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

ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343 doi:10.1111/j.1439-0388.2011.00928.x

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,

Porcine fatty acid QTL network B. Yang et al.

330 ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343

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

ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 329–343 331

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



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.



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



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.



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.



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.



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.



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.



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



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.

References

Andersson L., Georges M. (2004) Domestic-animal

genomics: deciphering the genetics of complex traits.

Nat. Rev. Genet., 5, 202–212.

Andersson L., Haley C.S., Ellegren H., Knott S.A.,

Johansson M., Andersson K., Andersson-Eklund L.,

Edfors-Lilja I., Fredholm M., Hansson I., Hakansson J.,

Lundstrom K. (1994) Genetic mapping of quantitative

trait loci for growth and fatness in pigs. Science, 263,

1771–1774.

Banerjee S., Yandell B.S., Yi N. (2008) Bayesian quantita-

tive trait loci mapping for multiple traits. Genetics, 179,

2275–2289.

Broman K.W., Wu H., Sen S., Churchill G.A. (2003)

R ⁄ qtl: QTL mapping in experimental crosses. Bioinfor-

matics, 19, 889–890.

Carlborg O., Haley C.S. (2004) Epistasis: too often

neglected in complex trait studies? Nat. Rev. Genet., 5,

618–625.

Chaibub Neto E., Ferrara C.T., Attie A.D., Yandell B.S.

(2008) Inferring causal phenotype networks from seg-

regating populations. Genetics, 179, 1089–1100.

Clop A., Ovilo C., Perez-Enciso M., Cercos A., Tomas A.,

Fernandez A., Coll A., Folch J.M., Barragan C., Diaz I.,

Oliver M.A., Varona L., Silio L., Sanchez A., Noguera

J.L. (2003) Detection of QTL affecting fatty acid com-

position in the pig. Mamm. Genome, 14, 650–656.

Della Casa G., Bochicchio D., Faeti V., Marchetto G.,

Poletti E., Rossi A., Panciroli A., Mordenti A.L., Brogna

N. (2010) Performance and fat quality of heavy pigs

fed maize differing in linoleic acid content. Meat Sci.,

84, 152–158.

Estelle J., Fernandez A.I., Perez-Enciso M., Fernandez A.,

Rodriguez C., Sanchez A., Noguera J.L., Folch J.M.

(2009) A non-synonymous mutation in a conserved

site of the MTTP gene is strongly associated with pro-

tein activity and fatty acid profile in pigs. Anim. Genet.,

40, 813–820.

de la Fuente A., Bing N., Hoeschele I., Mendes P. (2004)

Discovery of meaningful associations in genomic data



using partial correlation coefficients. Bioinformatics, 20,

3565–3574.

Guo T., Ren J., Yang K., Ma J., Zhang Z., Huang L.

(2009) Quantitative trait loci for fatty acid composition

in longissimus dorsi and abdominal fat: results from a

White Duroc · Erhualian intercross F2 population.

Anim. Genet., 40, 185–191.

Haley C.S., Knott S.A., Elsen J.M. (1994) Mapping quan-

titative trait loci in crosses between outbred lines using

least squares. Genetics, 136, 1195–1207.

Jiang C., Zeng Z.B. (1995) Multiple trait analysis of

genetic mapping for quantitative trait loci. Genetics,

140, 1111–1127.

Jump D.B., Clarke S.D., Thelen A., Liimatta M. (1994)

Coordinate regulation of glycolytic and lipogenic gene

expression by polyunsaturated fatty acids. J. Lipid Res.,

35, 1076–1084.

Kalisch M., Buhlmann P. (2007) Estimating high-dimen-

sional directed acyclic graphs with the PC-Algorithm.

J. Mach. Learn. Res., 8, 613–636.

Katan M.B., Zock P.L., Mensink R.P. (1994) Effects of fats

and fatty acids on blood lipids in humans: an overview.

Am. J. Clin. Nutr., 60, 1017S–1022S.

Knott S.A., Haley C.S. (2000) Multitrait least squares for

quantitative trait loci detection. Genetics, 156, 899–911.

Ledur M.C., Navarro N., Perez-Enciso M. (2009) Data

modeling as a main source of discrepancies in single

and multiple marker association methods. BMC Proc.,

3(Suppl. 1), S9.

Lee C., Chung Y., Kim J.H. (2003) Quantitative trait loci

mapping for fatty acid contents in the backfat on por-

cine chromosomes 1, 13, and 18. Mol. Cells, 15, 62–67.

Li R., Tsaih S.W., Shockley K., Stylianou I.M., Wergedal

J., Paigen B., Churchill G.A. (2006) Structural model

analysis of multiple quantitative traits. PLoS Genet., 2,

e114.

Liu B., de la Fuente A., Hoeschele I. (2008) Gene net-

work inference via structural equation modeling in

genetical genomics experiments. Genetics, 178, 1763–

1776.

Logsdon B.A., Mezey J. (2010) Gene expression network

reconstruction by convex feature selection when incor-

porating genetic perturbations. PLoS Comput. Biol., 6,

e1001014.

Ma J., Ren J., Guo Y., Duan Y., Ding N., Zhou L., Li L.,

Yan X., Yang K., Huang L., Song Y., Xie J., Milan D.

