Building phenotype networks to improve QTL detection: a...
Transcript of Building phenotype networks to improve QTL detection: a...
ORIGINAL ARTICLE
Building phenotype networks to improve QTL detection:a comparative analysis of fatty acid and fat traits in pigsB. Yang1,2, N. Navarro
3, J.L. Noguera4, M. Munoz5, T.F. Guo2, K.X. Yang2, J.W. Ma2, J.M. Folch1,L.S. Huang2 & M. Perez-Enciso1,6
1 Department of Food and Animal Science, Veterinary School, Universitat Autonoma de Barcelona, Bellaterra, Spain
2 Key Laboratory for Animal Biotechnology of Jiangxi Province and the Ministry of Agriculture of China, Jiangxi Agricultural University, Nanchang,
China
3 Department of Zoology and Animal Biology, Sciences III, Geneve, Switzerland
4 Genetica i Millora Animal, Centre IRTA-Lleida, Lleida, Spain
5 Departamento de Mejora Animal SGIT-INIA, Madrid, Spain
6 ICREA, Passeig Lluıs Companys, Barcelona, Spain
Introduction
QTL mapping has been very effective to associate
genomic regions with quantitative traits, although
20 years of studies have shown that most complex
traits are, indeed, complex (Weiss 2008). In domes-
tic animals, as in the rest of species, very few causal
mutations have been convincingly reported (An-
dersson & Georges 2004). This lack of success has
been tried to be remedied by (i) increasing the
amount of genomic resources and augmenting the
number of polymorphisms genotyped: while cur-
rently whole genome association studies are flour-
ishing, soon will we be able to carry out whole
sequence association studies; and (ii) by devising
more powerful statistical methods to model the
Keywords
Complex trait; multivariate data; pig; QTL;
structural modelling.
Correspondence
M. Perez-Enciso, Departament de Ciencia
Animal i dels Aliments, Facultat de
Veterinaria, Universitat Autonoma de
Barcelona, Bellaterra 08193, Spain. Tel:
+34 93 581 42 25; Fax: +34 93 581 21 06;
E-mail: [email protected]
L.S. Huang, Key Laboratory for Animal
Biotechnology of Jiangxi Province and the
Ministry of Agriculture of China, Jiangxi
Agricultural University, Nanchang 330045,
China. Tel: 0086 791 3813080;
Fax: 0086 791 3900189;
E-mail: [email protected]
Received: 3 December 2010;
accepted: 15 March 2011
Summary
Models in QTL mapping can be improved by considering all potential
variables, i.e. we can use remaining traits other than the trait under
study as potential predictors. QTL mapping is often conducted by cor-
recting for a few fixed effects or covariates (e.g. sex, age), although
many traits with potential causal relationships between them are
recorded. In this work, we evaluate by simulation several procedures to
identify optimum models in QTL scans: forward selection, undirected
dependency graph and QTL-directed dependency graph (QDG). The lat-
ter, QDG, performed better in terms of power and false discovery rate
and was applied to fatty acid (FA) composition and fat deposition traits
in two pig F2 crosses from China and Spain. Compared with the typical
QTL mapping, QDG approach revealed several new QTL. To the con-
trary, several FA QTL on chromosome 4 (e.g. Palmitic, C16:0; Stearic,
C18:0) detected by typical mapping vanished after adjusting for pheno-
typic covariates in QDG mapping. This suggests that the QTL detected in
typical mapping could be indirect. When a QTL is supported by both
approaches, there is an increased confidence that the QTL have a pri-
mary effect on the corresponding trait. An example is a QTL for C16:1
on chromosome 8. In conclusion, mapping QTL based on causal pheno-
typic networks can increase power and help to make more biologically
sound hypothesis on the genetic architecture of complex traits.
J. Anim. Breed. Genet. ISSN 0931-2668
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relationship between traits and genetic variations,
e.g. allowing epistatic QTL interaction (Carlborg &
Haley 2004), adjusting sample structure (Yu et al.
2006) or mapping QTL simultaneously for multiple
traits (Banerjee et al. 2008).
The use of all traits in assessing the best model has
received comparatively less attention. Although mul-
tivariate methods have indeed been developed (Jiang
& Zeng 1995; Knott & Haley 2000; Banerjee et al.
2008), one common feature of these QTL mapping
approaches is that each trait is represented as linear
combinations of genotypes and a few well-estab-
lished environmental factors. We have proposed, in
addition, that a good model at least should take into
account all potential predictors, i.e. traits other than
the trait under study should be considered as poten-
tial covariates in genetic mapping models (Perez-
Enciso et al. 2007). Such a model includes both
genetic and phenotypic predictors and should aid to
gain more insight into genetic basis of complex
traits. The choice of covariate ⁄phenotypic predictor
in a statistical model has been shown to have a dra-
matic impact on the genetic parameter inferences
like positions and effects of QTL (Schadt et al. 2005;
Li et al. 2006; Ledur et al. 2009). However, how to
select covariates and the influence of covariate selec-
tion on QTL parameter inferences is a difficult topic
and remains a relatively unexplored area. Structural
Equations Model (SEM) provides a powerful tool in
this context (Shipley 2000).
