Motivation: Epistatic interactions are important for quantitative traits. To maximize the power to detect epistatic quantitative trait loci (QTLs), a simultaneous search is necessary. The computational complexity demands that the traditional exhaustive search be replaced by a more efficient global optimization algorithm.
Results: We have adapted DIRECT, an algorithm presented in [Jones93], to the problem of simultaneous mapping of two and three QTL. We have compared DIRECT, in terms of accuracy and speed analyzing real data sets, with standard exhaustive search and a genetic algorithm previously used for QTL mapping in two dimensions. In all two- and three-QTL test cases, DIRECT accurately finds the global optimum two to four orders of magnitude faster than when using an exhaustive search, and one order of magnitude faster than when using the genetic algorithm. A search using a model with three fully interacting QTL is finished in six CPU minutes when using DIRECT, while an exhaustive search takes 142 CPU days. Thus three-QTL randomization testing for determining empirical significance thresholds is made feasible by the use of DIRECT. This opens the possibility to thoroughly investigate the power of simultaneous search to detect at least three interacting QTL.
Availability: The source code of the prototype implementation is available at http://www.tdb.uu.se/~kl/qtl_software.html.
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