(2009) Genome-wide identification of quantitative trait

loci for carcass composition and meat quality in a

large-scale White Duroc x Chinese Erhualian resource

population. Anim. Genet., 40, 637–647.

Manichaikul A., Moon J.Y., Sen S., Yandell B.S., Broman

K.W. (2009) A model selection approach for the identi-

fication of quantitative trait loci in experimental

crosses, allowing epistasis. Genetics, 181, 1077–1086.

Nakamura M.T., Nara T.Y. (2004) Structure, function,

and dietary regulation of delta6, delta5, and delta9

desaturases. Annu. Rev. Nutr., 24, 345–376.

Ntawubizi M., Colman E., Janssens S., Raes K., Buys N.,

De Smet S. (2010) Genetic parameters for intramuscu-

lar fatty acid composition and metabolism in pigs.

J. Anim. Sci., 88, 1286–1294.

Ovilo C., Clop A., Noguera J.L., Oliver M.A., Barragan

C., Rodriguez C., Silio L., Toro M.A., Coll A., Folch

J.M., Sanchez A., Babot D., Varona L., Perez-Enciso M.

(2002) Quantitative trait locus mapping for meat qual-

ity traits in an Iberian x Landrace F2 pig population.

J. Anim. Sci., 80, 2801–2808.

Perez-Enciso M., Misztal I. (2004) Qxpak: a versatile

mixed model application for genetical genomics and

QTL analyses. Bioinformatics, 20, 2792–2798.

Perez-Enciso M., Clop A., Noguera J.L., Ovilo C., Coll A.,

Folch J.M., Babot D., Estany J., Oliver M.A., Diaz I.,

Sanchez A. (2000) A QTL on pig chromosome 4 affects

fatty acid metabolism: evidence from an Iberian by

Landrace intercross. J. Anim. Sci., 78, 2525–2531.

Perez-Enciso M., Quevedo J.R., Bahamonde A. (2007)

Genetical genomics: use all data. BMC Genomics, 8, 69.

Rudel L.L., Parks J.S., Sawyer J.K. (1995) Compared with

dietary monounsaturated and saturated fat, polyunsat-

urated fat protects African green monkeys from coro-

nary artery atherosclerosis. Arterioscler. Thromb. Vasc.

Biol., 15, 2101–2110.

Sanchez M.P., Iannuccelli N., Basso B., Bidanel J.P., Bil-

lon Y., Gandemer G., Gilbert H., Larzul C., Legault C.,

Riquet J., Milan D., Le Roy P. (2007) Identification of

QTL with effects on intramuscular fat content and fatty

acid composition in a Duroc · Large White cross. BMC

Genet., 8, 55.

Schadt E.E., Lamb J., Yang X., Zhu J., Edwards S., Gu-

hathakurta D., Sieberts S.K., Monks S., Reitman M.,

Zhang C., Lum P.Y., Leonardson A., Thieringer R.,

Metzger J.M., Yang L., Castle J., Zhu H., Kash S.F.,

Drake T.A., Sachs A., Lusis A.J. (2005) An integrative

genomics approach to infer causal associations between

gene expression and disease. Nat. Genet., 37, 710–717.

Shipley B. (2000) Cause and Correlation in biology: A

User’s Guide to Path Analysis Structural Equations and

Causal Inference. Cambridge University Press, Cam-

bridge, UK.

Sonesson A.K., Greef K.H.d., Meuwissen T.H.E. (1998)

Genetic parameters and trends of meat quality, carcass

composition and performance traits in two selected

lines of large white pigs. Livest. Sci., 57, 23–32.

Suzuki K., Ishida M., Kadowaki H., Shibata T., Uchida

H., Nishida A. (2006) Genetic correlations among fatty

acid compositions in different sites of fat tissues, meat

production, and meat quality traits in Duroc pigs.

J. Anim. Sci., 84, 2026–2034.



Varona L., Ovilo C., Clop A., Noguera J.L., Perez-Enciso

M., Coll A., Folch J.M., Barragan C., Toro M.A., Babot

D., Sanchez A. (2002) QTL mapping for growth and

carcass traits in an Iberian by Landrace pig intercross:

additive, dominant and epistatic effects. Genet. Res., 80,

145–154.

Webb E.C., O’Neill H.A. (2008) The animal fat paradox

and meat quality. Meat Sci., 80, 28–36.

Weiss K.M. (2008) Tilting at quixotic trait loci (QTL): an

evolutionary perspective on genetic causation. Genetics,

179, 1741–1756.

Yang K.X., Ma J.W., Guo Y.M., Guo T.F., Zhao Y.G.,

Ding N.S., Betti M., Plastow G.S., Huang L.S. (2010)

Correlations between fat depot traits and fatty acid

composition in abdominal subcutaneous adipose tissue

and longissimus muscle: results from a White Duroc x

Erhualian intercross F2 population. J. Anim. Sci., 88,

3538–3545.

Yu J., Pressoir G., Briggs W.H., Vroh Bi I., Yamasaki M.,

Doebley J.F., McMullen M.D., Gaut B.S., Nielsen D.M.,

Holland J.B., Kresovich S., Buckler E.S. (2006) A uni-

fied mixed-model method for association mapping that

accounts for multiple levels of relatedness. Nat. Genet.,

38, 203–208.

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


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


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.



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