Here, we study a two-step procedure to build up
such models. First, a subset of covariates ⁄pheno-typic predictors are chosen from all traits other
than the one under study, and next, a multi-QTL
mapping (Manichaikul et al. 2009) is conducted to
build up a complete model for each trait. We eval-
uate three approaches for covariate selection: (i)
stepwise forward selection (FS), (ii) undirected
dependency graph (UDG) (de la Fuente et al. 2004),
and (iii) QTL-directed dependency graph (QDG)
(Chaibub Neto et al. 2008). FS is a classic variable
selection method; UDG is generated using partial
correlations and can be represented as an undi-
rected network where nodes (phenotypes ⁄ traits) are
connected by an undirected edge if there exists a
direct dependency between them. Note that the
edges in UDG are symmetric, i.e. they have no
direction (de la Fuente et al. 2004). Neighbour
nodes are determined as phenotypic predictors, i.e.
included in the model, for the target phenotype.
More recently, Chaibub Neto et al. (2008) proposed
a method to build up QDG by inferring the direc-
tion of edges in UDG using multiple QTL informa-
tion. The method was shown to have high power
and low error in recovering simulated networks.
Moreover, this approach has several advantages
over other causal network inference methods, e.g.
compared with Bayesian networks, QDG can
include feedback loops. It does not require any
prior knowledge of traits such as cis or trans acting
in gene expression traits (Liu et al. 2008); thus, it
can be widely applied to a variety of traits, like
metabolites. QDG is a directed network where the
direction of edges implies a causal relationship
between phenotypes. Using QDG, we selected
‘parental nodes’ (traits), which have a direct and
causal link to the target node (the trait studied) as
phenotypic predictors.
This work is divided into two parts. First, we eval-
uate and compare the three proposed approaches
together with classical QTL mapping in simulated
data. Second, we apply the best covariate selection
approach to fatty acid (FA) profiles and fat deposi-
tion traits from two experimental populations that
have been analysed extensively in the past, a Span-
ish Iberian · Landrace (Perez-Enciso et al. 2000; Clop
et al. 2003) and a Chinese Duroc · Erhualian inter-
cross (Guo et al. 2009; Ma et al. 2009).
Material and methods
Simulated data
We simulated 20 replicates of directed acyclic net-
works, each made up of 100 phenotype nodes. For
each replicate, first, a skeleton of phenotypic net-
work was simulated using randomDAG function from
the pcalg R package (Kalisch & Buhlmann 2007).
The probability of connecting a node to a down-
stream node was set to be 0.03, and the expected
number of edges in the simulated network was 150.
A typical skeleton of the phenotypic network is
shown in Figure S1. To simulate QTL effects, we
used the estimated QTL additive coefficients (Haley
et al. 1994) of the 18 autosomes from the 693 indi-
viduals in the Duroc · Erhualian cross (described
below). The 18 autosomes with total length of
2266 cM were evenly divided into 30 intervals.
From each interval, we uniformly sampled one QTL,
i.e. 30 candidate QTL were sampled. The QTL for
each phenotype were randomly selected among
these 30 QTL. The number of QTL per phenotype
was simulated from a Poisson distribution with mean
1. Two or more phenotypes were allowed to share
common QTL. For simulating the phenotype values,
the model in Equation (2) described below was used,
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except that the indicator variable d is dictated by the
acyclic graph (e.g. Figure S1). Additive QTL effects
(a) were sampled uniformly between 0.2–0.6, covari-
ate effects (b) were sampled uniformly between 0.6–
1, and the error term ei ! N(0,1).
Real data
The Iberian · Landrace and Duroc · Erhualian inter-
crosses have been extensively studied, and main
results are reported elsewhere (Clop et al. 2003; Guo
et al. 2009; Ma et al. 2009). Here, we focus the
analyses of FA compositions and fat deposit traits
like backfat thickness (BFT), abdominal fat weight
(AFW) and intramuscular fat content (IMF). A com-
plete list together with main statistics is summarized
in Table 1. The numbers of F2 animals with data
were approximately 320 and 680 on average for
Spanish and Chinese crosses, respectively. Whenever
possible, we chose the same trait in both crosses.
This was sometimes difficult, for instance, while FA
was analysed in both crosses, these were measured
in backfat in the Spanish cross and in abdominal fat
and longissimus muscle in the Chinese experiment.
For carcass weight (CW), the entire CW was mea-
sured in the Spanish cross, whereas the left-side
weights were used in the Chinese experiment. The
positions of backfat measures were also slightly dif-
ferent. The microsatellites genotyped differed as well.
To make the positions comparable, we used the con-
sensus map from USDA (http://www.genome.iastate.
edu/maps/marc.html), even if estimated recombina-
tion fractions could be different (Tables S1 and S2).
This should not affect the marker interval containing
the QTL. FAs and CW were corrected for sex, batch
and additive infinitesimal effects. Fat deposit traits
AFW, BFT and IMF were corrected for sex, batch,
CW and additive infinitesimal effects using qxpak4
(Perez-Enciso & Misztal 2004), the residuals were
used for the subsequent analysis.
