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ORIGINAL PAPER
Genome-wide association mapping of agronomic and morphologic
traits in highly structured populations of barley cultivars
Minghui Wang •Ning Jiang •Tianye Jia •
Lindsey Leach •James Cockram •Robbie Waugh •
Luke Ramsay •Bill Thomas •Zewei Luo
Received: 27 April 2011 / Accepted: 29 August 2011 / Published online: 14 September 2011
Springer-Verlag 2011
Abstract Genome-wide association study (GWAS) has
become an obvious general approach for studying traits of
agricultural importance in higher plants, especially crops.
Here, we present a GWAS of 32 morphologic and 10
agronomic traits in a collection of 615 barley cultivars
genotyped by genome-wide polymorphisms from a
recently developed barley oligonucleotide pool assay.
Strong population structure effect related to mixed sam-
pling based on seasonal growth habit and ear row number
is present in this barley collection. Comparison of seven
statistical approaches in a genome-wide scan for significant
associations with or without correction for confounding by
population structure, revealed that in reducing false posi-
tive rates while maintaining statistical power, a mixed
linear model solution outperforms genomic control, struc-
tured association, stepwise regression control and principal
components adjustment. The present study reports signifi-
cant associations for sixteen morphologic and nine agro-
nomic traits and demonstrates the power and feasibility of
applying GWAS to explore complex traits in highly
structured plant samples.
Introduction
With the growing availability of genome sequence data and
advances in technology for rapid identification and scoring
of genetic markers, linkage disequilibrium (LD) based
genome-wide association study (GWAS) has gained favour
in higher plants, especially crops, for the mapping of
genetic factors responsible for complex trait variation
(Remington et al. 2001; Gupta et al. 2005; Mackay and
Powell 2007; Cockram et al. 2008; Sneller et al. 2009;
Atwell et al. 2010). While conventional linkage analysis
works on an experimental population derived from a cross
of bi-parents divergent for a trait of interest, association
mapping applies to collections of samples of a much wider
germplasm base. Providing the intrinsic nature of exploit-
ing historical recombination events, association mapping
offers increased mapping resolution to polymorphisms at
sequence level and should therefore enhance the efficiency
of gene discovery and facilitate marker assisted selection
(MAS) in plant breeding (Gupta et al. 2005; Moose and
Mumm 2008). Plants offer an ease of genetic manipulation
allowing production of genetically uniform cultivars
through inbreeding, making it possible to conduct repli-
cated assays for many different traits under multiple
environmental conditions. Once the plant cultivars are
genotyped with high-density markers, association mapping
Communicated by J. Yu.
Electronic supplementary material The online version of this
article (doi:10.1007/s00122-011-1697-2) contains supplementary
material, which is available to authorized users.
M. Wang N. Jiang T. Jia Z. Luo (&)
School of Biosciences, The University of Birmingham,
Edgbaston, Birmingham B15 2TT, UK
e-mail: z.luo@bham.ac.uk
N. Jiang R. Waugh L. Ramsay B. Thomas
BioSS Unit, Scottish Crop Research Institute, Invergowrie,
Dundee DD2 5DA, UK
L. Leach
Department of Plant Sciences, University of Oxford,
South Parks Road, Oxford OX1 3RB, UK
J. Cockram
John Bingham Laboratory, National Institute
of Agricultural Botany, Cambridge CB3 0LE, UK
123
Theor Appl Genet (2012) 124:233–246
DOI 10.1007/s00122-011-1697-2
is promising in resolving the genetic basis of complex traits
of both economic and ecological importance.
In the present study, we applied GWAS to analyse a
number of continuous and categorical traits in a collection
of 615 elite UK barley cultivar samples, some of which
were recently reported in an association mapping study
(Cockram et al. 2010). Barley (Hordeum vulgare L.), the
world’s fourth most important cereal crop, is an econom-
ically important model plant for genetics research (Hayes
et al. 2003; Taketa et al. 2008). Due to its narrow genetic
base of breeding and also the population bottleneck during
the domestication of modern barley cultivars, it was
reported that barley exhibited an extensive extent of LD
(Kraakman et al. 2004; Rostoks et al. 2006; Malysheva-
Otto et al. 2006). Barley cultivars thus potentially provide
extant genetic resources that allow successful association
mapping using a relatively small density of markers,
although the resolution could be limited. Plant species such
as barley present exclusive features that could cause
striking difference from human GWAS. For example,
barley is a diploid and hermaphroditic species in which
self-pollination and homozygosity are normal, thus
observed heterozygosity is limited in barley cultivars
(Rostoks et al. 2006). Moreover, due to the nature of
inbreeding and isolation by distance, barley samples may
present a much larger scale of population structure and
relatedness, introducing the potential for serious con-
founding in the association study (Balding 2006; Atwell
et al. 2010; Hamblin et al. 2010; Platt et al. 2010). In
addition, human intervention plays an essential role in
modern barley cultivation, hence strong selection on
agronomic/economically important traits is expected
(Rostoks et al. 2006). Furthermore, the whole genome
sequences of many plant species including barley are cur-
rently unavailable, hindering any attempt to fine map
genetic determinants to sequence level. Given the various
complicating factors exhibited in plant samples, it raises
concerns about the general applicability of many standard
population genetics models well established for human
GWAS to plants such as barley.
It is recognized that the barley germplasms are highly
partitioned, predominantly due to the number of ear rows
(two-row and six-row samples), and the requirement of
vernalization (winter- and spring-sown samples) (von
Zitzewitz et al. 2005; Yan et al. 2006; Rostoks et al. 2006;
Komatsuda et al. 2007; Hamblin et al. 2010). The present
barley samples comprise several combinations of these
characters. As the molecular bases of ear row number and
vernalization requirement in barley have been relatively well
characterised (Cockram et al. 2008; Komatsuda et al. 2007),
these barley samples present an ideal test bed to evaluate the
applicability of various statistical methods established for
association mapping in highly structured samples. In this
paper, we first investigated the LD structure and its rela-
tionship with the barley population division. Methodologi-
cally, we tested the performances of one parametric model
(STRUCTURE) and one dimensional reduction technique
(principal component analysis, PCA) in the inference of
population structure of the barley samples. Second, we
undertook a genome-wide scan for significant markers
associated with a number of traits using six major population
structure correction methods (reviewed extensively in Astle
and Balding 2009). A comparison of empirical Pvalue dis-
tribution and a simulation study of statistical power were
conducted to evaluate the performances of different meth-
ods. Finally, association mapping results from the best
structure correction method were reported.
