Animal Breeding and Genomics Centre, Wageningen University, PO Box 338, 6700 AH Wageningen, The Netherlands

Aarhus University, DJF Department of Genetics and Biotechnology, PO Box 50, 8830 Tjele, Denmark

Clinical Sciences of Companion Animals, Faculty of Veterinary Medicine, Utrecht University, PO Box 80163, 3508 TD Utrecht, The Netherlands

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 QTL-MAS workshop offers the opportunity to test different methods to perform a genome-wide 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 multi-locus 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 (

Conclusions

Bayesian Variable Selection using thousands of SNP was successfully applied to genome-wide 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 genome-wide association studies. Different methods are available to perform a genome-wide association study. Bayesian Variable Selection is a powerful method in association studies

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 }QTL-MAS workshop using Bayesian Variable Selection implemented in the Bayz software

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 full-sib 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 }QTL-MAS workshop

QTL analysis and breeding value estimation

The model used for QTL detection and breeding value estimation simultaneously fitted polygenic and SNP effects:

where **y **is the quantitative trait and **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 **A **is the numerator relationship matrix between the individuals based on pedigree and _{k}_{k}_{k }**α _{k }**is a vector with allele substitution effects with

Bayesian Variable Selection implemented in the Bayz software

where the 'null' distribution modelled the majority of SNP with (virtually) no effect using prior settings _{0 }= 0.98 and _{1 }= 0.02 and

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 (

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 burn-in 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

Bayes Factor (BF) was used to identify associated SNP as the odds ratio between the estimated posterior and prior probabilities for a SNP:

where _{1 }= prior 1/101 related to the Beta distribution. Using guidelines from Kass and Raftery

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

Estimated posterior mean heritability of the simulated quantitative trait was 0.30 (SD = 0.02). The genome-wide association analysis resulted in 14 significant SNP and 43 putative SNP (Additional file

**Overview of associated SNP**.

Click here for file

Manhattan plot of SNP for the simulated quantitative trait

**Manhattan plot of SNP for the simulated quantitative trait**. SNP above the line are considered to be significant; SNP above the dashed line are considered to be putative.

Mean posterior probability of SNP modelled having a large effect (

Posterior probability density plot of proportion of SNP with large effect (

**Posterior probability density plot of proportion of SNP with large effect (****)**.

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 (0.85-0.94) when the data were analysed using Bayesian Variable Selection methods.

Conclusions

Bayesian Variable Selection model showed to be a successful method for genome-wide 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.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

AS analysed the data and wrote the manuscript. LLGJ developed the software (Bayz) and participated in the analyses design. HCMH conceived the project, participated in the analyses and helped to draft the manuscript.

Acknowledgements

This article has been published as part of