Analyses
In a typical QTL analysis, the phenotype is adjusted
based on a small number of environmental effects
(say sex and batch) and on the probability of the
QTL genotype; a scan is then performed along the
genome region of interest. The model whose QTL
position explains better the phenotypic variability is
retained as the best model and therefore the most
likely QTL position. This typical QTL scan strategy
can be formalized for a multi-QTL model as follows:
yi " l#X
j
djajqij # ei; $1%
where yi represents the phenotype value for ith indi-
vidual, l the fixed effects fitted, d is an indicator that
takes 1 if that variable is included in the model and
0 otherwise, aj denotes the additive QTL effect at jth
position, and qij is the additive QTL coefficient (Ha-
ley et al. 1994) corresponding to ith individual at jth
position, ei is the error term. Note that in our nota-
tion, the sum on j runs over all genome positions
analysed, and it is the dj which establishes the model
and QTL positions. Without loss of generality, here,
we consider only QTL additive effects (no
Table 1 Descriptive statistics for the traits in this study
Fat and growth traits
Iberian · Landrace cross Duroc · Erhualian cross
N Mean SD N Mean SD N Mean SD
Intramuscular fat (%) 312 1.47 0.53 621 1.83 0.84
Backfat thickness (cm) 318 2.83 0.79 693 2.36 0.95
Abdominal fat weight (kg) 318 2.51 0.76 692 1.11 0.34
Carcass weight (kg) 322 74.93 9.84 693 32.41 5.96
Fatty acid compositions (%) Backfat (BF) Abdominal fat (AF) Longissimus muscle (LM)
Myristic (C14:0) 322 1.51 0.17 666 1.10 0.14 685 1.09 0.16
Palmitic (C16:0) 322 21.08 1.46 666 24.30 1.31 687 23.49 1.31
Palmitoleic (C16:1 n-7) 322 2.47 0.37 666 1.74 0.39 687 3.00 0.52
Stearic (C18:0) 322 10.87 1.00 666 14.65 1.95 687 13.05 1.23
Oleic (C18:1 n-9) 322 44.13 1.68 666 40.98 3.54 687 44.25 3.47
Linoleic (C18:2 n-6) 322 14.43 1.45 666 12.98 2.78 687 9.08 2.77
Linolenic (C18:3 n-3) 322 1.08 0.18 666 0.44 0.12 685 0.19 0.06
Eicosenoic (C20:1) 322 0.86 0.21 666 0.91 0.23 687 0.83 0.18
Eicosadienoic (C20:2 n-6) 322 0.63 0.17 666 0.62 0.14 686 0.44 0.13
B. Yang et al. Porcine fatty acid QTL network
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dominance). Now, consider a more general, struc-
tural model
yil " l#X
k 6"l
dklbklyik #X
j
djlajlqij # ei; $2%
where bkl is the covariate effect of trait k on trait l.
We will call variables yk external traits as opposed to
the trait yl under study. In fact, the trait y can be
levels of mRNA, abundance of protein and metabo-
lite, or physiological trait like milk production or dis-
ease status. A set of Equation (2), i.e. structure
equation models (SEM) can be represented by a net-
work, where the traits and the QTL are nodes, and a
directed edge from trait k or QTL j to trait l (indi-
cated by dkl and djl, respectively) means trait k or
QTL j are included in model for trait l. In this study,
we build up Equation (2) for each trait in two steps:
in step 1, a subset of traits is selected as phenotypic
predictors from rest of traits other than the trait
under study; in step 2, QTL mapping is implemented
by adjusting for the phenotypic predictors to build
up the full models. We used FS, UDG or QDG to
select such predictors.
Selecting phenotypic predictors
In FS, the phenotypic predictors were included into
the model one by one, and the p-value threshold
for entry of a phenotypic predictor was set to be
0.001. UDG and QDG for traits in both simulated
and real data sets were built up using qdgAlgo func-
tion of R package qdg (Chaibub Neto et al. 2008),
available at https://github.com/byandell/qdg; briefly,
the UDG were built up based on second-order par-
tial correlations (de la Fuente et al. 2004), where an
edge is assigned to a pair of traits if their partial
correlation conditional on all possible combinations
of other trait pairs remain significant (p < 0.05). To
obtain QDG, the direction of edges in UDG is
inferred using QTL detected by typical QTL map-
ping. To eliminate spurious edges caused by effects
of common QTL in a pair of traits (Chaibub Neto
et al. 2008), two QTL located within 10 cM of dis-
tance were treated as a single QTL. The locations of
the common QTL for multiple traits were set to be
the location of QTL for the trait with larger loga-
rithm of the odds (LOD) score. Finally, the edges
with absolute LOD scores, which indicate the confi-
dence of edge direction (obtained by comparing log
likelihood of the two conflicting models dictated by
edge direction), were removed if <2. The parental
nodes in the final QDG were treated as phenotypic
predictors for the target traits.
