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QTL Mapping Using a Memetic Algorithm with Modifications of BIC as Fitness Function

Author

Listed:
  • Frommlet Florian

    (Medical University Vienna)

  • Ljubic Ivana

    (University Vienna)

  • Arnardóttir Helga Björk
  • Bogdan Malgorzata

    (Wroclaw University of Technology)

Abstract

The problem of locating quantitative trait loci (QTL) for experimental populations can be approached by multiple regression analysis. In this context variable selection using a modification of the Bayesian Information Criterion (mBIC) has been well established in the past. In this article a memetic algorithm (MA) is introduced to find the model which minimizes the selection criterion. Apart from mBIC also a second modification (mBIC2) is considered, which has the property of controlling the false discovery rate. Given the Bayesian nature of our selection criteria, we are not only interested in finding the best model, but also in computing marker posterior probabilities using all models visited by MA. In a simulation study MA (with mBIC and mBIC2) is compared with a parallel genetic algorithm (PGA) which has been previously suggested for QTL mapping. It turns out that MA in combination with mBIC2 performs best, where determining QTL positions based on marker posterior probabilities yields even better results than using the best model selected by MA. Finally we consider a real data set from the literature and show that MA can also be extended to multiple interval mapping, which potentially increases the precision with which the exact location of QTLs can be estimated.

Suggested Citation

  • Frommlet Florian & Ljubic Ivana & Arnardóttir Helga Björk & Bogdan Malgorzata, 2012. "QTL Mapping Using a Memetic Algorithm with Modifications of BIC as Fitness Function," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-26, May.
    • Handle: RePEc:bpj:sagmbi:v:11:y:2012:i:4:n:2
    DOI: 10.1515/1544-6115.1793
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Frommlet, Florian & Ruhaltinger, Felix & Twaróg, Piotr & Bogdan, Małgorzata, 2012. "Modified versions of Bayesian Information Criterion for genome-wide association studies," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1038-1051.
    3. Karl W. Broman & Terence P. Speed, 2002. "A model selection approach for the identification of quantitative trait loci in experimental crosses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 641-656, October.
    4. Baierl, Andreas & Futschik, Andreas & Bogdan, Malgorzata & Biecek, Przemyslaw, 2007. "Locating multiple interacting quantitative trait loci using robust model selection," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6423-6434, August.
    5. Chang Myron N & Wu Rongling & Wu Samuel S & Casella George, 2009. "Score Statistics for Mapping Quantitative Trait Loci," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-37, February.
    6. Zak-Szatkowska, Malgorzata & Bogdan, Malgorzata, 2011. "Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2908-2924, November.
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