Abstract Background: Existing software for quantitative trait mapping is either not able to model polygenic variation or does not allow incorporation of more than one genetic variance component. Improperly modeling the genetic relatedness among subjects can result in excessive false positives. We have developed an R package, QTLRel, to enable more flexible modeling of genetic relatedness as well as covariates and non-genetic variance components. Results: We have successfully used the package to analyze many datasets, including F 34 body weight data that contains 688 individuals genotyped at 3105 SNP markers and identified 11 QTL. It took 295 seconds to estimate variance components and 70 seconds to perform the genome scan on an Linux machine equipped with a 2.40GHz Intel(R) Core(TM)2 Quad CPU. Conclusions: QTLRel provides a toolkit for genome-wide association studies that is capable of calculating genetic incidence matrices from pedigrees, estimating variance components, performing genome scans, incorporating interactive covariates and genetic and non-genetic variance components, as well as other functionalities such as multiple-QTL mapping and genome-wide epistasis

Abraham A Palmer

Andrew D Skol

Mark Abney

Riyan Cheng

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SOFTWARE Open Access
QTLRel: an R Package for Genome-wide
Association Studies in which Relatedness
is a Concern
Riyan Cheng1, Mark Abney1, Abraham A Palmer1,2* and Andrew D Skol3
Abstract
Background: Existing software for quantitative trait mapping is either not able to model polygenic variation or
does not allow incorporation of more than one genetic variance component. Improperly modeling the genetic
relatedness among subjects can result in excessive false positives. We have developed an R package, QTLRel, to
enable more flexible modeling of genetic relatedness as well as covariates and non-genetic variance components.
Results: We have successfully used the package to analyze many datasets, including F34 body weight data that
contains 688 individuals genotyped at 3105 SNP markers and identified 11 QTL. It took 295 seconds to estimate
variance components and 70 seconds to perform the genome scan on an Linux machine equipped with a
2.40GHz Intel(R) Core(TM)2 Quad CPU.
Conclusions: QTLRel provides a toolkit for genome-wide association studies that is capable of calculating genetic
incidence matrices from pedigrees, estimating variance components, performing genome scans, incorporating
interactive covariates and genetic and non-genetic variance components, as well as other functionalities such as
multiple-QTL mapping and genome-wide epistasis.
Background
Methods to search for quantitative trait loci (QTL) in
common experimental designs are well established, and
software to analyze these populations is widely available.
One popular package, R/qtl [1], provides a comprehen-
sive toolset for QTL mapping. Since it does not allow
random effects, R/qtl is most suitable for mapping
populations such as F2 and backcross where individuals
are equally genetically related. Software that can model
polygenic effects due to genetic relatedness includes
TASSEL [2] and EMMA [3]. Both allow covariates as
fixed effects but are only capable of incorporating a ran-
dom term to account for one genetic variance compo-
nent. However, both additive and dominance modes of
inheritance are common for many quantitative traits.
Ignoring these variance components may result in
excessive false positives. Moreover, researchers may also
be interested in interactive covariates, epistasis and
non-genetic random effects. We have developed an R
package QTLRel that meets all these needs.
Implementation
Statistical model
Consider the following statistical model
y = Xβ + Qγ + Zu + ε (1)
where y is a vector of phenotypes, b is a vector of cov-
ariate effects, g is a vector of putative QTL effects, u is a
vector of polygenic effects and ε is a vector of residual
effects. X, Q and Z are incidence matrices. b can be
fixed, random or a mix of both fixed and random.
Assume that u ~ N(0, G), ε ~ N(0, Is2), and u is inde-
pendent of ε. G consists of five genetic variance compo-
nents including additive and dominance components as
well as three other components that model excess simi-
larity due to inbreeding [4]. The incidence matrices cor-
responding to these five genetic variance components
can be obtained from condensed identity coefficients as
defined in [[5], pp.133].* Correspondence: aap@uchicago.edu1Department of Human Genetics, The University of Chicago, IL 60637 USA
Full list of author information is available at the end of the article
Cheng et al. BMC Genetics 2011, 12:66
http://www.biomedcentral.com/1471-2156/12/66
© 2011 Cheng et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
Condensed identity coefficients
While other programs are available for calculating con-
densed identity coefficients from pedigrees [6], we pro-
vide a function that is especially feasible for pedigrees
with a large number of generations. Condensed identity
coefficients can be derived from generalized kinship
coefficients [7]. Bottom-up and top-down are two com-
putational strategies for calculating generalized kinship
coefficients from a pedigree. The bottom-up approach
starts from the target individuals and moves up the ped-
igree until reaching the founders. It requires minimal
storage but the computational load increases approxi-
mately exponentially with the number of generations.
The bottom-up approach is computationally infeasible if
both the number of generations and the number of indi-
viduals are large. The top-down approach starts from
founders and moves down to the target individuals. The
computational load is approximately linear in the num-
ber of generations. However, the intermediate general-
ized kinship coefficients need to be stored, which may
require extensive storage if the number of individuals in
a generation is large. We have implemented a function