QTL mapping
The initial model for QTL mapping was either an
empty model (typical QTL mapping) or based on phe-
notype covariates selected by FS, UDG or QDG. We
employed slightly different QTL mapping methods for
simulated and real data. In simulated data, we
applied FS based only on additive QTL coefficients.
The QTL was added into the model individually by a
criterion of p-value <0.001 in a t-test of partial regres-
sion coefficients. For real data, in contrast, QTL map-
ping was implemented by stepwiseqtl function in R ⁄qtl(Broman et al. 2003) using regression (Haley et al.
1994), and we allowed for dominance and additive
effects. Penalties for inclusion of QTL were empiri-
cally determined by the 20% percentile (LOD
approximately 2.9) of 2000 permutations. LOD scores
for the 1% genome wise significance were approxi-
mately 4.2 in Iberian · Landrace cross and 4.35 in
Duroc · Erhualian cross.
Evaluation criteria
In both simulated and real data, we computed deter-
mination coefficient (R2), Bayesian Information Cri-
terion (BIC) and predictive mean square errors
(PMSE) of cross-validation for inferred models. To
compute PMSE, observations were randomly divided
into K subgroups, where each subgroup has 10
observations. For each subgroup, the 10-leave out
observations were predicted using the parameters
inferred with the rest of data. Mean squared errors
of all observations were used in this study as cross-
validation statistics. In simulated data, we also deter-
mined the power and false discovery rate (FDR) of
each strategy in recovering the QTL-phenotype and
phenotype–phenotype edges. An inferred QTL edge
was called true if it directly connected to the pheno-
type and was located within 10 cM of any true QTL,
and it was called false otherwise. Note that some
QTL have indirect effects via parental nodes on tar-
get phenotype in true network might be detected
and were considered as false QTL in this study. All
calculations were implemented in R (R Development
Core Team, 2009).
Results and discussion
Simulations
Network modelling improves power and reduces FDR in
‘direct’ QTL detection
As can be seen in Figure 1a, a typical QTL scan is
the worst strategy among those considered in terms
Porcine fatty acid QTL network B. Yang et al.
332 ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343
Figure 1 Average QTL detection power, QTL detection false discovery rate (FDR), covariate detection power and covariate FDR of the four strate-
gies (typical QTL mapping and QTL mapping based on the three covariate selection methods: forward selection, undirected dependency graph
and QTL-directed dependency graph) across the 20 simulated networks, considering (a) all 100 phenotype nodes, (b) the 30 upstream nodes, (c)
the 30 downstream nodes.
B. Yang et al. Porcine fatty acid QTL network
ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343 333
of both QTL power detection and FDR. Interestingly,
the network strategies considered improved primar-
ily on FDR whereas power increased only margin-
ally; specifically for FS and UDG, the gain in power
ranged from 3% (FS) to 16% (QDG). The average
FDR in QTL detection dropped from 54% (typical
mapping) to 45% (FS), 40% (UDG) and 25%
(QDG). As for covariate detection, i.e. the terms not
included in the typical QTL scan, QDG resulted in a
moderate loss in power, but this loss is more than
compensated by a dramatic decrease in FDR. This
means that the relationships between phenotypes
inferred by QDG are far more reliable than their
competing strategies.
It is also of interest to consider the performance
of each of the strategies according to topological
order of the phenotype. By topological order, we
mean how many levels of edges affect each trait.
Given that we are analysing acyclic graphs, the
direction of edges can only point from upstream
nodes (lower topological order) to downstream
nodes (higher topological order) (Figure S1). For
instance, the most upstream node is one that is
affected directly only the QTL, whereas the most
downstream node is affected by other phenotypes
and itself does not point to any other node. We
compared results for the 30 phenotype nodes with
lowest topological level (30 upstream nodes, e.g.
nodes labelled by number 1–30 in Figure S1) and
the 30 phenotype nodes with highest topological
level (30 downstream nodes, e.g. nodes labelled by
number 71–100 in Figure S1) in the simulated
networks. Interestingly, the strategies performed
very differently according to topological levels (Fig-
ure 1b,c).
First, the typical QTL mapping performs much bet-
ter for upstream (81%) than for downstream (50%)
nodes (Figure 1b,c). This seems logical, because
upstream nodes are primarily affected by QTL
directly so there is little to gain by complicating the
analyses; in fact, typical QTL mapping performs bet-
ter than either FS or UDG (Figure 1b). Nevertheless,
even in these unfavourable circumstances, QDG is at
least as efficient as the typical strategy. Second, for
downstream nodes (Figure 1c), the performance of
typical QTL mapping is much worse than the rest of
strategies, which in turn have a similar performance
for QTL detection. As for covariate (phenotypic)
detection, the pattern is similar and QDG results in
much better FDR at the expense of some loss in
power (Figure 1b,c). Therefore, the critical issue is
how many of the phenotypes analysed in a real
experiment can be better described as ‘upstream’ or
‘downstream’ nodes. As this is not known in prac-
tice, the safest option seems to be to use QDG. Inter-
estingly, covariate FDR is much higher for upstream
than for downstream nodes, i.e. FS and UDG tend to
result in overfitting, which is the likely explanation
for reduced power and increased FDR for QTL detec-
tion.
