased again
when the phenotyping intensity was increased above two
locations. In this sense, slightly filtering the training set by
phenotyping intensity could be a feasible way to improve
the prediction ability of genomic selection.
Implementing genomic selection and the reliability
concept into applied wheat plant breeding programs
In the past, different strategies completely or partially
relying on genomic selection have been proposed to be
implemented into wheat breeding programs and in gen-
eral, picking the best strategy would completely depend
on the prediction ability achieved by the genomic selection
models (Longin et al. 2015). Commonly, during the early
stages of a commercial breeding program there is a massive
amount of individuals available for selection but the limited
budget would restrict the phenotyping process to a limited
number of locations. In this sense, if we consider that the
costs of genotyping are comparable to the costs of a single
location yield trial (Heffner et al. 2010) and that genomic
selection can achieve prediction abilities (Fig. 3) which are
equivalent to the selection accuracy for grain yield evalu-
ated in three locations (Supplementary Fig. S4), replacing
the phenotyping process for the first selection stage by their
genomic predictions is feasible. By means of this strategy,
1 year of breeding cycle could be saved.
Alternatively, doing selection completely based on
genomic predictions (without phenotyping in any genera-
tion) was only recommended when high prediction abilities
are achieved by the genomic selection models (Longin et al.
2015). Our results suggest that this last strategy could be
possible for genotypes exhibiting high reliability estimates.
We found a positive association between average reliability
and genomic prediction ability (Fig. 5), which agrees with
past findings of genomic selection in dairy cattle (Hayes
et al. 2009b) and implies that the genomic predictions of

Theor Appl Genet
1 3
highly reliable genotypes would be (in average) more cor-
related to the BLUEs of these genotypes. Since phenotypic
selection in plant breeding is normally based on the mean
performance of each breeding line (represented by their
BLUEs) and prediction abilities of the 10 % most reliable
genotypes approached 0.79 (Fig. 5), phenotypic selection
for highly reliable individuals could be directly replaced
by implementing genomic selection for them. Therefore,
plant breeders benefit tremendously by using the reliabil-
ity parameter in combination with the genomic predictions
of non-phenotyped individuals. Consequently, we expect
that genomic selection would assist (and not completely
replace) phenotypic selection in the future, because on one
side highly reliable genotypes with high genomic predicted
performances might be directly put into the ultimate mar-
ket and, on the contrary, low or medium reliability geno-
types would deserve higher phenotyping intensity for culti-
var release. We believe that this integrated approach would
allow a better allocation of resources for plant breeding
companies.
Last but not least, in the course of wheat breeding, a
vast amount of phenotypic data will be generated for the
selected genotypes during the breeding cycle (Supplemen-
tary Fig. S5); hence one question that naturally arises is
whether all these phenotypic data should be used for updat-
ing the information contained within the training popula-
tion. As it was mentioned before, one way to improve the
prediction ability of genomic selection would be by means
of filtering the training population by phenotyping inten-
sity (Fig. 4). However, genetic variation is expected to be
decreased through conventional one tail (unidirectional)
selection within the training population and this decre-
ment in genetic variation is expected to have a significant
negative impact on the prediction ability of genomic selec-
tion (Zhao et al. 2012). Therefore, the update of the train-
ing population can not only rely on intensively phenotyped
genotypes, because of its implicit cost in genetic variation.
This suggests that a balance between phenotyping intensity
and genetic variation should be found for the recalibra-
tion of the genomic selection models. In the past, picking
extremely performing lines by means of two tail (bidirec-
tional) selection has shown to successfully maintain the
prediction abilities reached by a training population with-
out filtering (Boligon et al. 2012; Jiménez-Montero et al.
2012; Zhao et al. 2012). In this sense, selecting a propor-
tion of low performing genotypes in addition to the highly
performing ones would not only increase the genetic vari-
ation but also would allow maintaining the phenotyping
intensity at a sufficient level. To find the optimal propor-
tion of high and low performing genotypes allowing a cost
effective balance between genetic variation and phenotyp-
ing intensity within the training population is beyond the
scope of our study, but certainly this particular topic should
be explored in the future. We anticipate that this new
knowledge will provide a better understanding on how to
routinely optimize the architecture of the training popula-
tion used to recalibrate the genomic selection models based
on historical plant breeding data.
Author contribution statement JCR, EE, and RB con-
ceived the design of this study. VK coordinated the SNP
genotyping. EE and RB coordinated the experiments
including the phenotypic trait measurements of the plant
materials. SH, AWS, VM, YJ, YZ and JCR made the con-
cept and wrote the manuscript. SH conducted the analyses.
All authors have read and approved the final manuscript.
Compliance with ethical standards
Conflict of interest All authors agree that there are not conflicts of
interest to be reported.
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