that allows users to adjust the arguments to achieve a
hybrid bottom-up/top-down approach, which can
accommodate very deep pedigrees.
Variance components
QTLRel can estimate variance components given the
appropriate incidence matrices. QTLRel estimates these
variance components using maximum likelihood. These
estimates are nearly equivalent to those obtained by
restricted maximum likelihood for typical sample sizes.
The maximum likelihood estimates are found numeri-
cally using one of several methods. We default to
Nelder-Mead since we have found it to be more
numerically stable. QTLRel allows users to select var-
iance components using a model selection procedure or
perform statistical significance tests for them.
Genome scans
Re-estimating variance components at each marker in a
genome scan may not be computationally feasible. The
approach used by QTLRel is to first estimate the correla-
tion matrix due to polygenic, residual and other random
effects, which is based on the estimated variance compo-
nents, and then use this matrix as known to scan the gen-
ome. Testing fixed effects conditional on estimated
random effects is a general approach in mixed-effect mod-
els [2,3,8,9]. Our method is most similar to the measured-
genotype fixed-heritability method in Aulchenko et al. [9].
Empirical significance thresholds
QTLRel implements two methods for estimating gen-
ome-wide significance thresholds. The first is a
permutation test in which the genotypes are permuted
while the phenotypes and incidence matrices are held
constant. We have previously demonstrated that when
polygenic effects are ignored in the model type I error
rates are inflated when a permutation is used; however,
when the model is appropriate, permutation performs
well [10]. The second method is gene dropping which
can appropriately control type I error rates even when
polygenic variation is ignored in the model.
Results
QTLRel has been successfully used in an AIL to identify
QTL for methamphetamine sensitivity [10], muscle
weight [11], prepulse inhibition [12] and body weight
[13]. In the analysis of body weight we calculated all five
genetic incidence matrices, but only estimated additive
and dominance variance components because the other
variance components are negligible in general [14]. We
then performed a genome scan using 688 individual
genotyped at 3,105 SNP markers. We identified 11 QTL
that exceeded the .05 genome-wide significance thresh-
old estimated from 1800 gene dropping samples. These
11 QTL were confirmed as distinct signals using a for-
ward step-wise multiple-QTL mapping function imple-
mented in QTLRel. We also investigated genome-wide
epistatic effects but found none. The analysis was
accomplished on an Linux machine equipped with a
2.40GHz Intel(R) Core(TM)2 Quad CPU. It took 295
seconds to estimate variance components and 70 sec-
onds to perform the genome scan.
Conclusions
QTLRel provides a toolkit for genome-wide association
studies that is capable of calculating genetic incidence
matrices from pedigrees, estimating variance compo-
nents, performing genome scans, and estimating signifi-
cance thresholds. It can model interactive covariates and
multiple genetic and non-genetic variance components.
Other functions include multiple-QTL mapping and
genome-wide epistasis. QTLRel can perform interval
mapping based on the Haley-Knott method [15] for
markers with 2 alleles. Because QTLRel is implemented
in R users can take advantage of numerous other statis-
tical packages; however, there is room to improve on
QTLRel’s speed since it makes use of many intermediate
R functions. It is our intention to extend some function-
alities, e.g., the Haley-Knott method to markers with
more than two alleles. In summary, QTLRel provides a
stand-alone, comprehensive tool to perform QTL ana-
lyses in populations in which relatedness is a concern.
Availability
QTLRel is an R package. It is publicly available on R
CRAN http://cran.r-project.org/web/packages/QTLRel
Cheng et al. BMC Genetics 2011, 12:66
http://www.biomedcentral.com/1471-2156/12/66
Page 2 of 3
for Windows, Linux and Mac machines under the GNU
GPL license. A tutorial is available in the package as
well as on the Palmer lab web page http://www.palmer-
lab.org/software.
Acknowledgements
We appreciate helpful comments from the anonymous reviewers. This
project was supported by NIH grants R01DA021336, R01MH079103 and
R21DA024845.
Author details
1Department of Human Genetics, The University of Chicago, IL 60637 USA.
2Department of Psychiatry and Behavioral Neuroscience, The University of
Chicago, IL 60637 USA. 3Department of Medicine, The University of Chicago,
IL 60637 USA.
Authors’ contributions
RC wrote the program, this paper and the tutorial and has made seminal
intellectual contributions throughout this project. MA worked with the other
authors and lent his considerable experience addressing similar issues in
human populations such as the Hutterites. AAP initiated the projects that
lead to the development of the software and has interacted extensively with
all other authors. ADS worked with the other authors and lent his
considerable experience with the analysis of animal breeding designs and
helped to develop earlier versions of both this paper and the tutorial. All
authors read and approved the final manuscript.
Received: 19 May 2011 Accepted: 27 July 2011 Published: 27 July 2011
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doi:10.1186/1471-2156-12-66
Cite this article as: Cheng et al.: QTLRel: an R Package for Genome-wide
Association Studies in which Relatedness is a Concern. BMC Genetics
2011 12:66.
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QTLRel: An R package for genome-wide association studies in which relatedness is a concern

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QTLRel: An R package for genome-wide association studies in which relatedness is a concern

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