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Significance test and genome selection in bayesian shrinkage analysis.

Che X, Xu S - Int J Plant Genomics (2010)

Bottom Line: A nice property of the shrinkage analysis is that it can estimate effects of QTL as small as explaining 2% of the phenotypic variance in a typical sample size of 300-500 individuals.In most cases, QTL can be detected with simple visual inspection of the entire genome for the effect because the false positive rate is low.However, it is still desirable to put some confidences on the estimated QTL effects.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California, Riverside, California 92521, USA.

ABSTRACT
Bayesian shrinkage analysis is the state-of-the-art method for whole genome analysis of quantitative traits. It can estimate the genetic effects for the entire genome using a dense marker map. The technique is now called genome selection. A nice property of the shrinkage analysis is that it can estimate effects of QTL as small as explaining 2% of the phenotypic variance in a typical sample size of 300-500 individuals. In most cases, QTL can be detected with simple visual inspection of the entire genome for the effect because the false positive rate is low. As a Bayesian method, no significance test is needed. However, it is still desirable to put some confidences on the estimated QTL effects. We proposed to use the permutation test to draw empirical thresholds to declare significance of QTL under a predetermined genome wide type I error. With the permutation test, Bayesian shrinkage analysis can be routinely used for QTL detection.

No MeSH data available.


The true and estimated QTL effects for the entire genome of the simulated data. (a) The true positions and effects of the simulated QTL. (b) The estimated positions and effects of QTL using the Bayesian shrinkage method.
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fig1: The true and estimated QTL effects for the entire genome of the simulated data. (a) The true positions and effects of the simulated QTL. (b) The estimated positions and effects of QTL using the Bayesian shrinkage method.

Mentions: The design of the simulation experiment conducted by Wang et al. [8] was adopted here exepct that the population simulated was an F2 rather than a BC population. The sample size was fixed at 500, which is a typical sample size used in most QTL mapping experiments. The genome size was 2400 cM long covered by 241 evenly distributed markers (10 cM per marker interval). A total of 20 QTLs were placed on the genome and the positions and effects of the 20 QTL are presented in Table 1. The QTL size varied from 0.3% phenotypic variation to 13% phenotypic variation. The proportions of QTL explaining the total phenotypic variance were calculated based on the following method. The genotype indicator variable for individual j at locus k is defined as Xjk = {1, 0, −1} for the three genotypes (A1A1, A1A2, A2A2), respectively. Dominance effects were not simulated and also not included in the model for this simulation experiment because they do not help answer questions addressed in this study. These parameter values were used to generate a quantitative trait with a population mean b0 = 10.0 and a residual error variance σ2 = 10.0. The total genetic variance for the trait is (7)VG=∑k=120 ∑k′=120bkbk′cov (zk,zk′)=12∑k=120 ∑k′=120bkbk′(1−2rkk′), where rkk′ is the recombination frequency between QTL k and k′, cov (zk, zk′) = var(z)(1 − 2rkk′) is the covariance between Zk and Zk′, and var(z) = 1/2 is the variance of Z (assuming no segregation distortion). The total genetic variance for the quantitative trait is VG = VQ + VL = 66.384, which is the sum of the genetic variances due to QTL (VQ) and covariance between linked QTL (VL), where (8)VQ=12∑k=120bk2=46.7804,VL=∑k′>k20bkbk′(1−2rkk′)=19.6034. The residual error variance for the trait is σ2 = VE = 10.0. Therefore, the total phenotypic variance is VP = VG + VE = 76.384. The proportion of the genetic variance contributed by each QTL is 0.5bk2/VG for the kth QTL (given in the column headed with Prop-G in Table 1). The corresponding proportion of the phenotypic variance contributed by the kth QTL is 0.5bk2/VP and given in the column headed with Prop-P in Table 1. The true QTL effects are depicted in Figure 1.


Significance test and genome selection in bayesian shrinkage analysis.

Che X, Xu S - Int J Plant Genomics (2010)

The true and estimated QTL effects for the entire genome of the simulated data. (a) The true positions and effects of the simulated QTL. (b) The estimated positions and effects of QTL using the Bayesian shrinkage method.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2902048&req=5

fig1: The true and estimated QTL effects for the entire genome of the simulated data. (a) The true positions and effects of the simulated QTL. (b) The estimated positions and effects of QTL using the Bayesian shrinkage method.
Mentions: The design of the simulation experiment conducted by Wang et al. [8] was adopted here exepct that the population simulated was an F2 rather than a BC population. The sample size was fixed at 500, which is a typical sample size used in most QTL mapping experiments. The genome size was 2400 cM long covered by 241 evenly distributed markers (10 cM per marker interval). A total of 20 QTLs were placed on the genome and the positions and effects of the 20 QTL are presented in Table 1. The QTL size varied from 0.3% phenotypic variation to 13% phenotypic variation. The proportions of QTL explaining the total phenotypic variance were calculated based on the following method. The genotype indicator variable for individual j at locus k is defined as Xjk = {1, 0, −1} for the three genotypes (A1A1, A1A2, A2A2), respectively. Dominance effects were not simulated and also not included in the model for this simulation experiment because they do not help answer questions addressed in this study. These parameter values were used to generate a quantitative trait with a population mean b0 = 10.0 and a residual error variance σ2 = 10.0. The total genetic variance for the trait is (7)VG=∑k=120 ∑k′=120bkbk′cov (zk,zk′)=12∑k=120 ∑k′=120bkbk′(1−2rkk′), where rkk′ is the recombination frequency between QTL k and k′, cov (zk, zk′) = var(z)(1 − 2rkk′) is the covariance between Zk and Zk′, and var(z) = 1/2 is the variance of Z (assuming no segregation distortion). The total genetic variance for the quantitative trait is VG = VQ + VL = 66.384, which is the sum of the genetic variances due to QTL (VQ) and covariance between linked QTL (VL), where (8)VQ=12∑k=120bk2=46.7804,VL=∑k′>k20bkbk′(1−2rkk′)=19.6034. The residual error variance for the trait is σ2 = VE = 10.0. Therefore, the total phenotypic variance is VP = VG + VE = 76.384. The proportion of the genetic variance contributed by each QTL is 0.5bk2/VG for the kth QTL (given in the column headed with Prop-G in Table 1). The corresponding proportion of the phenotypic variance contributed by the kth QTL is 0.5bk2/VP and given in the column headed with Prop-P in Table 1. The true QTL effects are depicted in Figure 1.

Bottom Line: A nice property of the shrinkage analysis is that it can estimate effects of QTL as small as explaining 2% of the phenotypic variance in a typical sample size of 300-500 individuals.In most cases, QTL can be detected with simple visual inspection of the entire genome for the effect because the false positive rate is low.However, it is still desirable to put some confidences on the estimated QTL effects.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California, Riverside, California 92521, USA.

ABSTRACT
Bayesian shrinkage analysis is the state-of-the-art method for whole genome analysis of quantitative traits. It can estimate the genetic effects for the entire genome using a dense marker map. The technique is now called genome selection. A nice property of the shrinkage analysis is that it can estimate effects of QTL as small as explaining 2% of the phenotypic variance in a typical sample size of 300-500 individuals. In most cases, QTL can be detected with simple visual inspection of the entire genome for the effect because the false positive rate is low. As a Bayesian method, no significance test is needed. However, it is still desirable to put some confidences on the estimated QTL effects. We proposed to use the permutation test to draw empirical thresholds to declare significance of QTL under a predetermined genome wide type I error. With the permutation test, Bayesian shrinkage analysis can be routinely used for QTL detection.

No MeSH data available.