Effect on R2, BIC and PMSE
All three proposed strategies improved dramatically
upon typical QTL mapping in both simulated and
real data (Figure 2), suggesting that a considerable
larger phenotypic variance can be explained and bet-
ter predictions can be achieved by including pheno-
typic predictors in the model. However, average R2
of models inferred by FS and UDG mapping was
even larger, and average BIC and PMSE were smal-
ler than when employing true models. This suggest
that models obtained by FS and UDG mapping tend
to overfit, again in agreement with observations dis-
cussed earlier. According to the three criteria, FS is
the best strategy for simulated data; however, as
shown earlier (Figure 1), QDG has a better perfor-
mance in terms of power and FDR in QTL detection
and FDR in covariate recovery in simulation studies.
Thus, for the real data analysis, we only compared
QTL mapping with QDG versus typical QTL map-
ping.
Real data
Changing QTL landscapes with network modelling
Figure 3 illustrates the changes of LOD score profiles
brought about by QDG modelling in three traits of
the Duroc · Erhualian cross. In Figure 3a, two
highly significant QTL on chromosomes 4 and 7 for
C18:3 in abdominal fat vanished after adjusting for
C18:2 in abdominal fat. This suggests that the effects
of both QTL on C18:3 were indirect, i.e. mediated by
C18:2. For C20:1 in abdominal fat (Figure 3b), after
adjusting for C20:2 in abdominal fat and BFT, the
LOD scores of the QTL on chromosome 7 dropped
dramatically from 50 to 15, i.e. despite a large
decrease in significance, the QTL are still highly sig-
nificant. This would suggest that a large proportion –
but not all – of effect of the chromosome 7 QTL on
C20:1 in abdominal fat is mediated through C20:2.
Figure 3c shows a different situation, after including
C14:0 in longissimus muscle as covariate for CW,
the majority of QTL for CW became more significant.
Note that these QTL were not detected for muscle
C14:0, suggesting adding C14:0 into the model
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reduced the error variances and thus increases the
significance of the QTL.
A genome-wide picture of QTL detected by typical
and QDG mapping is shown in Figure 4 for all traits
in both experimental populations. The QTL are rep-
resented by circles, red for typical mapping, green
for QDG mapping; the size of circles is proportional
to the significance (LOD score) of corresponding
QTL. In the Chinese experiment, 39 of 129 QTL
were identified with both modelling approaches,
whereas 37 QTL found with typical mapping van-
ished when using QDG. Finally, 14 new QTL were
found with QDG that were not significant in a classi-
cal scan. In the Spanish experiment, 13 QTL were
detected by both approaches, 11 and 3 QTL were
detected only by typical mapping and QDG
approach, respectively.
The new QTL uncovered by QDG mapping
The green circles that do not overlap with red circles
in Figure 4, are particularly interesting because,
according to the simulation results, they may repre-
sent ‘downstream nodes’ relative to the phenotypic
predictors selected by QDG approach. In these cases,
Figure 2 Summary of R2, Bayesian Information Criterion (BIC) and predictive mean square errors (PMSE) of cross-validation of models obtained
from modelling strategies for (a) 20 realizations of simulated data, (b) Iberian · Landrace cross data, (c) Duroc · Erhualian cross data. To facilitate
comparison, BIC and PMSE for four models of each trait were standardized to mean 0 and variance 1. In (a) real means, the results obtained with
the true model.
B. Yang et al. Porcine fatty acid QTL network
ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343 335
Figure 3 Comparison of LOD score profiles obtained with typical QTL mapping and QTL-directed dependency graph (QDG) mapping for (a) C18:3
in abdominal fat (b) C20:1 in abdominal fat (c) Carcass weight. In QDG mapping, these three traits were corrected by (a) C18:2 in abdominal fat,
(b) backfat thickness and C20:2 in abdominal fat and (c) C14:0 in longissimus muscle, respectively.
Porcine fatty acid QTL network B. Yang et al.
336 ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343
the QTL are uncovered because we have corrected
for the environmental noise caused by external phe-
notypes, increasing power (Figure 1c). We observed
several such ‘downstream nodes’ in both Spanish
and Chinese experiments. For instance, a QTL on
SSC7 in the Iberian · Landrace cross affecting oleic
acid (C18:1). Other authors, Guo et al. (2009) and
Sanchez et al. (2007), also reported QTL for the same
(a)
(b)
Figure 4 Summary of QTL detected by typical mapping (red) and QTL-directed dependency graph mapping (green) in (a) Iberian · Landrace cross
(b) Duroc · Erhualian cross; here, ‘A14:0’ and ‘D14:0’ mean C14:0 in abdominal fat and longissimus muscle, respectively. The size of circles is pro-
portional to the significance (LOD score) of the QTL.