Materials
Germplasm and genotyping
The present study recruits the barley cultivars that have
undergone at least 2 years of the UK National List (NL)
trials since 1993, together with additional confidential elite
lines supplied by major UK barley breeding companies. In
total, there are 615 UK barley cultivars (they are also
referred as to samples in followings) collected in the
present study, among which 490 cultivars were reported in
a GWAS of barley morphological traits in Cockram et al.
(2010) (ESM, Table S1). Among this collection, 461
samples have records for ear row number, in which 433 are
two-row barley and 28 are six-row barley. 472 samples are
known for seasonal growth habit, in which 256 are winter
barley and 216 are spring barley. The 433 two-row barley
samples are almost equally partitioned into winter (220)
and spring (209) groups, while 4 are unknown for seasonal
growth habit. Of the 28 six-row barley samples, 27 are
winter barleys and 1 is unknown for seasonal growth habit.
The barley samples were genotyped at 1,536 single
nucleotide polymorphism (SNP) markers by using a
recently developed genotyping platform, the Illumina
GoldenGate oligonucleotide pool assay 1 (BOPA1).
Details were described elsewhere for development of the
markers as well as construction of the genetic consensus
linkage map based on genotypes of BOPA1 and its sister
production assay (BOPA2) (Close et al. 2009). Markers
genotyped in less than 95% of the samples, with a minor
allele frequency (MAF) below 0.1 or unmapped in the
barley consensus genetic map were excluded from further
analysis. Heterozygous genotypes were rare (0.8%) in the
present data as expected from extensive inbreeding and
backcrossing in cultivation and were removed to simplify
the subsequent analysis. After quality control checking,
1,042 markers remained for further analysis.
234 Theor Appl Genet (2012) 124:233–246
123
Phenotype
Phenotypic data was recorded on 32 highly heritable mor-
phological characters as well as on 10 agronomic characters
including yield and malting traits (ESM, Table S2a, b). The
32 morphological characters, including seasonal growth
habit and ear row number, were scored as binary or cate-
gorical characters according to the guidelines of Interna-
tional Union for the Protection of New Varieties of Plants
(UPOV) protocols (http://www.upov.int/) (Cockram et al.
2010). These morphological phenotype data were loaded at
NIAB (http://www.niab.com/) and named Distinctness,
Uniformity and Stability (DUS) traits hereafter. For each of
the agronomic characters, the phenotype data were collected
from a series of performance assessment trials involving at
least four site by season combinations, and thus the data so
collected represent agronomic performance of the cultivars
in a wide range of environments. A mixed linear model was
first fitted to account for the time, trial and regional effects
together with their interactions and the predicted mean val-
ues after removing the fixed effects were taken as the final
agronomic trait measure for each barley sample. For con-
venience, we called the summarized agronomic measure-
ments as BLUP traits which were sourced as the archived
database at the Association Genetics of UK Elite Barley
(AGOUEB, http://www.agoueb.org). In this primitive
BLUP analysis of the agronomic traits, considerable year and
site differences as well as their interactions were observed
for most of the agronomic traits while the differences
between trials were rarely significant and generally negli-
gible. With regard to the difference between the genotypes,
heritabilities were generally high with an average of 36% for
spring and 45% for winter barley (data not shown). It should
be noted that, the present barley collection has 125 extra
samples compared to those used in Cockram et al. (2010).
Although none of these extra samples has phenotypic records
for the DUS or BLUP traits, they had been genotyped with
the BOPA1 platform and hence were recruited in the present
study for the purpose to investigate the population structure
in a larger collection of UK barley germplasm.
Methods
Unless otherwise stated, all analyses were carried out using
R, a statistical software package freely available at http://
www.r-project.org.
Inference of population structure
Program STRUCTURE v2.2.3 (http://pritch.bsd.uchicago.
edu/structure.html) was first applied to estimate the number
of historical populations in the present barley samples
using default setting of admixture model for the ancestry of
individuals and correlated allele frequencies. Population
sub-structure was modelled with a burnin of 2.5 910
5
cycles followed by 10
6
Markov Chain Monte Carlo
(MCMC) repeats for prior assumed ancestral population
number, K=1,…, 20. Since STRUCTURE analysis is
computationally intensive, we did not load in all 1,042
markers but instead used 4 subsets of markers. The first
marker set contained seven markers, each of which was
selected from the middle of a chromosome while the
remaining three sets consisted of 305, 96 and 54 markers
selected every 2, 10 or 20 cM, respectively, along the
barley chromosomes.
Principal component analysis (PCA) was also used as in
Price et al. (2006) to infer the population structure in the
barley samples. Let gbe a matrix of genotypes with ele-
ment g
ij
being the genotype of variety iat marker j, where
i=1toN(the number of samples) and j=1toM(the
number of markers). Re-scale matrix gby subtracting the
column mean and then dividing by the column standard
deviation for each entry in column j, to give a matrix
denoted by X.AnNNsample covariance matrix was
computed from Xand then decomposed into eigenvalues
and eigenvectors V. In Price et al. (2006), the kth top
eigenvector in Vwas regarded as the kth axis of variation
due to ancestry difference.
Association scan
A naive single marker association (SMA) test without
correction for confounding was first carried out to search
for associations between trait phenotype and marker
genotype. SMA refers to linear regression for continuous
quantitative traits, Wilcoxon rank-sum test for ordinal
categorical traits and chi-square test for other categorical
traits. Six statistical methods widely used for controlling
population structure were applied to analyze the data.
These are structured association (SA) (Pritchard et al.
2000b), genomic control (GC) (Devlin and Roeder 1999),
EIGENSTRAT (Price et al. 2006), stepwise regression
(SWR) (Setakis et al. 2006), and the mixed linear model
(MLM) methods with or without incorporating an inferred
population structure matrix as cofactor (Yu et al. 2006).
Except for Wilcoxon rank-sum test and chi-square test,
the other methods can be formulated within standard
regression models that express the expected value of y
i
, the
phenotype of the ith sample, as a function of its genotype x
i
at the test marker:
gðE½yiÞ ¼ aþxibð1Þ
where gis a link function, ais model intercept, and bis
genetic effect parameter at the marker. Here, x
i
is simply
coded as 0 and 1 for two different homozygous genotypes
Theor Appl Genet (2012) 124:233–246 235
123
at a test marker. For categorical traits, gis a logit link
function, while for quantitative traits, gis an identity link
function.
The GC approach was originally developed to correct
inflation in a chi-square statistic estimated by Armitage’s
trend test in structured case-control samples. Bacanu et al.
