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Numerical Algorithms for Mapping of Multiple Quantitative Trait Loci in Experimental Populations
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (ndim)
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Most traits of medical or economic importance are quantitative, i.e. they can be measured on a continuous scale. Strong biological evidence indicates that quantitative traits are governed by a complex interplay between the environment and multiple quantitative trait loci, QTL, in the genome. Nonlinear interactions make it necessary to search for several QTL simultaneously. This thesis concerns numerical methods for QTL search in experimental populations. The core computational problem of a statistical analysis of such a population is a multidimensional global optimization problem with many local optima. Simultaneous search for d QTL involves solving a d-dimensional problem, where each evaluation of the objective function involves solving one or several least squares problems with special structure. Using standard software, already a two-dimensional search is costly, and searches in higher dimensions are prohibitively slow.

Three efficient algorithms for evaluation of the most common forms of the objective function are presented. The computing time for the linear regression method is reduced by up to one order of magnitude for real data examples by using a new scheme based on updated QR factorizations. Secondly, the objective function for the interval mapping method is evaluated using an updating technique and an efficient iterative method, which results in a 50 percent reduction in computing time. Finally, a third algorithm, applicable to the imputation and weighted linear mixture model methods, is presented. It reduces the computing time by between one and two orders of magnitude.

The global search problem is also investigated. Standard software techniques for finding the global optimum of the objective function are compared with a new approach based on the DIRECT algorithm. The new method is more accurate than the previously fastest scheme and locates the optimum in 1-2 orders of magnitude less time. The method is further developed by coupling DIRECT to a local optimization algorithm for accelerated convergence, leading to additional time savings of up to eight times. A parallel grid computing implementation of exhaustive search is also presented, and is suitable e.g for verifying global optima when developing efficient optimization algorithms tailored for the QTL mapping problem.

Using the algorithms presented in this thesis, simultaneous search for at least six QTL can be performed routinely. The decrease in overall computing time is several orders of magnitude. The results imply that computations which were earlier considered impossible are no longer difficult, and that genetic researchers thus are free to focus on model selection and other central genetical issues.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2005. , p. 61
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 133
Keywords [en]
Scientific computing
National Category
Bioinformatics (Computational Biology)
Research subject
Scientific Computing
Identifiers
URN: urn:nbn:se:uu:diva-6248ISBN: 91-554-6427-0 (print)OAI: oai:DiVA.org:uu-6248DiVA, id: diva2:167517
Public defence
2006-01-13, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2005-12-22 Created: 2005-12-22 Last updated: 2018-01-13Bibliographically approved
List of papers
1. Efficient algorithms for quantitative trait loci mapping problems
Open this publication in new window or tab >>Efficient algorithms for quantitative trait loci mapping problems
2002 (English)In: Journal of Computational Biology, ISSN 1066-5277, E-ISSN 1557-8666, Vol. 9, p. 793-804Article in journal (Refereed) Published
National Category
Bioinformatics (Computational Biology)
Identifiers
urn:nbn:se:uu:diva-67952 (URN)10.1089/10665270260518272 (DOI)12614547 (PubMedID)
Available from: 2008-07-05 Created: 2008-07-05 Last updated: 2018-01-10Bibliographically approved
2. Simultaneous search for multiple QTL using the global optimization algorithm DIRECT
Open this publication in new window or tab >>Simultaneous search for multiple QTL using the global optimization algorithm DIRECT
2004 (English)In: Bioinformatics, ISSN 1367-4803, E-ISSN 1367-4811, Vol. 20, p. 1887-1895Article in journal (Refereed) Published
National Category
Bioinformatics (Computational Biology)
Identifiers
urn:nbn:se:uu:diva-67950 (URN)10.1093/bioinformatics/bth175 (DOI)15044246 (PubMedID)
Note

An efficient algorithm for solving least-squares problems with a specific structure is combined with an extended algorithm for global optimization. The scheme is applied to problems in genetics, where the solution can be computed several orders of magnitude faster than with previous methods.

Available from: 2007-02-20 Created: 2007-02-20 Last updated: 2018-01-10Bibliographically approved
3. Efficient algorithms for multidimensional global optimization in genetic mapping of complex traits
Open this publication in new window or tab >>Efficient algorithms for multidimensional global optimization in genetic mapping of complex traits
2010 (English)In: Advances and Applications in Bioinformatics and Chemistry, ISSN 1178-6949, Vol. 3, p. 75-88Article in journal (Refereed) Published
National Category
Computational Mathematics Bioinformatics (Computational Biology)
Identifiers
urn:nbn:se:uu:diva-93884 (URN)10.2147/AABC.S9240 (DOI)
Projects
eSSENCE
Available from: 2005-12-22 Created: 2005-12-22 Last updated: 2018-01-13Bibliographically approved
4. Efficient evaluation of the residual sum of squares for quantitative trait locus models in the case of complete marker genotype information
Open this publication in new window or tab >>Efficient evaluation of the residual sum of squares for quantitative trait locus models in the case of complete marker genotype information
2005 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2005-033
National Category
Computational Mathematics Bioinformatics (Computational Biology)
Identifiers
urn:nbn:se:uu:diva-76701 (URN)
Available from: 2007-02-04 Created: 2007-02-04 Last updated: 2018-01-13Bibliographically approved
5. Using parallel computing and grid systems for genetic mapping of quantitative traits
Open this publication in new window or tab >>Using parallel computing and grid systems for genetic mapping of quantitative traits
2007 (English)In: Applied Parallel Computing: State of the Art in Scientific Computing, Berlin: Springer-Verlag , 2007, p. 627-636Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Berlin: Springer-Verlag, 2007
Series
Lecture Notes in Computer Science ; 4699
National Category
Bioinformatics (Computational Biology)
Identifiers
urn:nbn:se:uu:diva-11546 (URN)10.1007/978-3-540-75755-9_76 (DOI)000250904900076 ()978-3-540-75754-2 (ISBN)
Available from: 2007-09-26 Created: 2007-09-26 Last updated: 2018-01-12Bibliographically approved

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