B. Yang et al. Porcine fatty acid QTL network
ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343 337
trait in the vicinity of this locus. This particular locus
effect was confirmed in the Chinese data for abdomi-
nal fat C18:1 but not muscle C18:1 (Figure 4). Simi-
larly, a QTL for C18:0 (LOD score = 4.9) located at
121 cM on SSC6 was detected only with the QDG
approach. This region harbours QTL for several other
FAs like C14:0, C16:0 and C18:2 in the same popula-
tion. In the Duroc · Erhualian cross, a new QTL
(LOD = 3.5) at 40 cM for C14:0 in IMF was found
on SSC8; this region is very close to the QTL
reported by Lee et al. (2003) for the same trait.
Another example is the QTL at 61.7 cM on SSC13
for C16:1 in abdominal fat, a QTL near this region
(73 cM on SSC13) for the same FA in longissimus
muscle was also detected.
Interpretation of ‘hotspot’ QTL by QDG mapping
Figure 5 shows a graphical representation of the
phenotype and genetic networks obtained with
QDG. The average number of covariates per pheno-
type was 0.8 and 1.6 for the Spanish and Chinese
data, respectively. The average number of QTL per
trait was 1.2 and 2.5. The network was much more
complex in the Chinese than in the Spanish experi-
ment, likely because there were more FAs measured
in the Chinese data and because the larger the
experiment, the larger the power to identify more
QTL and trait to trait relations (Table 1).
Previous studies revealed that SSC4 and SSC6 in
Iberian · Landrace cross (Ovilo et al. 2002; Varona
et al. 2002; Clop et al. 2003) and SSC4, SSC7 and
SSC8 in Duroc · Erhualian cross (Guo et al. 2009;
Ma et al. 2009) were enriched in QTL responsible for
FA compositions, fat thickness, or both. These results
are confirmed by our analyses (Figures 4 and 5). As
described in simulations, when the target pheno-
types were ‘downstream nodes’, the FDR in ‘direct’
QTL detection for QDG mapping was much lower
than typical QTL mapping. Therefore, the QDG strat-
egy corrects the phenotypes by the spurious QTL
effects that are in fact indirect, making it possible to
disentangle direct and indirect effects of QTL.
As shown in Figure 5 or Figure S2, there are sig-
nificant QTL with primary effects on C18:2 and BFT
on position 70 cM of chromosome 4 for both experi-
ments, the FAT1 region (Andersson et al. 1994). In
the Duroc · Erhualian cross, this region has also pri-
mary effects on AFW and C20:2 in both abdominal
fat and longissimus muscle. In contrast, the QTL
effects in this region on IMF and other FAs might be
indirect, i.e. mediated through intermediate pheno-
types. On SSC6, our analysis supports that the QTL
region around 118 cM has a primary effect on
C16:0, C18:0, C18:2, IMF and BFT in Ibe-
rian · Landrace cross (Figure 5a). A similar situation
is observed on SSC7 in the Duroc · Erhualian cross,
a QTL region around 63 cM was found to have pri-
mary effects on FA compositions in both tissues and
fat deposit traits, like AFW and BFT, and CW. The
QTL region around 78 cM seems to be specific to
C20:1 and C20:2. In the Spanish data, a region
around 80 cM (SSC8) shows a direct effect on C16:0
and C16:1, indirect association with C18:1, but no
association with fat deposit traits. In the Chinese
cross, similarly, two QTL regions in 62 and 92 cM on
SSC8 have primary effects on C16:0 and C16:1,
respectively. Moreover, two QTL regions around 40
and 92 cM in the same chromosome again show pri-
mary effects simultaneously on both FA composition
and fat deposition.
In summary, the QTL hotspots on these chromo-
somes, SSC4, SSC6, SSC7 and SSC8, seem to have
primary effects on both FA composition and fat
deposition. There are at least two implications: (i)
these QTL might be responsible for the regulations
of both FAs and fat metabolism; and (ii) the correla-
tion between FA compositions and fat deposition
may be accounted for by common genetic factors,
i.e. pleiotropy.
Phenotype networks
In the pig breeding industry, lean pigs with higher
IMF content are favoured. However, carcass fat is
usually positively correlated with IMF. In this study,
we observe that the correlation between IMF and
carcass fat (BFT or AFW) is partially caused by a
pleiotropic QTL on SSC6 (approximately 118 cM) in
the Iberian · Landrace cross. In the Chinese cross,
some loci (e.g. 91 cM, SSC5) have pleiotropic effects
on both BFT and IMF; yet, some other relations are
indirect only, like that mediated by muscle C18:2.
FA composition is crucial for both taste and nutri-
tional value of meat; however, growth performance
is often negatively correlated with ideal FA composi-
tions (Webb & O’Neill 2008). For instance, high con-
tents of myristic acid (C14:0) and palmitic acid
(C16:0) in diet are risk factors of human cardiovas-
cular disease (Katan et al. 1994). In this study, the
correlation between C16:0 and IMF was 0.26 in the
Iberian · Landrace cross and is likely caused in part
by the shared QTL on SSC6 (Figure 5a). In the
Duroc · Erhualian cross, intramuscular C14:0 and
C16:0 were significantly correlated with IMF (Yang
et al. 2010), the correlations in this case could be
explained by the common QTL at approximately
40 cM on SSC8.
Porcine fatty acid QTL network B. Yang et al.
