Department of Human Genetics, The University of Chicago, IL 60637 USA

Department of Psychiatry and Behavioral Neuroscience, The University of Chicago, IL 60637 USA

Department of Medicine, The University of Chicago, IL 60637 USA

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.

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 _{2 }and backcross where individuals are equally genetically related. Software that can model polygenic effects due to genetic relatedness includes TASSEL

Implementation

Statistical model

Consider the following statistical model

where **
y
**is a vector of phenotypes,

Condensed identity coefficients

While other programs are available for calculating condensed identity coefficients from 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 numerically 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 variance 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 correlation matrix due to polygenic, residual and other random effects, which is based on the estimated variance components, and then use this matrix as known to scan the genome. Testing fixed effects conditional on estimated random effects is a general approach in mixed-effect models

Empirical significance thresholds

QTLRel implements two methods for estimating genome-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

Results

QTLRel has been successfully used in an AIL to identify QTL for methamphetamine sensitivity

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, and estimating significance 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

Availability

QTLRel is an R package. It is publicly available on R CRAN

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.

Acknowledgements

We appreciate helpful comments from the anonymous reviewers. This project was supported by NIH grants R01DA021336, R01MH079103 and R21DA024845.