# Genome wide association analysis of the QTL MAS 2012 data investigating pleiotropy

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## Abstract

### Background

Different genome wide association methods (GWAS) including multivariate analysis techniques were applied to identify quantitative trait loci (QTL) and pleiotropy in the simulated data set provided by the QTL-MAS workshop 2012 held in Alghero (Italy).

### Methods

Genetic correlations and heritabilities for all three quantitative traits were obtained by a multivariate animal model. In a second step the data were corrected for a polygenic component containing the genomic-based kinship matrix. Residuals from this model were later used for QTL detection in a regression analysis, to achieve genome-wide rapid association (GRAMMAR). In order to take pleiotropic effects into account, all three traits were condensed via principle component techniques to two principal components (PC) which reflect the phenotypic variance covariance structure of all traits. The PCs were analyzed by single trait analysis by GRAMMAR. As an alternative to GRAMMAR, the data set was analyzed by Bayesian methods implemented in the package snptest. The program allows the analysis of the data in a univariate and a multivariate way, where all three traits are investigated simultaneously.

### Results

According to the polygenic model, analyses the three traits revealed high heritability (0.56, 0.55, and 0.66). Traits 1 and 2 were highly correlated (r_{g} = 0.84). All applied GWAS revealed 10 QTL on four different chromosomes. No QTL was detected on chromosome 5. The Bayesian multivariate analysis revealed significant pleiotropic SNPs.

### Conclusions

Principal component and multivariate analyses seem to be promising in order to characterize the genetic basis of trait relationships.

## Keywords

Quantitative Trait Locus Genetic Correlation Genomic Selection Quantitative Trait Locus Region Polygenic Model## Background

Recently, the high-density single nucleotide polymorphism (SNP) arrays have been developed for almost all domestic animals. These tools offer the prerequisite of genome-wide association studies (GWAS), a powerful approach for high-resolution mapping of loci controlling phenotypic traits [1]. In agriculture many economically important traits share a common genetic background leading to positive or negative correlations [2, 3]. Considering correlation effects (pleiotropy) in genomic selection allow to increase the mapping accuracy and to develop strategies to control unfavourable effects on a correlated trait.

The aim of this study was to apply different genome wide association methods to identify quantitative trait loci (QTL) in the simulated data set provided by the QTL-MAS workshop 2012 Alghero (Italy) and to investigate pleiotropic effects among the three simulated quantitative traits.

## Methods

In a first step genetic correlations and heritabilities for all three quantitative traits were obtained by a multivariate animal model analyzed by VCE6 [4]. In order to condensate the 3 traits, principal component techniques were applied based on the phenotypic correlation matrix. Resulting principal components (PCs) were used as additional phenotypes for GWAS.

A quality control was performed for 10000 SNPs equally spaced on five chromosomes using a minor allele frequency < 0.01 and a significant deviation from Hardy Weinberg equilibrium (p < 0.01). Markers, which deviated from these criteria, were removed from the data set, so that 9596 were used for the GWAS.

where **y**_{ i } is the phenotype (trait or principal component) of the *i*^{th} individual, **a**_{ i } are the random additive polygenic effects with $a~N\left(0,\text{G}{\sigma}_{a}^{2}\right)$

**e**

_{ i }are the random residual effects. The kinship coefficients

**G**from genomic data were estimated using the formula [6]:

where *g*_{ ik } is the genotype of the *i*^{ th } person at the *k*^{ th } SNP, *p*_{ k } is the frequency of the major allele and *n* is the number of SNPs used for kinship estimation.

where **y**^{ * } represents residuals from model (3) of *i*^{ th } individuals (), *µ*^{ * } the intercept, *k* is the regression on the genotype (**g**_{ i }), where **g** contains a dose effect of a target allele for each SNP and *e*^{ * } is the random residual [7]. A Χ^{2} test-statistic is used to determine whether a SNP is significantly associated with the trait.

In addition permutation resampling techniques, as implemented in GenABEL [8], were used to correct for multiple testing. Genome wide significance (P-value < 0.05) was derived by applying 1000 permutations.

with $\left({\text{y}}_{\text{i}1}^{*},...,{\text{y}}_{\text{iq}}^{*}\right)$

*i*

^{th}individual. The residuals of the three traits (

*q*) were scaled to a mean of zero and a unit variance.