(2002) demonstrated the GC can also be applied to the
analysis of quantitative traits by taking ½^
b=SEð^
bÞ2(where
^
bis the estimate of regression coefficient band SE is the
standard error) as a chi-square test statistic and hence the
inflation factor kcan be estimated from a number of ‘null’
markers using similar methodology to the case–control
settings (Devlin and Roeder 1999). As we do not know
a priori which markers are ‘null’, parameter kwas esti-
mated in the present study as the median of genome-wide
chi-square scores divided by 0.455, the median of the
empirical chi-square distribution under null hypothesis as
suggested in Devlin and Roeder (1999). Whenever kis
larger than 1, the chi-square statistic at each test marker is
divided by k.
In the standard SA approach, association test is condi-
tional on the assignment of a population structure inferred
by STRUCTURE (the Qmatrix). In the present study, a
reliable inference of Qmatrix was not achievable (see
‘‘ Results’’); instead, a design matrix indicating the cluster
membership derived from k-means clustering of top three
PCA axes (termed Pmatrix for simplicity) was incorpo-
rated into Eq. 1with a form of
gðE½yiÞ ¼ aþxibþPivð2Þ
where P
i
is the ith row of the Pmatrix and vis a column
vector of regression coefficients. The best cluster model of
the k-means clustering was determined through a model
selection based on Bayesian information criterion (BIC)
which is detailed in ‘‘Results’’ .
The EIGENSTRAT method adjusts the genotype and
phenotype by using eigenvectors Vestimated from the
PCA method as described. In detail, let g
ij
be the genotype
of individual iat marker j, the adjusted genotype is
gij;adj ¼gij cjai, where aiis the ancestry of the ith indi-
vidual along a given axis of variation and cj¼
Piaigij=Pia2
iis a regression coefficient (Price et al.
2006). Adjustments are performed using the top ten axes of
variation following Price et al. (2006). Phenotype y
i
is
adjusted analogously. A linear regression is then carried
out to test the association between adjusted phenotype and
genotype.
The SWR approach uses a stepwise regression proce-
dure to select for a ‘random’ set of markers as covariates to
control for population structure. By including into the
regression model the genotype of covariate markers, the
linear equation becomes
gðE½yiÞ ¼ aþxibþXjCijujð3Þ
where Cij is the genotype of the ith individual at the jth
covariate marker and ujis the partial regression coefficient.
Covariate markers are selected prior to testing a marker of
interest by using a forward and backward (stepwise)
selection from a random set of 305 markers chosen every
2 cM along the chromosomes. In this study, the stepwise
algorithm for selecting covariate markers was implemented
by an R function step, using a penalty score log(n), where n
is the number of markers. It should be stressed that step-
wise regression is computationally intensive in R and it
may even become impractically doable when all markers
are incorporated in the model fitting. Moreover, because
barley exhibit extensive extent of LD along the chromo-
somes, it is not necessary to include all markers as adjacent
markers tend to provide redundant information regarding
the population structure.
The MLM model extends equation (2) by including a
random polygenic effect term such that the model is
expressed as
E½yijdi¼aþxibþPivþdið4Þ
where diis interpreted as a polygenic contribution to the
phenotype (Yu et al. 2006; Astle and Balding 2009) and
assumed to have a distribution of dNð0;2Kr2
gÞ, where
Kis a kinship matrix and r2
gis the genetic variance
attributable to genome-wide effects. In this study, Kis
estimated as a pairwise identical-by-state (IBS) allele-
sharing matrix (Kang et al. 2008). As both population
structure and kinship were incorporated, we called this full
model the MLM (P ?K) model. Meanwhile, we tested a
Konly model, called MLM (K), which omits the popula-
tion structure Pfrom the full model. Both MLM (P ?K)
and MLM (K), together with the calculation of IBS allele-
sharing matrix, have been implemented in R package
EMMA (Kang et al. 2008).
Simulation study
A candidate quantitative trait nucleotide (QTN) simulation
similar to that of Yu et al. (2006) was conducted. The
simulation starts by randomly choosing from the 1,042
markers, a marker with minor allele frequency in the range
of 0.1–0.4 as a causal marker. Next, a constant genetic
effect explaining a proportion of phenotype variance is
added to this causal marker. Later, the phenotype value for
an individual is generated by summation of population
mean, its genotypic value at the causal marker and a ran-
dom number. Given the size of genetic effect, a, the per-
centage of phenotypic variation explained by the causal
marker in a pure homozygote type population is calculated
236 Theor Appl Genet (2012) 124:233–246
123
by pð1pÞa2=r2, where pis the allele frequency and r2is
the total phenotype variance (Falconer and Mackay 1996).
For a categorical trait with ncategories, we considered a
liability model that a set of thresholds h
j
(s) determines the
explicit categories from the (underlying) quantitative phe-
notype values. The ith sample falls in trait category jif its
simulated quantitative trait value T
i
satisfying the condition
of h
j-1
\T
i
Bh
j
(j=1, …,n), in which h
n
=-h
0
=?.In
the present simulation study, thresholds h
j
(s) are deter-
mined in a way that maintains the same categorical dis-
tributions (i.e. keeping the same proportion of samples in
each category) as that of the observed traits.
Results
Statistical prediction of population structure
The genome-wide LD structure in the 615 barley samples
was inferred with software Haploview (see Supplementary
Material Fig. S2a–c for the genome-wide r
2
pattern). High
LD values were observed across a wide range of the gen-
ome with 88.6% significant pairwise marker associations
(Bonferroni corrected Pvalue threshold 9.2 910
-8
) being
inter-chromosomal, suggesting strong population structure
effect in the barley samples. Furthermore, significant intra-
chromosomal LD was evident across the full length of
chromosomes (mean =57.4 cM). When isolating winter
samples and spring samples from the whole barley col-
lection, we found that 52.6% of the markers had allele
frequencies differing more than twofold between winter
and spring subpopulations. Analysis of the LD structure in
the two separate seasonal growth type samples revealed
that the proportion of significant inter-chromosome mar-
ker-pair associations reduced to 18.9% in winter samples
and 10.8% in spring samples while the mean span of sig-
nificant intra-chromosomal LD was 8.5 and 5.2 cM
accordingly. This result suggests the presence of significant
population structure in the 615 barley samples is primarily
due to the divergence in winter and spring growth habit.
The absence of seasonal growth habit information for
some barley samples necessitated a more detailed investi-
gation of the population structure in the whole barley
collection, for which we employed two statistical approa-
ches making use of marker genotype data. The first
approach was using the program STRUCTURE, a para-
metric method developed by Pritchard et al. (2000a), which
uses a Bayesian Markov Chain Monte Carlo (MCMC)
approach to infer the number of ancestral subpopulations,
K, and then to assign samples probabilistically to each of
the Ksubpopulations. Under the same program parameter
setting we carried out STRUCTURE analyses using four
sets of markers selected according to the criteria described
above. Figure 1a shows the estimated log probabilities of
the sample data on subpopulation number Kfrom 1 to 20.
