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1.  MAPfastR: Quantitative Trait Loci Mapping in Outbred Line Crosses 
G3: Genes|Genomes|Genetics  2013;3(12):2147-2149.
MAPfastR is a software package developed to analyze quantitative trait loci data from inbred and outbred line-crosses. The package includes a number of modules for fast and accurate quantitative trait loci analyses. It has been developed in the R language for fast and comprehensive analyses of large datasets. MAPfastR is freely available at: http://www.computationalgenetics.se/?page_id=7
doi:10.1534/g3.113.008623
PMCID: PMC3852377  PMID: 24122053
QTL mapping; inbred line cross; outbred line cross; quantitative genetics
2.  Fast and Accurate Detection of Multiple Quantitative Trait Loci 
Journal of Computational Biology  2013;20(9):687-702.
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.
doi:10.1089/cmb.2012.0242
PMCID: PMC3761440  PMID: 23919387
algorithms; branch-and-bound; genetic mapping; genomics; statistical models; statistics
3.  Efficient algorithms for multidimensional global optimization in genetic mapping of complex traits 
We present a two-phase strategy for optimizing a multidimensional, nonconvex function arising during genetic mapping of quantitative traits. Such traits are believed to be affected by multiple so called quantitative trait loci (QTL), and searching for d QTL results in a d-dimensional optimization problem with a large number of local optima. We combine the global algorithm DIRECT with a number of local optimization methods that accelerate the final convergence, and adapt the algorithms to problem-specific features. We also improve the evaluation of the QTL mapping objective function to enable exploitation of the smoothness properties of the optimization landscape. Our best two-phase method is demonstrated to be accurate in at least six dimensions and up to ten times faster than currently used QTL mapping algorithms.
doi:10.2147/AABC.S9240
PMCID: PMC3170002  PMID: 21918629
global optimization; QTL mapping; DIRECT

Results 1-3 (3)