**C**

_{ i }is the coded version of the genotype of the

*i*

^{th}individual. For this model a conjugated prior was used that based on an inverse Wishart prior IW(c,

**Q**) on the error covariance matrix

**∑**and a matrix normal (

**N**) prior on the vector of parameters:

where **M** is a mean vector and V is a constant. Further information of the matrix nomal distribution can be found in Dawid [10]. For the priors the default values (IW(6,4Iqxq), **M** = 0, V = 0.02) were used as recommended by the authors Marchini and Howie [9].

_{1}) and a null model (M

_{0}) of no association:

## Results and discussion

### Polygenic investigation

_{g}= 0.84) (Table 1). A strong genetic correlation among trait 1 and trait 2, a negative correlation between trait 1 and trait 3 and a low positive correlation between trait 2 and trait 3 were observed. In order to investigate pleiotropy, all three traits were rearranged via principal component techniques to 3 independent principal components (PC). The variances explained by each PC were 62.1%, 37.5% and 0.4%, respectively (Table 2). PC 3 was excluded for further analyses, because of the low variance explained. PC1 was significantly correlated with trait 1 and trait 2 whereas PC2 was mainly influenced by the relationship between trait 2 and trait 3 (Table 2).

Heritability, phenotypic and genetic correlations between the three traits calculated with an animal model.

h | Trait 1 | Trait 2 | Trait 3 |
---|---|---|---|

| 0.56 (±0.04) | 0.84 (±0.02) | -0.43 (±0.06) |

| 0.82 | 0.55 (±0.04) | 0.11 (±0.07) |

| -0.44 | 0.14 | 0.66 (±0.03) |

Canonical correlation coefficients and proportions of the variance explained by each principal component (PC).

Trait 1 | Trait 2 | Trait 3 | % of variance | |
---|---|---|---|---|

| 0.99 | 0.86 | -0.36 | 62.1 |

| -0.09 | 0.50 | 0.93 | 37.5 |

| 0.07 | -0.07 | 0.04 | 0.4 |

### Single trait analysis using GRAMMAR

Identified significant SNP using GRAMMAR approach.