As illustrated, none of the four marker sets was able to
achieve a convergence for the estimation of parameter K,
implying failure to obtain a reliable inference of population
structure. It is also observed from Fig. 1a an upward trend
in the estimated log probabilities of the data as parameter
Kincreases when using genotypes of 305 markers which
were chosen every 2 cM along barley chromosomes.
However, this trend is not evident when genotypes of fewer
markers were used, suggesting disagreement in STRUC-
TURE inferences drawn from different marker genotypes.
The second approach used PCA analysis to search for
the internal patterns of population structure in the barley
samples. Figure 1b and c presents the top three principal
components (PCs) decomposed from the covariance
matrix. The first three PCs explained, respectively, 20.1,
5.2 and 3.1% of the total variance among the barley col-
lections. The majority of winter samples and spring sam-
ples were clearly separated from each other by the first PC,
except for five winter samples which were clustered with
spring samples. An isolated cluster was also evident con-
sisting of more than 30 samples unknown for both ear row
number and seasonal growth habit (Fig. 1b). Of the 27 six-
row and also winter samples, 22 tend to aggregate to a
separate cluster together with 1 two-row sample and some
samples with unknown ear row number (Fig. 1b). The third
PC reveals dispersions within either winter or spring
samples, e.g. a group of 57 winter barleys are apparently
separated from the majority within the winter barley cluster
(Fig. 1c). These observations confirm the winter and spring
growth habit as the major source that gives rise to the
population structure in the barley samples, and additionally
suggest the existence of subdivisions in either winter or
spring barley samples. The results also manifest the sepa-
ration between two-row and six-row types. However,
clustering with the top three features extracted from PCA
by using an x-means cluster algorithm (Pelleg and Moore
2000), which extends the commonly used k-means cluster
with efficient estimation of the optimized number of clus-
ters based on Bayesian information criterion (BIC), shows
that the best cluster model has a cluster number k=2
(BIC =-160.1). The resulting cluster membership with
k=2 was written in a matrix form and taken as the
Pmatrix in the following association analyses.
Confounding due to population structure
Since variation of winter and spring growth habit contrib-
utes the major source of barley population structure, we
were interested in whether the traits were distributed dif-
ferentially between winter and spring barley samples.
Theor Appl Genet (2012) 124:233–246 237
123
Supplementary Material (ESM, Fig. S2a, b) presents the
distributions of BLUP and DUS traits in the two seasonal
growth habit samples. All BLUP and a number of DUS
traits clearly presented differential distribution between
winter and spring barley samples (those significantly
associated with seasonal growth habit are indicated in
Table S2). This observation raises a concern that any
marker that differs in allele frequency between seasonal
growth types will show association with these differentially
distributed traits. Because more than half of the markers
had allele frequencies differing more than twofold between
winter and spring barley samples, an association test
without accounting for the population structure will result
in an increased rate of systematic false positives (Balding
2006).
A single marker association (SMA) test was first carried
out to scan for markers in significant association with trait
variation in the winter and spring barley samples sepa-
rately. As shown in Supplementary Material (ESM, Table
S3), a greater number of significant markers were predicted
in winter barley varieties than in spring barley varieties. By
visualizing the Pvalue distribution in a quantile–quantile
plot (Wilk and Gnanadesikan 1968), we found that all
BLUP and a majority of DUS traits gave rise to a distri-
bution of Pvalues strongly skewed towards significance
(GC k[1.0) (ESM, Fig. S4a, b), though we also observed
distributions of Pvalues that showed skewness against
significance in four DUS traits (numbers 1, 7, 18 and 31).
Because population structure may lead to excess of both
false positive and false negative associations (Ziv and
Burchard 2003), the present observation of skewed Pvalue
distributions suggests that the expected confounding indeed
exists in winter and spring samples.
By analyzing all 615 barley samples, a large number of
genome-wide distributed markers were detected to be sig-
nificant from the naive SMA approach in all of the BLUP
and in about half of the 32 DUS traits (ESM, Table S3). For
example, with DUS trait number 28 (seasonal growth
habit), there were 793 significant markers (more than 76%
of the total markers). Quantile–quantile plot of the Pvalue
Fig. 1 a Estimated log
probability, Ln(p), of the data
on different population number
Kfrom STRUCTURE analyses.
Curves from top to bottom are
for analyses using genotypes
from markers selected by
picking one marker on every
chromosome, or markers at
intervals of 20 cM, 10 cM, and
2 cM, respectively. b, c The top
three principal components
(PCs) in PCA analysis of the
variation of the present 615
barley samples. Blank,
shadowed and crossed symbols
indicate barley samples with
winter, spring and unknown
seasonal growth habit,
respectively
238 Theor Appl Genet (2012) 124:233–246
123
distributions indicated a very strong skew towards signifi-
cance for almost every trait (ESM, Fig. S4a, b). Although
we expected some of the significant associations to be true,
an excessive number of significant detections obfuscate the
genuine association signals from the true causal genes.
Statistical approaches for reducing confounding
Six different structure correction methods were applied in
an attempt to separate the genuine associations from
background noise in the genome-wide mapping using all
615 barley samples. The number of significant markers
surpassing Bonferroni genome-wide Pvalue threshold
4.8 910
-5
from each of these methods was listed in
Supplementary Material (ESM, Table S3), from which we
observed, as expected, a remarkable drop in the number of
significant associations from the six correction methods
compared to the naive SMA method. For most of the BLUP
and DUS traits, the SWR and SA methods had a compa-
rable number of significant predictions, followed in
descending order by MLM (K), MLM (P ?K), and lastly
GC. EIGENSTRAT presented different conservativeness
between DUS and BLUP traits; it is a bit more liberal than
MLM (K) in DUS traits but as conservative as GC in BLUP
traits.
Following a similar approach used by Potokina et al.
