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Bayesian shrinkage mapping of quantitative trait loci in variance component models.

Fang M - BMC Genet. (2010)

Bottom Line: The new method can estimate the variance of zero-effect QTL infinitely to zero, but nearly unbiased for non-zero-effect QTL.The results showed that the proposed method was efficient in mapping multiple QTL simultaneously, and moreover it was more competitive than the reversible jump MCMC (RJMCMC) method and may even out-perform it.The newly developed Bayesian shrinkage method is very efficient and powerful for mapping multiple QTL in outbred populations.

View Article: PubMed Central - HTML - PubMed

Affiliation: Life Science College, Heilongjiang August First Land Reclamation University, Daqing, China. fangming618@126.com

ABSTRACT

Background: In this article, I propose a model-selection-free method to map multiple quantitative trait loci (QTL) in variance component model, which is useful in outbred populations. The new method can estimate the variance of zero-effect QTL infinitely to zero, but nearly unbiased for non-zero-effect QTL. It is analogous to Xu's Bayesian shrinkage estimation method, but his method is based on allelic substitution model, while the new method is based on the variance component models.

Results: Extensive simulation experiments were conducted to investigate the performance of the proposed method. The results showed that the proposed method was efficient in mapping multiple QTL simultaneously, and moreover it was more competitive than the reversible jump MCMC (RJMCMC) method and may even out-perform it.

Conclusions: The newly developed Bayesian shrinkage method is very efficient and powerful for mapping multiple QTL in outbred populations.

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Typical profiles of QTL intensity (a) and weighted QTL variance (b) from the proposed method.
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Figure 3: Typical profiles of QTL intensity (a) and weighted QTL variance (b) from the proposed method.

Mentions: I use a special RWM-H algorithm to update the variance components, and the new proposal variance σ2 (QTL variance, polygenic variance or residual variance) is sampled from the scaled inverted chi-squared distribution with degree of freedom ν and scaled parameter the variance of the current round. In order to test the influence of ν, I set ν as 3, 15, 30, 50, 100, 150 and 200, respectively. The QTL intensity histogram [28] is plotted in Figure 3a. There are three peaks bumped on the chromosome, but QTL intensity is not used in QTL detection. I also plot the profile of weighted QTL variance, and the general pattern is given in Figure 3b. All other experiments have performed similar pattern, so the figures are not shown. I find the profile of weighted QTL variance is rather flat for the positions that have no QTL, which makes the signals of QTL clearer than QTL intensity. The parameter estimates are listed in Table 1, and there are no clear differences in parameter and standard deviation estimates for different ν. Furthermore, I summarized the acceptance rate of the M-H sampler for the variance components. Because it is cumbersome to show them separately, I averaged the acceptance rate over all variance components under different setting of ν. I further plot the profile of the change of the acceptance rate against ν in Figure 4. It shows that the acceptance rate increases by ν, but the rate of change decease by ν. When ν is smaller than 30, the curve is much steeper, but it flatten when ν is larger than 30. The degree of freedom ν may influence the acceptance rate in the special RWM-H algorithm, and hence it is equivalent to the tuning parameter in the traditional Metropolis-Hastings algorithm. Finally, I found that when ν is larger than 200, the shrinkage character is hardly held. The reasons will be addressed in Discussion.


Bayesian shrinkage mapping of quantitative trait loci in variance component models.

Fang M - BMC Genet. (2010)

Typical profiles of QTL intensity (a) and weighted QTL variance (b) from the proposed method.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2874758&req=5

Figure 3: Typical profiles of QTL intensity (a) and weighted QTL variance (b) from the proposed method.
Mentions: I use a special RWM-H algorithm to update the variance components, and the new proposal variance σ2 (QTL variance, polygenic variance or residual variance) is sampled from the scaled inverted chi-squared distribution with degree of freedom ν and scaled parameter the variance of the current round. In order to test the influence of ν, I set ν as 3, 15, 30, 50, 100, 150 and 200, respectively. The QTL intensity histogram [28] is plotted in Figure 3a. There are three peaks bumped on the chromosome, but QTL intensity is not used in QTL detection. I also plot the profile of weighted QTL variance, and the general pattern is given in Figure 3b. All other experiments have performed similar pattern, so the figures are not shown. I find the profile of weighted QTL variance is rather flat for the positions that have no QTL, which makes the signals of QTL clearer than QTL intensity. The parameter estimates are listed in Table 1, and there are no clear differences in parameter and standard deviation estimates for different ν. Furthermore, I summarized the acceptance rate of the M-H sampler for the variance components. Because it is cumbersome to show them separately, I averaged the acceptance rate over all variance components under different setting of ν. I further plot the profile of the change of the acceptance rate against ν in Figure 4. It shows that the acceptance rate increases by ν, but the rate of change decease by ν. When ν is smaller than 30, the curve is much steeper, but it flatten when ν is larger than 30. The degree of freedom ν may influence the acceptance rate in the special RWM-H algorithm, and hence it is equivalent to the tuning parameter in the traditional Metropolis-Hastings algorithm. Finally, I found that when ν is larger than 200, the shrinkage character is hardly held. The reasons will be addressed in Discussion.

Bottom Line: The new method can estimate the variance of zero-effect QTL infinitely to zero, but nearly unbiased for non-zero-effect QTL.The results showed that the proposed method was efficient in mapping multiple QTL simultaneously, and moreover it was more competitive than the reversible jump MCMC (RJMCMC) method and may even out-perform it.The newly developed Bayesian shrinkage method is very efficient and powerful for mapping multiple QTL in outbred populations.

View Article: PubMed Central - HTML - PubMed

Affiliation: Life Science College, Heilongjiang August First Land Reclamation University, Daqing, China. fangming618@126.com

ABSTRACT

Background: In this article, I propose a model-selection-free method to map multiple quantitative trait loci (QTL) in variance component model, which is useful in outbred populations. The new method can estimate the variance of zero-effect QTL infinitely to zero, but nearly unbiased for non-zero-effect QTL. It is analogous to Xu's Bayesian shrinkage estimation method, but his method is based on allelic substitution model, while the new method is based on the variance component models.

Results: Extensive simulation experiments were conducted to investigate the performance of the proposed method. The results showed that the proposed method was efficient in mapping multiple QTL simultaneously, and moreover it was more competitive than the reversible jump MCMC (RJMCMC) method and may even out-perform it.

Conclusions: The newly developed Bayesian shrinkage method is very efficient and powerful for mapping multiple QTL in outbred populations.

Show MeSH