@TechReport{ it:2003-043,
author = {Kajsa Ljungberg and Sverker Holmgren and {\"O}rjan
Carlborg},
title = {Simultaneous Search for Multiple {QTL} Using the Global
Optimization Algorithm {DIRECT}},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2003},
number = {2003-043},
month = aug,
abstract = {\textbf{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.
\textbf{Results:} We have adapted DIRECT, an algorithm
presented in \cite{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.
\textbf{Availability:} The source code of the prototype
implementation is available at
\url{http://www.tdb.uu.se/~kl/qtl_software.html}.
\textbf{Contact:} kl@tdb.uu.se}
}