(2008) to separate cis- from trans- expression quantitative
trait loci (eQTL), we divided the barley genome into seg-
ments of 2 cM length (hereafter referred to as bins), and
represented the significance of each segment by the Pvalue
of the most significant marker within it. In doing so, the
barley genome was split into 303 chromosome bins. Since
the barley genome displays extensive LD blocks, this
effectively reduced the redundancy of significant signals
from linked loci within a short chromosome region, espe-
cially for the naive SMA method (ESM, Table S3). A
comparison of shared significant chromosome bins among
seven analytical methods was summarized as mutual pre-
dictabilities and given in Table 1. Here, mutual predict-
ability of method jto method iis calculated as the
percentage of significant predictions from method ithat
were recovered by method j. For example, in DUS traits,
SMA predicted 43.1% of those significant markers detected
from SWR, while the mutual predictability of SWR to
SMA is 4.3%. In general, a method with a larger number of
predictions had higher mutual predictability than a method
with fewer predictions, leading SMA (the most liberal
method) to have the highest mutual predictability and GC
(the most conservative method) to have the lowest mutual
predictability. SWR and SA had more predictions and
hence higher mutual predictabilities than EIGENSTRAT,
MLM (K), MLM (P ?K) and GC. However, SWR and SA
showed poor mutual predictability with each other (e.g., in
DUS traits, SWR recovered a proportion of 21.2% of sig-
nificant chromosome bins called by SA, while SA recov-
ered 12.6% of significant chromosome bins called by
SWR), which diminished the credibility of their added
predictions in comparison to methods with fewer predic-
tions. EIGENSTRAT had higher mutual predictabilities in
DUS than in BLUP traits, which is consistent with the fact
that EIGENSTRAT was more liberal in DUS than in BLUP
traits. For the two MLM models, the MLM (K) model had
better mutual predictability in BLUP traits while the two
were comparable in DUS traits.
Since the six structure correction methods presented
poor agreement on significant predictions, we evaluated
their control of type I error and statistical power by fol-
lowing a similar process to Yu et al. (2006), in which the
type I error was assessed through comparing observed and
expected cumulative Pvalue distributions, while the
power was assessed through a QTN simulation study as
described above. Figure 2a, b shows the cumulative dis-
tributions of observed Pvalues in genome scans from six
different methods in two barley DUS traits, seasonal
growth habit and ear row number. Under the null
hypothesis that random markers are not in LD with the
genetic loci controlling the trait, approaches that have
appropriate control of type I errors are expected to show a
uniform distribution of Pvalues (a diagonal line in these
plots). Generally, two mixed model analyses, MLM
(P ?K) and MLM (K), showed good approximation to
the expected Pvalue distributions in the two traits.
EIGENSTRAT gave liberal results in both traits and GC
and SA gave conservative results for seasonal growth
habit, whereas results from SWR were liberal for seasonal
growth habit but slightly conservative for ear row number.
The statistical power simulation was conducted by adding
a genetic effect to each of 100 randomly selected markers,
one at a time, and then testing, in each simulation, whe-
ther the QTN marker could be detected by different
models under empirical Bonferroni Pvalue threshold
(4.8 910
-5
). The proportion of QTN detected across all
random markers was used as the measurement of the
control of type II error for each model. Figure 2c, d
present the results of statistical power simulation in barley
seasonal growth habit and ear row number traits. The
average statistical power was consistently higher for MLM
(K) than for MLM (P ?K), SA, EIGENSTRAT and GC.
For seasonal growth habit, the SWR had a slightly higher
power than the MLM (K), but for ear row number, the
opposite was true. It is noted that all six-structure cor-
rection methods had higher powers in barley seasonal
growth habit than in barley ear row number at any given
variance proportion, which could be attributed to the fact
that seasonal growth habit had equal numbers of samples
in two different trait categories. Further results of
Theor Appl Genet (2012) 124:233–246 239
123
cumulative Pvalue distributions as well as statistical
power for all 10 BLUP traits were given in Supplementary
Material (ESM, Fig S4). Without exception, the MLM
(K) method outperformed its rivals in terms of both con-
trolling false positives and maintaining statistical power
for all BLUP traits.
Table 1 Comparison of shared significant predictions among seven analytical methods
Methods # Mutual predictability (%)
SMA SWR SA EIGENSTRAT MLM (P ?K) MLM (K) GC
BLUP
SMA 2,347 100.0 13.8 6.4 0.3 0.8 1.4 0.8
SWR 327 99.1 100.0 21.7 1.5 4.9 9.5 5.5
SA 171 87.7 41.5 100.0 2.3 10.5 17.5 8.2
EIGENSTRAT 6 100.0 83.3 66.7 100.0 50.0 50.0 0.0
MLM (P ?K) 19 94.7 84.2 94.7 15.8 100.0 89.5 36.8
MLM (K) 34 97.1 91.2 88.2 8.8 50.0 100.0 38.2
GC 18 100.0 100.0 77.8 0.0 38.9 72.2 100.0
DUS
SMA 2,522 100.0 4.3 4.4 4.8 1.7 2.0 0.3
SWR 253 43.1 100.0 12.6 11.9 8.7 9.1 1.2
SA 151 74.2 21.2 100.0 46.4 20.5 22.5 2.6
EIGENSTRAT 180 67.8 16.7 38.9 100.0 18.9 20.0 2.8
MLM (P ?K) 43 97.7 51.2 72.1 79.1 100.0 97.7 14.0
MLM (K) 51 100.0 45.1 66.7 70.6 82.4 100.0 11.8
GC 7 100.0 42.9 57.1 71.4 85.7 85.7 100.0
#, the total number of significant chromosome bins of 2 cM length pooled from all of the BLUP or DUS traits. Mutual predictability is calculated
as the percentage (%) of significant predictions from the method in row i(i= 1st,…,7th row) that were also predicted from the method in column
j(j= 1st,…,7th column). For example, in DUS traits, SMA predicted 43.1% of those significant markers detected from SWR, while conversely,
the predictability of SWR to SMA is 4.3%
Fig. 2 Model comparison with
barley seasonal growth habit
and ear row number traits. a, b
Cumulative distribution of the
Pvalues in the genome-wide
association scan in 615 barley
samples. c,dAverage statistical
power to detect a QTN based on
Bonferroni correction threshold
(0.05/100 =5910
-4
). The
power is averaged across all 100
simulated QTN for each given
variance proportion
240 Theor Appl Genet (2012) 124:233–246
123
Mapping results
As the MLM (K) method consistently achieved good control
of false positives while yielding the highest power among
six structure correction methods, we concentrated on the
significant predictions from this method in the following
text. The MLM (K) method detected significant associations
(exceeding Bonferroni genome-wide Pvalue threshold
4.8 910
-5
) for 9 out of 10 BLUP and 16 out of 32 DUS
traits (Fig. 3a–d). The complete list of significant marker-
trait associations, as well as peak markers, marker names,
R2
LR (a likelihood-ratio based R
2
-like statistic), and putative
rice (Oryza sativa) homologue loci were provided in Table 2
for BLUP traits and Supplementary Material (ESM, Table
S4) for DUS traits. In the present paper, marker names were
designated in the form of Xn-nn.nn (where n is a digit), in
which the digit after letter X indicates chromosome number
while the digits after the hyphen indicate map position.
A number mof additional markers at the same chromosomal
position are appended ‘‘.i’’, where i=1,…,m(e.g. X2-96.
82.1 is the second marker at 96.82 cM on chromosome 2).