338 ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343
Figure 5 Network depicting all relationships between QTL and phenotypes obtained by QTL-directed dependency graph mapping in (a) Ibe-
rian · Landrace cross and (b) Duroc · Erhualian cross. Circles represent fatty acid compositions in abdominal fat (blue) and longissimus muscle
(red), hexagons (yellow) denote phenotypes: fat deposit traits backfat thickness, abdominal fat weight, intramuscular fat content and carcass
weight. Rectangles (green) are QTL with chromosome at position in cM inside. The detailed positions and other estimates of QTL in the two exper-
iments are summarized in Tables S3–S6.
B. Yang et al. Porcine fatty acid QTL network
ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343 339
In pigs, C18:2 is the most abundant essential FA;
it is also one of the precursors of other polyunsatu-
rated FAs (PUFA), which are important for human
health (Rudel et al. 1995) A negative correlation
between C18:2 and fat deposition has been reported
(Suzuki et al. 2006; Ntawubizi et al. 2010) and was
also observed in these two data sets. In the Ibe-
rian · Landrace cross, the correlation seems to be
mediated by the FAT1 locus on SSC4 as well as an
additional QTL on SSC6 (Figure 5a). Interestingly,
we observed several edges that directly connect
C18:2 and fat deposition traits in the Chinese experi-
ment (Figure 5b): from C18:2 in longissimus muscle
to AFW and IMF and from BFT to C18:2 in abdo-
minal fat. This suggests that, in addition to the
common genetic or environmental effects, the corre-
lations could also possibly be partly caused by a
direct causal relationship between C18:2 and fat
depositions. The edges pointing from C18:2 to AFW
and IMF support a regulatory role of C18:2 in lon-
gissimus muscle on fat deposition. Some authors
(Jump et al. 1994) report that PUFAs can inhibit
lipogenesis by suppressing lipogenic genes expression
in liver. Further, (Della Casa et al. 2010) showed that
feeding pigs with maize differing in C18:2 affected
subcutaneous fat and IMF.
As shown in Figure 5b or Figure S3b, we observed
both within and between tissue edges in the Chinese
FA network. Often, FAs in one tissue were linked to
the same FAs in the other tissue. Nevertheless, the
edge LOD values, which indicate confidence of edge
directions (Tables S7 and S8), were much larger
within than between tissues, 27.0 versus 7.2 on
average. This is concordant with previous observa-
tions (Yang et al. 2010). The within tissue relation-
ships between FAs did not necessarily reflect known
biochemical routes. For instance, saturated and
monounsaturated FAs n-3PUFA and n-6PUFA are
synthesized by different elongation and desaturation
pathways (Nakamura & Nara 2004); however, as
shown in Figure 5, several edges connect FAs that
belong to ‘separate pathways’, feedback loops were
also observed. This suggests that the ‘separate
pathways’ are in fact associated with each other and
subject to feedback regulations. Despite the complex-
ities, we found two edges C18:2 fi C18:3 and
C18:2 fi C18:1 that were conserved in both tissues
and in both experiments.
Concluding remarks
Following previous ideas on the importance of mod-
elling for QTL studies when many phenotypes are
available (Perez-Enciso et al. 2007), here we have
confirmed how the directed graph QDG approach by
Chaibub Neto et al. (2008) can improve upon a typi-
cal QTL scan strategy. By simulation, we have illus-
trated that QDG results in increased power and
lower FDR in QTL detection than the three other
strategies. This should aid to distinguish direct from
indirect QTL effects, which is important for under-
standing the nature of QTL ‘hotspots’ (Schadt et al.
2005; Li et al. 2006). It is also worth mentioning that
the performance of the methods differed according
to the topological order of the phenotype, i.e. loosely
speaking in how far a phenotype is from the ulti-
mate genetic cause. QDG mapping was also robust
regarding topological order of phenotypes, whereas
FS and UDG were less so. FS and undirected graphs
may suffer from overfitting and increased FDR, espe-
cially in upstream nodes (Figure 1), despite the fact
that they may exhibit better properties in terms of
R2 or BIC (Figure 2).
Always a matter of concern is the reliability of
reconstructed networks. QDG has been shown to
have, in general, good properties. Chaibub Neto et al.
(2008) simulated acyclic networks with 100
nodes ⁄phenotypes (sample size = 60, 300 or 500)
and three cyclic networks with six nodes (sample
size = 100 or 200). The power and FDR improved as
the sample size increased. For the acyclic network,
at sample size of 500, the power was approximately
93% and FDR was 0.2%. In our analysis, for the
simulated 20 replicates of acyclic networks with 100
phenotypes (sample size = 693), the residual stan-
dard deviation was set to 1 as compared with 0.1–
0.5 by Chaibub Neto et al. (2008); thus, our simu-
lated networks are noisier. The average power was
82%, and FDR was 8%. Logsdon & Mezey (2010)
simulated cyclic and acyclic networks with 10 or 30
nodes, as well as with different topologies and sam-
ple size (from 50 to 1000). Their results showed that
QDG performed better in sparse than denser net-
works. Therefore, QDG is sensitive to density and
noise in the network. However, it should generate
reasonable results in sparse networks with approxi-
mately 100 variables using approximately 500 indi-
viduals.