trait | chr. | position | effect | se | Χ |
---|---|---|---|---|---|

Trait 1 | 1 | 84.05 | 14.81 | 3.45 | 18.39*** |

1 | 84.10 | -13.97 | 3.48 | 16.09*** | |

4 | 24.85 | -14.74 | 3.84 | 14.70*** | |

4 | 24.90 | 23.06 | 3.47 | 44.23*** | |

4 | 25.00 | 12.64 | 3.40 | 13.83** | |

4 | 25.25 | 13.58 | 3.97 | 11.69* | |

Trait 2 | 1 | 14.60 | -0.96 | 0.19 | 26.20*** |

1 | 14.70 | 0.62 | 0.18 | 11.80* | |

1 | 14.75 | 0.65 | 0.18 | 12.61* | |

1 | 14.85 | 0.87 | 0.22 | 16.28*** | |

3 | 2.15 | -1.04 | 0.27 | 14.39** | |

4 | 24.85 | -0.83 | 0.21 | 16.37*** | |

4 | 24.90 | 1.40 | 0.19 | 57.50*** | |

4 | 25.00 | 0.77 | 0.18 | 17.93*** | |

4 | 25.25 | 0.73 | 0.21 | 11.83* | |

Trait 3 | 1 | 58.00 | -0.0021 | 0.0006 | 13.17*** |

1 | 58.25 | -0.0018 | 0.0005 | 10.96* | |

1 | 58.85 | 0.0013 | 0.0004 | 10.61* | |

1 | 84.05 | -0.0025 | 0.0004 | 39.27*** | |

1 | 84.10 | 0.0024 | 0.0004 | 37.30*** | |

1 | 84.80 | 0.0017 | 0.0005 | 10.93* | |

1 | 84.90 | -0.0019 | 0.0004 | 23.59*** | |

2 | 79.15 | -0.0015 | 0.0004 | 14.41*** | |

2 | 79.20 | -0.0023 | 0.0004 | 29.32*** | |

3 | 2.15 | -0.0022 | 0.0006 | 14.26*** | |

3 | 36.85 | -0.0014 | 0.0004 | 12.50** | |

PC 1 | 1 | 14.60 | -0.07 | 0.02 | 12.98* |

1 | 84.05 | 0.07 | 0.02 | 14.30** | |

1 | 84.10 | -0.07 | 0.02 | 12.23* | |

4 | 24.85 | -0.09 | 0.02 | 16.08*** | |

4 | 24.90 | 0.14 | 0.02 | 49.33*** | |

4 | 25.00 | 0.07 | 0.02 | 15.27** | |

4 | 25.25 | 0.08 | 0.02 | 12.42* | |

PC 2 | 1 | 14.60 | -0.07 | 0.02 | 15.50*** |

1 | 14.70 | 0.05 | 0.02 | 10.35* | |

1 | 84.05 | -0.09 | 0.02 | 30.50*** | |

1 | 84.10 | 0.09 | 0.02 | 29.76*** | |

1 | 84.90 | -0.07 | 0.02 | 19.80*** | |

2 | 79.15 | -0.07 | 0.02 | 16.33*** | |

2 | 79.20 | -0.09 | 0.02 | 26.57*** | |

3 | 2.15 | -0.11 | 0.02 | 21.32*** | |

3 | 2.30 | -0.08 | 0.02 | 10.40* | |

3 | 36.85 | -0.06 | 0.02 | 10.57* |

### Multivariate analysis

Additionally, the two identified principal components (PC1, PC2) were treated as independent phenotypes analyzed with GRAMMAR and allowed to investigate pleiotropy between the traits. For PC1 three and for PC2 seven QTL regions were identified (Table 3). Principal components are uncorrelated and reflect the phenotypic variance covariance structure of traits. This might be helpful for genomic selection when negatively correlated traits are processed. Furthermore, several authors described that the analysis of PCs were generally more powerful and accurate than the single trait analysis [13, 14]. Although a higher statistical power can be achieved by this approach, a clear biological interpretation is hardly possible. Moreover, only pleiotropic QTL creating correlations between traits in the direction of phenotypic and/or genetic correlations can be detected with this approach [13, 15].

Identified significant SNP using a multivariate Bayesian analysis method.

Chr. | Position | Bayes factor |
---|---|---|

1 | 14.60 | 4.3952 |

84.05 | 8.0932 | |

84.10 | 7.6726 | |

84.90 | 3.9167 | |

2 | 79.15 | 3.8483 |

79.20 | 7.2374 | |

3 | 2.15 | 4.5439 |

4 | 24.90 | 10.283 |

Genetic correlations with and without fitting identified SNPs with the different association analyses as fixed effects.

trait 1/trait 2 | trait 1/trait 3 | trait 2/trait 3 | |
---|---|---|---|

| 0.79 | -0.36 | 0.08 |

| 0.81 | -0.46 | 0.13 |

| 0.86 | -0.45 | 0.03 |

| 0.81 | -0.46 | 0.08 |

## Conclusions

The investigation of the QTL-MAS 2012 data set using different multivariate approaches allowed identifying most of the simulated QTL with large effects. Smaller effects might not be detected due to the chosen threshold correction. The analysis of the PCs and multivariate approaches seem to be promising in order to detect QTLs mainly involved in pleiotropic effects.

## Notes

### Acknowledgements

We thank the anonymous reviewer for the careful reading of our manuscript and the valuable comments. Sarah Bergfelder was supported by the European Union and Ministry for Economic Affairs, Energy and Industry of the Federal State of North Rhine-Westphalia (Grant no. 005-NA02-018C, project pigGS).

**Declarations**

The publication was funded by the University of Bonn, Institute of Animal Science, Germany.

This article has been published as part of *BMC Proceedings* Volume 8 Supplement 5, 2014: Proceedings of the 16th European Workshop on QTL Mapping and Marker Assisted Selection (QTL-MAS). The full contents of the supplement are available online at http://www.biomedcentral.com/bmcproc/supplements/8/S5

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