The R2
LR statistic was estimated following a likelihood-
ratio based formula suggested by Sun et al. (2010),
R2
LR ¼1exp½2ðL0LMÞ=n, where L
M
and L
0
are
respectively the maximum log-likelihood of the mixed
models with or without incorporating a SNP of interest, and
nis the number of individuals. While the R2
LR statistic, like
the coefficient of determination (R
2
) in linear fixed effect
model, serves as a measurement of how well different model
agrees with the data, it also provides an intuitive indication
of the genetic effect of the SNP of interest; the changes in
R2
LR values resulted from fitting with different SNPs suggest
the relative importance of these SNPs in explaining the
phenotypic variation. We also experimented another R
2
-like
statistic used in some literatures (e.g. Atwell et al 2010),
R2
^
b¼^
b2Piðxi
xÞ2=Piðyi
yÞ2, where ^
bis the estimate
of SNP fixed effect derived from mixed model analysis.
Comparison showed that these two R
2
-like statistics pro-
duced very similar estimates with a median correlation
coefficient of 0.904 although in majority of the cases the R2
^
b
statistic tended to provide higher estimates than the likeli-
hood ratio based statistic (data not shown). The putative rice
homologue loci were derived through BLASTX sequence
alignments with SNP marker source sequences against the
version 6 rice genome sequence as in Close et al. (2009).
For DUS traits, we replicated most of the previously
reported association signals, with the exception of signifi-
cance on barley chromosome 3 for traits seasonal growth
habit and ear row number reported in Cockram et al.
(2010). This discrepancy was probably due to use of dif-
ferent models to account for population structure in the
mixed model analyses (K only model here, Q?K model in
Cockram et al. 2010 where Q is a fractional subpopulation
membership matrix estimated from STRUCTURE).
Among the association signals detected for barley seasonal
growth habit, we noted that significant marker X1-96.92.1
(Pvalue \1.0 910
-220
) had a R2
LR value of 40.9%. An
analysis of colinearity with rice genome indicated that this
marker mapped to the barley short-day photoperiod locus
PPD-H2, one major QTL for seasonal growth habit
(Cockram et al. 2010). Detailed examination of allele fre-
quencies revealed that different alleles at this marker were
almost fixed within winter (0.988) and spring (0.005)
samples; similarly, the significant marker X4-26.19.4 was
almost fixed for different alleles between the two-row
(0.998) and six-row (0.071) barley samples, with R2
LR value
of 45.9%.
Several BLUP traits showed significant associations at
markers also detected for the two barley diversity charac-
teristics, ear row number and seasonal growth habit
(Fig. 3b–d; Table 2). For example, marker X4-26.19.4,
which was highly significantly associated with variation of
ear row number, was detected for two grain weight traits
TKW and SpecW. In addition, several markers at or near
96.92 cM on chromosome 1 were highly significantly
associated with variation of seasonal growth habit, and also
detected for four BLUP traits (GrainN, MaltN, SolN and
GE4ml). Common association predictions among these
traits may be coincidental or represent pleiotropic effects of
underlying genetic factors. However, traits MaltN and
GE4ml presented high levels of phenotypic correlations
with seasonal growth habit (Pearson correlation coeffi-
cients 0.97–0.98), likely explaining the common
predictions.
Some BLUP traits were closely connected to each other
and hence phenotypic similarities and common predictions
were observed as expected. For example, two-grain weight
related traits, TKW and SpecW, had a Pearson correlation
coefficient of 0.427 and shared a common signal at marker
X4-26.19.4 (Fig. 3d; Table 2). GrainN, MaltN and SolN
measured the percentage of nitrogen in dry grain, dry
malted grain and malt extract, respectively. While GrainN
and MaltN showed a high degree of phenotypic similarities
(Pearson correlation coefficient is 0.888), SolN showed a
strong negative correlation with GrainN and MaltN
(Pearson correlation coefficients is -0.647 and -0.824,
respectively). Association analyses revealed a common
association at 93.95–96.92 cM on chromosome 1 shared
among the three traits, which was detected for barley
seasonal growth habit. There are also several unique
association signals for each trait, such as marker X5-2.81
for GrainN, X5-63.31 for MaltN and X1-54.73.1 for SolN
(Fig. 3d; Table 2).
Theor Appl Genet (2012) 124:233–246 241
123
Three BLUP traits, GE4ml, Dorm4ml and Dorm8ml,
measured grain germinations (seedling development) one
month after watering in 4 ml water (GE4ml), or 72 h after
watering in 4 ml (Dorm4ml) and 8 ml (Dorm8ml) of water,
respectively. GE4ml had negative correlations with the
latter two germination traits (Pearson correlation coeffi-
cients -0.562 and -0.483, respectively). As stated above,
GE4ml presented a very strong correlation with seasonal
growth habit and hence had identical association markers.
In contrast, the latter two germination traits presented
positive correlation (Pearson correlation coefficient 0.667)
and their association markers were different from those of
GE4ml. Dorm4ml was associated with three markers at
61.53 cM on chromosome 1 and with a region at
68.35–80.61 cM on chromosome 5, while Dorm8ml gave
associations at 75.4–80.61 cM on chromosome 5 (Fig. 3d;
Table 2). We also performed a joint analysis of treating
Dorm4ml and Dorm8ml as a single trait but incorporating
water treatment as a fixed effect in the MLM (K) model. In
the joint analysis, only the region at 68.35–80.61 cM on
chromosome 5 was predicted significant, while markers at
61.53 cM on chromosome 1 did not exceed genome-wide
threshold (Pvalue 3.3 910
-4
). One marker at 61.53 cM
on chromosome 1 is mapped to barley gene Uni-
Ref90_Q02400, which encodes a late embryogenesis
abundant (LEA) protein associated with desiccation toler-
ance of seeds (Goyal et al. 2005). For the region on
chromosome 5, BLASTX sequence alignments revealed
that a marker at 69.90 cM (BOPA2 marker 12_30080)
mapped to Rice homologue LOC_Os09g26620 (Escore
2.0 910
-51
), a putative auxin-repressed gene. This marker
locus is also mapped to Arabidopsis homologue gene
AT1G56220.1 (Escore 2.0 910
-16
), which belongs to a
dormancy/auxin associated gene family. The fact that the
growth (germination) of seeds in dormant state commences
with the uptake of water under suitable condition (Bewley
1997) suggests we have successfully identified two barley
germination controlling loci.
