title: Fast and accurate detection of multiple quantitative trait Loci.
abstract: We present a new computational scheme that enables efficient and reliable quantitative trait loci (QTL) scans for experimental populations. Using a standard brute-force exhaustive search effectively prohibits accurate QTL scans involving more than two loci to be performed in practice, at least if permutation testing is used to determine significance. Some more elaborate global optimization approaches, for example, DIRECT have been adopted earlier to QTL search problems. Dramatic speedups have been reported for high-dimensional scans. However, since a heuristic termination criterion must be used in these types of algorithms, the accuracy of the optimization process cannot be guaranteed. Indeed, earlier results show that a small bias in the significance thresholds is sometimes introduced. Our new optimization scheme, PruneDIRECT, is based on an analysis leading to a computable (Lipschitz) bound on the slope of a transformed objective function. The bound is derived for both infinite- and finite-size populations. Introducing a Lipschitz bound in DIRECT leads to an algorithm related to classical Lipschitz optimization. Regions in the search space can be permanently excluded (pruned) during the optimization process. Heuristic termination criteria can thus be avoided. Hence, PruneDIRECT has a well-defined error bound and can in practice be guaranteed to be equivalent to a corresponding exhaustive search. We present simulation results that show that for simultaneous mapping of three QTLS using permutation testing, PruneDIRECT is typically more than 50 times faster than exhaustive search. The speedup is higher for stronger QTL. This could be used to quickly detect strong candidate eQTL networks.
authors.affiliation: Division of Scientific Computing, Department of Information Technology, Uppsala University, Uppsala, Sweden.
authors.forename: Carl
authors.initials: C
authors.lastname: Nettelblad
authors.forename: Behrang
authors.initials: B
authors.lastname: Mahjani
authors.forename: Sverker
authors.initials: S
authors.lastname: Holmgren
mesh_terms: D000465:Algorithms; D008957:Models, Genetic; D058885:Multilocus Sequence Typing / Q000379:methods*; D040641:Quantitative Trait Loci / Q000502:physiology*
references.citation: Genetics. 2000 Aug;155(4):2003-10
references.pmid: 10924492
references.citation: Bioinformatics. 2004 Aug 12;20(12):1887-95
references.pmid: 15044246
references.citation: Genetics. 1989 Jan;121(1):185-99
references.pmid: 2563713
references.citation: Genetics. 1994 Nov;138(3):963-71
references.pmid: 7851788
references.citation: Nat Rev Genet. 2004 Aug;5(8):618-25
references.pmid: 15266344
references.citation: Nat Rev Genet. 2002 Jan;3(1):43-52
references.pmid: 11823790
references.citation: Heredity (Edinb). 1992 Oct;69(4):315-24
references.pmid: 16718932