As expected in the real data analyses, there was a
global agreement between results from typical map-
ping in this study with those previously reported in
both the Spanish and Chinese crosses (Clop et al.
2003; Guo et al. 2009; Ma et al. 2009). The minor dif-
ferences are likely because of different choice of sig-
nificance thresholds and covariates, as well as in the
algorithm to compute QTL probabilities. However, in
Porcine fatty acid QTL network B. Yang et al.
340 ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343
both data sets, the differences between the typical
naıve scan and the QDG model were dramatic (Fig-
ures 3 and 4). These differences could enlighten
some interpretation on the functions of QTL. For
instance, several FA QTL on chromosome 4 (C16:0
and C18:0) were detected by typical mapping van-
ished after adjusting for phenotypic predictors in
QDG mapping. This suggests that the QTL detected
in typical mapping could be indirect. On the con-
trary, when a QTL is supported by both approaches,
there is an increased confidence that the QTL have a
primary effect on the corresponding traits. An exam-
ple is the QTL for C16:1 on SSC8 (80–102 cM),
which was uncovered in both experiments and by
both QDG and typical mapping. Remarkably, Estelle
et al. (2009) reported a non-synonymous polymor-
phism in the MTTP gene, which is located in this QTL
region. According to our simulations, this QTL should
affect an upstream node, i.e. the QTL should have a
direct effect on the trait. MTTP is critical for the
assembly of nascent lipoproteins that transport FAs in
the blood so a direct effect cannot be ruled out.
Animal or plant breeders often face the difficult
challenge that selection on one trait often has
adverse effects on other traits, e.g. in pigs, selection
on lean carcass is often accompanied by reduction in
IMF (Sonesson et al. 1998). The QDG mapping in
this study draws a whole picture of how genetic
variations and phenotypes are causally or indirectly
associated. This should provide more information
than simple correlations or QTL mapping results and
help us to overcome undesirable pleiotropic effects.
For instance, previous studies have shown that cor-
relations between IMF and carcass fat were approxi-
mately 0.30 (Yang et al. 2010). This study (Figure 5)
supports the hypothesis that the connection between
IMF and carcass fat like BFT or AFW is mediated
through C18:2 in longissimus muscle and through a
QTL on SSC5. Furthermore, our data also suggest
that the FAT1 locus in chromosome 4 has pleiotropic
and direct effects on both fat depositions and PUFA,
like C18:2n-6 and C20:2n-6.
In conclusion, directed networks are an option to
be preferred over FS or undirected graphs and cer-
tainly over simplistic QTL mapping. Incorporating
causal relationship between phenotypes in QTL map-
ping framework can help to improve power and gain
more insight into the genetic basis of complex traits.
An application to Spanish and Chinese data evi-
dences how genetic architectures can differ, e.g. the
striking absence of QTL in SSC6 in the Chinese cross
and the reciprocal observation in SSC7. But it also
shows that some QTL are consistently confirmed in
both crosses and with different modelling strategies,
like the loci affecting C16:1 in SSC8 and in SSC2.
Acknowledgements
BY is funded by a scholarship (File No. 2008836039)
from China Scholarship Council (CSC); N. Navarro
was funded by a Beatriu de Pinos post doc fellowship
(Spain). Work funded by Natural Science Founda-
tion of China (30425045) to LSH and AGL2007-
65563-C02-01 ⁄GAN and PCI2006-A7-0523 (Ministe-
rio de Ciencia e Innovacion, Spain) to MPE.
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Supporting information
Additional Supporting Information may be found in
the online version of this article.
Figure S1 Graphical skeleton of a simulated phe-
notypic network (example).
Figure S2 Sub-network for phenotypes which
have QTL detected by typical mapping or QDG map-
ping on (a) SSC4, (b) SSC6, (c) SSC7 and (d) SSC8.
Figure S3 Causal networks for the fatty acids and
fat deposition traits from (a) Iberian · Landrace cross
and (b) Duroc · Erhualian cross.
Table S1 Linkage map of 139 markers in the Ibe-
rian · Landrace cross.
Table S2 Linkage map of 187 markers in the
Duroc · Erhualian cross.
Table S3 QTL detected by typical QTL mapping in
the Iberian · Landrace cross.
Table S4 QTL and phenotypic predictors obtained
by QDG-based QTL mapping in the Iberian · Land-
race cross.
Table S5 QTL detected by typical QTL mapping in
Duroc · Erhualian cross.
Table S6 QTL and phenotypic predictors obtained
by QDG-based QTL mapping in Duroc · Erhualian
cross.
Table S7 Network inferred by QDG for pheno-
types in Iberian · Landrace cross.
Table S8 Network inferred by QDG for pheno-
types in Duroc · Erhualian cross.
Please note: Wiley-Blackwell is not responsible for
the content or functionality of any supporting mate-
rials supplied by the authors. Any queries (other
than missing material) should be directed to the
corresponding author for the article.
B. Yang et al. Porcine fatty acid QTL network
ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343 343