Viscosity of wort is a cytolytic character mainly related
to the breakdown of b-glucan, the main structure material
Fig. 3 Significant associations
detected from the MLM
(K) method for (a–c) DUS and
dBLUP traits under Bonferroni
genome-wide Pvalue threshold
4.8 910
-5
. The most
significant SNPs within 2 cM
chromosome bins are labelled
above each figure. SNP name is
designated in a form of Xn-
nn.nn, in which the digit n after
letter X indicates chromosome
while the digits after the
hyphen indicate map position
(see main text for detail). Any
–Log
10
(Pvalue) above 40 is
truncated to 40. Chromosomes 3
and 7 with no significant signals
are omitted
242 Theor Appl Genet (2012) 124:233–246
123
in barley endosperm cell walls (Schmalenbach and Pillen
2009). Here, we identified two regions on chromosome 1
(49.34–50.0 and 100.69 cM) significantly associated with
viscosity and consistent with strong quantitative trait locus
(QTL) effects on chromosome 1 at 39–70 cM detected by
Schmalenbach and Pillen (2009).
Discussion
This paper presents a GWAS of agronomic and morpho-
logic traits in a collection of 615 barley cultivars. Compared
to our previous association analysis (Cockram et al. 2010),
the present study recruited additional samples, reported
associations with 10 additional agronomic traits, and con-
ducted a comprehensive survey of association test methods.
The present analysis revealed that more than half of the
DUS traits and all BLUP traits had shown divergent phe-
notypic distributions between winter and spring samples
(ESM, Fig. S2). We also found shared common associations
between a number of agronomic traits and two barley
diversity traits, seasonal growth habit and ear row number
(Table 2). All these suggest that barley diversification had a
profound impact on variations in barley morphological and
agronomic traits, of which the latter are undoubtedly key
issues for cultivated barley. In other words, a number of
traits had undergone strong selection along with diversifi-
cation of seasonal growth habit in barley cultivars, com-
plicating the association mapping in the present structured
barley samples. Although we did not explicitly model the
selection effect in the present study, effective correction for
population structure should have simultaneously accounted
for the confounding from selection which accompanied the
diversification of barley samples.
Table 2 Significant marker-trait associations exceeding Bonferroni threshold (Pvalue 4.8 910
-5
) in the genome scan of BLUP traits
No. Trait Chromosome (interval, cM) Peak marker name Pvalue R2
LR(%) Putative rice homologue
Present
a
BOPA
b
2 TKW 4H (26.19)
c
X4-26.19.4 11_20606 1.1 910
-6
5.6 LOC_Os03g50040.1
3 SpecW 1H (100.69) X1-100.69 11_10357 2.4 910
-5
3.6 LOC_Os07g10256.1
4H (26.19)
c
X4-26.19.4 11_20606 1.0 910
-10
7.8 LOC_Os03g50040.1
4 GrainN 1H (93.95-96.92)
d
X1-96.92.1 11_10396 1.6 910
-7
5.9 LOC_Os05g44760.1
4H (123.29) X4-123.29 11_20013 1.1 910
-5
4.5 LOC_Os10g25060.1
5H (2.81) X5-2.81 11_20553 4.1 910
-7
6.6 LOC_Os12g44310.2
5 MaltN 1H (92.8-96.92)
d
X1-96.92.1 11_10396 7.3 910
-47
35.9 LOC_Os05g44760.1
4H (117.6-123.29)
c,d
X4-117.60.2 11_21210 1.4 910
-7
7.8 LOC_Os03g01750.5
5H (63.31) X5-63.31 11_11281 1.6 910
-5
5.5 LOC_Os09g23350.1
5H (122.38)
d
X5-122.38 11_10094 9.3 910
-7
6.4 LOC_Os09g38030.1
5H (151.36)
d
X5-151.36.3 11_20100 1.7 910
-6
6.5 LOC_Os03g57220.2
6 SolN 1H (54.73) X1-54.73.1 11_21217 4.4 910
-5
5.0 LOC_Os10g42780.1
1H (93.95-96.92)
d
X1-96.92.1 11_10396 5.2 910
-6
5.8 LOC_Os05g44760.1
7 Viscosity 1H (49.34-50.0) X1-50.00.1 11_10438 3.0 910
-11
11.7 LOC_Os07g10420.1
1H (100.69) X1-100.69 11_10357 4.2 910
-6
6.3 LOC_Os07g10256.1
8 GE4 ml 1H (92.8-96.92)
d
X1-96.92.1 11_10396 1.7 910
-83
40.8 LOC_Os05g44760.1
4H (111.68)
d
X4-111.68 11_11299 8.7 910
-7
6.4 LOC_Os03g02750.1
4H (117.6)
c,d
X4-117.60.2 11_21210 5.1 910
-14
15.1 LOC_Os03g01750.5
5H (122.38)
d
X5-122.38 11_10094 5.6 910
-10
10.5 LOC_Os09g38030.1
5H (151.36)
d
X5-151.36.3 11_20100 5.2 910
-8
8.5 LOC_Os03g57220.2
9 Dorm4 ml 1H (61.53) X1-61.53 11_11049 3.6 910
-5
5.3 LOC_Os05g28210.1
5H (68.35-80.61) X5-75.40 11_21001 1.6 910
-14
16.0 LOC_Os09g24980.1
10 Dorm8 ml 5H (75.4-80.61) X5-75.40 11_21001 8.5 910
-7
7.2 LOC_Os09g24980.1
R2
LR, a likelihood ratio based R
2
-like statistics. Putative rice homologue for each peak marker is derived by sequence alignment as indicated in
Close et al. (2009). Trait number is the same as in Supplementary Table S2a
a
Marker name is designated as Xn-nn.nn, in which the first digit nafter letter X indicates chromosome and digits after the hyphen indicate map
position. A number mof additional markers at the same chromosomal position are appended ‘‘.i’’, where i=1,…,m
b
Original marker name designated in Close et al (2009)
c
Significant association also detected for barley ear row number
d
Significant association also detected for barley seasonal growth habit
Theor Appl Genet (2012) 124:233–246 243
123
Significant associations were detected for 9 out of 10
BLUP and 16 out of 32 DUS traits. Notably, we found
novel associations at two chromosome regions for barley
seed germination, 61.53 cM on chromosome 1 and
68.35–80.61 cM on chromosome 5. Although the full
barley genome sequence is currently unavailable, infor-
mation from gene annotation and homologous sequence
alignment for marker sequences in the two regions suggests
two possible candidate genes for barley germination, a late
embryogenesis abundant (LEA) protein gene and a putative
gene homologous to Rice and Arabidopsis dormancy/auxin
associated gene. While further genetic study is required to
confirm the discovery, the present finding highlights the
feasibility of high resolution mapping with GWAS in
barley samples. As the markers in the present barley
genotyping platform (BOPA) were entirely developed from
transcribed gene SNPs (Close et al. 2009), efficient inter-
species homology sequence comparison, particularly
through gene synteny, between barley and other grass
genomes including Rice and Arabidopsis thaliana
(Dubcovsky et al. 2001; Bennetzen and Ma 2003), provides
a powerful tool for identifying and refining QTL in the
un-sequenced barley genome.
Factors including geographic localization, breeding
patterns and even human intervention (e.g., selective
breeding based on economic/agronomically significant
traits during crop domestication) may lead to complications
such as strong population structure and familial relatedness
within plant samples assembled in association mapping
studies (Atwell et al. 2010). In the present barley samples,
strong population structure is demonstrated primarily due
to division by seasonal growth habit and by ear row
number, both of which have close connection with breed-
ing activities of cultivated barley. In GWAS of human
complex diseases, population structure has been considered
an important cause of spurious associations and an expla-
nation of failure to replicate significant predictions, making
statistical methods accounting for population structure
essential to validate standard association tests (Balding
2006). This paper presents an evaluation of six association
test methods which are popular in correcting for population
structure, including genomic control (GC) (Devlin and
Roeder 1999), stepwise regression (SWR) (Setakis et al.
2006), structured association (SA) (Pritchard et al.
2000a,b), EIGENSTRAT (Price et al. 2006), and two
mixed linear model (MLM) analyses (Yu et al. 2006).
While a rich literature has reported comparisons of statis-
tical methods for population structure correction, most
studies concentrated on case and control sampling designs
(Astle and Balding 2009; Price et al. 2010; Wu et al. 2010).
Zhao et al. (2007) compared some of the methods con-
sidered here in a sample of Arabidopsis thaliana inbred
lines, though their study is severely under-powered due to
limited sample size (95 accessions). The present study
exploits a much larger sample of barley cultivars collected
from a wide range of germplasm resources and hence
delivers more reliable statistical inference. In addition, this
paper explored a larger number of complex traits of dif-
ferent types, including both continuous (BLUP) and cate-
gorical (DUS) traits, to achieve a more comprehensive
comparison of available methodologies.
Before correcting for population structure, it is critical to
detect and infer the hidden structure in a sample. Perhaps
the most commonly accepted statistical method to detect
population structure is a model-based cluster approach,
STRUCTURE (Pritchard et al. 2000a,b), which uses multi-
locus genotype data to infer the subpopulation number
Kand creates a subpopulation membership matrix Qto
represent the samples. However, with the present structured
barley collection, the STRUCTURE method failed to infer
a reliable parameter Kdespite using different panels of
genotypes with varying number of markers selected
(Fig. 1a). This failure is expected because STRUCTURE
attempts to account for population structure by allocating
population groupings in such a way that Hardy–Weinberg
Equilibrium (HWE) is met within subpopulations, whereas
the assumption of HWE is actually invalid given the nature
of extensive inbreeding in barley samples. Indeed, hetero-
zygous genotypes were rare (0.8%) and thus removed in
the present analysis, rendering this method entirely
impractical.
Dimension reduction techniques such as PCA do not
require a model assumption and hence can robustly predict
the hidden structure by extracting principal components
from a covariance matrix. Although PCA is computation-
ally fast and visually appealing in representing broad dif-
ferences across samples in a dataset, it could be difficult in
practice to make biological interpretations from principal
components (PCs) as population structure surrogates, and
hence further statistical assessment like clustering with
extracted PCs would be essential. We compared the cluster
result from PCA with that from another multidimensional
scaling (MDS) method, the principal coordinate (PCO)
analysis of pairwise IBS kinship estimates, which has been
widely utilized in GWAS to predict the hidden population
structure (Purcell et al. 2007; Simon-Sanchez et al. 2009).
K-means clustering using the top three axes extracted from
PCA and PCO methods showed similar partition patterns
when setting cluster number k=2 but different partition
patterns when setting k=3 (ESM, Fig. S5). A Bayesian
model selection with x-means cluster algorithm (Pelleg and
Moore 2000) indicated that the best cluster model from
PCO axes had cluster number k=3 (BIC =-70.5), dif-
ferent from the cluster result from PCA axes, from which
the best cluster model had cluster number k=2 (BIC =
-160.1). As the latter had a smaller BIC value, we
244 Theor Appl Genet (2012) 124:233–246
123
preferred the PCA based cluster membership to create the
Pmatrix in the present association analysis.
Association analyses with the six above mentioned
structure correction methods predicted highly varying
numbers of significant markers in the strongly structured
barley samples, suggesting caution should be taken to
interpret the associations predicted from different methods.
Through evaluating empirical Pvalue distributions and a
power simulation study, we demonstrated that two MLM
approaches, especially the MLM (K) method, outper-
formed their rivals for controlling the rate of false positives
while maintaining statistical power. The poor performance
of other methods probably results from failure to correct
the confounding caused by relatedness (genetic co-ances-
try) presented in the barley samples, which was captured
through a kinship matrix in the mixed model analyses. For
example, a model selection according to BIC indicated the
best cluster with top principal components to have cluster
number k=2, which was too simplistic given the number
of combinations of seasonal growth habit and ear number
characteristics. Note that the MLM (P ?K) method had
similar performance in controlling false positives but
showed a decreased statistical power when compared to the
MLM (K) method, which is probably because using the
Kmatrix alone is sufficient in capturing the complicating
factors in the present barley data, while a combination of
Pand Kmatrices might lead to over-correction.
It should be stressed that DUS traits in the present study
were either binary or categorical characters and hence a
generalized linear mixed model (GLMM) is more appro-
priate than the MLM based analysis. However, GLMM
method with correlated variance components is computa-
tionally inefficient with the currently available algorithms
and it has been suggested that a standard linear regression
framework is useful in binary phenotype analysis such as
with a case and control design (Kang et al. 2010). MLM has
been utilized in GWAS of categorical traits, for example,
Atwell et al. (2010) used MLM to correct for population
structure in a GWAS of both continuous and binary or cat-
egorical traits in Arabidopsis thaliana inbred lines. An
intensive comparison of various methods in the present study
demonstrates that the MLM method is the most promising for
analyzing either continuous and or categorical traits for
GWAS of plant populations with extensive structure.
Acknowledgments This study was supported by research grants for
the ‘Association Genetics of UK Elite Barley’ project, which was
funded by BBSRC and RERAD as part of the Sustainable Arable
LINK programme with industrial support from HGCA, KWS (UK),
LS Plant Breeding, Syngenta Seeds, Groupe Limagrain, Secobra UK,
Svalof Weibull, Perten Instruments AB, The Maltsters Association of
Great Britain, The Scotch Whisky Research Institute and Campden
BRi. ZWL is also supported by the Leverhulme Trust (RCEJ1471)
of UK, NSFC (31071084) and The Basic Research Program
(2012CB316505) of China.
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