mdh.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Increasing the Efficiency of Variance Component Quantitative Trait Loci Analysis by Using Reduced-Rank Identity-by-Descent Matrices
Uppsala University, Sweden .
Mälardalen University, Department of Mathematics and Physics. Uppsala University, Sweden .
Uppsala University, Sweden .
Uppsala University, Sweden .
2007 (English)In: Genetics, ISSN 0016-6731, Vol. 176, no 3, p. 1935-1938Article in journal (Refereed) Published
Abstract [en]

Recent technological development in genetics has made large-scale marker genotyping fast and practicable, facilitating studies for detection of QTL in large general pedigrees. We developed a method that speeds up restricted maximum-likelihood (REML) algorithms for QTL analysis bysimplifying the inversion of the variance-covariance matrix of the trait vector. The method was tested in an experimental chicken pedigree including 767 phenotyped individuals and 14 genotyped markers on chicken chromosome 1. The computation time in a chromosome scan covering 475 cM was reduced by 43% when the analysis was based on linkage only and by 72% when linkage disequilibrium information was included. The relative advantage of using our method increases with pedigree size, marker density, and linkage disequilibrium, indicating even greater improvements in the future. 

Place, publisher, year, edition, pages
2007. Vol. 176, no 3, p. 1935-1938
National Category
Genetics
Identifiers
URN: urn:nbn:se:mdh:diva-4226DOI: 10.1534/genetics.107.071977ISI: 000248416300044Scopus ID: 2-s2.0-34547132590OAI: oai:DiVA.org:mdh-4226DiVA, id: diva2:121267
Available from: 2008-04-28 Created: 2008-04-28 Last updated: 2015-07-02Bibliographically approved
In thesis
1. Numerical Algorithms for Optimization Problems in Genetical Analysis
Open this publication in new window or tab >>Numerical Algorithms for Optimization Problems in Genetical Analysis
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The focus of this thesis is on numerical algorithms for efficient solution of QTL analysis problem in genetics.

Firstly, we consider QTL mapping problems where a standard least-squares model is used for computing the model fit. We develop optimization methods for the local problems in a hybrid global-local optimization scheme for determining the optimal set of QTL locations. Here, the local problems have constant bound constraints and may be non-convex and/or flat in one or more directions. We propose an enhanced quasi-Newton method and also implement several schemes for constrained optimization. The algorithms are adopted to the QTL optimization problems. We show that it is possible to use the new schemes to solve problems with up to 6 QTLs efficiently and accurately, and that the work is reduced with up to two orders magnitude compared to using only global optimization.

Secondly, we study numerical methods for QTL mapping where variance component estimation and a REML model is used. This results in a non-linear optimization problem for computing the model fit in each set of QTL locations. Here, we compare different optimization schemes and adopt them for the specifics of the problem. The results show that our version of the active set method is efficient and robust, which is not the case for methods used earlier. We also study the matrix operations performed inside the optimization loop, and develop more efficient algorithms for the REML computations. We develop a scheme for reducing the number of objective function evaluations, and we accelerate the computations of the derivatives of the log-likelihood by introducing an efficient scheme for computing the inverse of the variance-covariance matrix and other components of the derivatives of the log-likelihood.

Place, publisher, year, edition, pages
Västerås: Mälardalens högskola, 2008
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 59
Keywords
Quantitative Trait Loci (QTL), restricted maximum likelihood (REML), variance components, average information (AI) matrix, Local optimization, Quasi-Newton method, Active Set method, Hessian approximation, BFGS update
National Category
Computational Mathematics
Research subject
Matematik/tillämpad matematik
Identifiers
urn:nbn:se:mdh:diva-650 (URN)978-91-85485-84-0 (ISBN)
Public defence
2008-06-05, Kappa, U, Högskoleplan 1, Västerås, 13:00
Opponent
Supervisors
Available from: 2008-04-28 Created: 2008-04-28

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus
By organisation
Department of Mathematics and Physics
Genetics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 28 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf