Volume 6 Supplement 2
Proceedings of the 15th European workshop on QTL mapping and marker assisted selection (QTLMAS)
Bayesian Variable Selection to identify QTL affecting a simulated quantitative trait
 Anouk Schurink^{1}Email author,
 Luc LG Janss^{2} and
 Henri CM Heuven^{1, 3}
DOI: 10.1186/175365616S2S8
© Schurink et al.; licensee BioMed Central Ltd. 2012
Published: 21 May 2012
Abstract
Background
Recent developments in genetic technology and methodology enable accurate detection of QTL and estimation of breeding values, even in individuals without phenotypes. The QTLMAS workshop offers the opportunity to test different methods to perform a genomewide association study on simulated data with a QTL structure that is unknown beforehand. The simulated data contained 3,220 individuals: 20 sires and 200 dams with 3,000 offspring. All individuals were genotyped, though only 2,000 offspring were phenotyped for a quantitative trait. QTL affecting the simulated quantitative trait were identified and breeding values of individuals without phenotypes were estimated using Bayesian Variable Selection, a multilocus SNP model in association studies.
Results
Estimated heritability of the simulated quantitative trait was 0.30 (SD = 0.02). Mean posterior probability of SNP modelled having a large effect (${\widehat{p}}_{i}$) was 0.0066 (95%HPDR: 0.00140.0132). Mean posterior probability of variance of second distribution was 0.409 (95%HPDR: 0.2860.589). The genomewide association analysis resulted in 14 significant and 43 putative SNP, comprising 7 significant QTL on chromosome 1, 2 and 3 and putative QTL on all chromosomes. Assigning single or multiple QTL to significant SNP was not obvious, especially for SNP in the same region that were more or less in LD. Correlation between the simulated and estimated breeding values of 1,000 offspring without phenotypes was 0.91.
Conclusions
Bayesian Variable Selection using thousands of SNP was successfully applied to genomewide association analysis of a simulated dataset with unknown QTL structure. Simulated QTL with Mendelian inheritance were accurately identified, while imprinted and epistatic QTL were only putatively detected. The correlation between simulated and estimated breeding values of offspring without phenotypes was high.
Background
Recent developments in genetic technology enable genotyping of many individuals for thousands of markers, thereby increasing the possibility to unravel the genetic background of various economically important complex traits and disorders using genomewide association studies. Different methods are available to perform a genomewide association study. Bayesian Variable Selection is a powerful method in association studies [1, 2], because it simultaneously estimates all SNP (Single Nucleotide Polymorphisms) effects and possible polygenic effects. Multilocus SNP models like Bayesian Variable Selection model should therefore improve our ability to find and localize the true association between genotype and phenotype [3].
The aim of our research was to accurately identify QTL (Quantitative Trait Locus) affecting the quantitative trait and to predict breeding values of offspring without phenotypes in the simulated data of the 15^{th} QTLMAS workshop using Bayesian Variable Selection implemented in the Bayz software [4].
Methods
Data
An outbred population was simulated with 1,000 generations of 1,000 individuals, which was followed by 30 generations of 150 individuals. The data used in the analysis corresponded to the last generations of the pedigree and contained 20 sire families. Each sire was mated with 10 dams and number of offspring per dam was 15 resulting in 3,000 offspring in total. Both pedigree and phenotypes of sires and dams were not provided. Genomic kinship between sires and dams indicated that sires and dams most likely descended from one population (data not shown). Only 10 out of 15 offspring per fullsib family were phenotyped for a quantitative trait that was normally distributed. All individuals were genotyped for 9,990 SNP, which were equally distributed on 5 chromosomes (size: 1 Morgan each). Monomorphic SNP (n = 2,869) and SNP with MAF (Minor Allele Frequency) <0.01 (n = 383) were excluded from the analysis. A complete description of the simulated data can be found on the website of the 15^{th} QTLMAS workshop [5].
QTL analysis and breeding value estimation
where y is the quantitative trait and μ is the mean; Z is the incidence matrix indicating for each observation the (polygenic) genetic effects by which it is influenced; a is the (polygenic) genetic effects with $\mathsf{\text{a}}~N\left(0,\mathsf{\text{A}}{\sigma}_{a}^{2}\right)$, where A is the numerator relationship matrix between the individuals based on pedigree and ${\sigma}_{a}^{2}$ is the (polygenic) genetic variance; ∑_{ k }X_{ k }α_{ k } fitted additive SNP association effects, where α_{ k } is a vector with allele substitution effects with $~N\left(0,\mathsf{\text{I}}{\sigma}_{{g}_{k}}^{2}\right)$, where I is an identity matrix of appropriate dimensions and ${\sigma}_{{a}_{k}}^{2}$ is the additive genetic variance of SNP and X_{ k } is an incidence matrix relating allele substitution effects to observed SNP genotypes; and e are residuals with $\mathsf{\text{e}}~N\left(0,\mathsf{\text{I}}{\sigma}_{e}^{2}\right)\phantom{\rule{1em}{0ex}}{}_{{}_{}}^{\mathrm{}}$, where I is an identity matrix of appropriate dimensions and ${\sigma}_{e}^{2}$ is the residual variance. SNP were also modelled to have a dominance effect on the simulated quantitative trait as well. However, no significant dominance effect was found (data not shown).
where the 'null' distribution modelled the majority of SNP with (virtually) no effect using prior settings π_{0} = 0.98 and ${\sigma}_{g0}^{2}=0.00\mathsf{\text{1}}$. The second distribution modelled SNP with large effects where prior settings were π_{1} = 0.02 and ${\sigma}_{g1}^{2}=0.\mathsf{\text{1}}$. Variances of the mixture distribution and other model effects were estimated using a uniform prior. A Bernoulli distribution specified probabilities for a SNP belonging to the 'null' or second distribution and proportions for the mixture were set to have a slightly informative prior distribution ~ Beta(100,1).
Applied MCMC techniques
The model estimated a 'mixture indicator' that indicated per MCMC (Markov ChainMonte Carlo) cycle for each SNP whether it was estimated to belong to the 'null' (= 0) or second distribution (= 1). After averaging in the MCMC, a value ranging from 0 to 1 indicated the posterior probability of each SNP to have a large effect (${\widehat{p}}_{i}$).
Most samplers were single site Gibbs samplers. An alternative Metropolis Hastings sampler was used to speed up mixing of estimated SNP variance components. Joint updates for 2 SNP effects and 2 'mixture indicators' were made. The Metropolis Hastings sampler updated the variance of the 'null' and second distribution thereby keeping a constant ratio (1:100) to allow for fast mixing by jointly shrinking or expanding variances together with all SNP effects. Tuning of step size from the Metropolis Hastings sampler was needed to reach an acceptance rate around 0.5.
One MCMC chain of 52,000 cycles with a burnin period of 2,000 cycles was run, which was found sufficient to obtain accurate estimates (effective number of samples was 39.6 for polygenic genetic variance and >180 for all other model effects).
Identification of associated SNP
where ${\widehat{p}}_{i}$ = 'mixture indicator' of a SNP and π_{1} = prior 1/101 related to the Beta distribution. Using guidelines from Kass and Raftery [7] to judge BF, a value above 10 was considered as 'strong' evidence. SNP with BF between 3.2 and 10 were considered to be 'putative'.
In case more SNP within a region showed significant association, the size of the region and LD (Linkage Disequilibrium) (r^{2}) among the SNP were used to call a single or multiple underlying QTL. When identified SNP showed clear LD blocks (r^{2} of most SNP ≥0.7), SNP were considered to be associated with the same QTL.
Results and discussion
Correlation between the simulated and estimated breeding values of 1,000 offspring without phenotypes was 0.91. Comparison of all applied methods by all researchers showed that the correlation between the simulated and estimated breeding values were highest (0.850.94) when the data were analysed using Bayesian Variable Selection methods.
Conclusions
Bayesian Variable Selection model showed to be a successful method for genomewide association using dense marker maps as it identified the simulated QTL with Mendelian inheritance. Imprinted and epistatic QTL were only putatively detected. The correlation between simulated and estimated breeding values of offspring without phenotypes was high.
List of abbreviations used
 SNP:

Single Nucleotide Polymorphisms
 QTL:

Quantitative Trait Locus
 MAF:

Minor Allele Frequency
 LD:

Linkage Disequilibrium
 MCMC:

Markov Chain Monte Carlo
 BF:

Bayes Factor
 HPD:

Highest Probability Density.
Declarations
Acknowledgements
This article has been published as part of BMC Proceedings Volume 6 Supplement 2, 2012: Proceedings of the 15th European workshop on QTL mapping and marker assisted selection (QTLMAS). The full contents of the supplement are available online at http://www.biomedcentral.com/bmcproc/supplements/6/S2.
Authors’ Affiliations
References
 Hoggart CJ, Whittaker JC, De Iorio M, Balding DJ: Simultaneous analysis of all SNPs in genomewide and resequencing association studies. PLoS Genetics. 2008, 4: e100013010.1371/journal.pgen.1000130.PubMed CentralView ArticlePubMed
 Sahana G, Guldbrandtsen B, Janss L, Lund MS: Comparison of association mapping methods in a complex pedigreed population. Genetic Epidemiology. 2010, 34: 455462. 10.1002/gepi.20499.View ArticlePubMed
 Fridley BL: Bayesian variable and model selection methods for genetic association studies. Genetic Epidemiology. 2009, 33: 2737. 10.1002/gepi.20353.View ArticlePubMed
 Janss LLG: Bayz manual version 2.03. Janss Biostatistics, Leiden, The Netherlands. 2010, [http://www.bayz.biz]
 Elsen JM, Tesseydre S, Filangi O, Le Roy P, Demeure O: XV^{th} QTLMAS: simulated dataset. Proceedings of the XVth QTLMAS Workshop: 1920 May 2011; Rennes France. Edited by: Demeure O, Elsen JM, Filangi O, Le Roy P. 2012
 Habier D, Fernando RL, Kizilkaya K, Garrick DJ: Extension of the Bayesian alphabet for genomic selection. BMC Bioinformatics. 2011, 12: 18610.1186/1471210512186.PubMed CentralView ArticlePubMed
 Kass RE, Raftery AE: Bayes Factors. Journal of the American Statistical Association. 1995, 90: 773795. 10.2307/2291091.View Article
Copyright
This article is published under license to 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.