Kajsa Ljungberg's home-page.

QTL mapping

Most traits of medical or economical importance, such as blood pressure and cholesterol levels in humans and body weight of broiler chickens, are quantitative in nature. These traits are usually determined by the joint effect of multiple genes and the environment. Since many interacting factors are involved it is very difficult to find the underlying genes.

Quantitative Trait Locus (QTL) mapping in experimental populations is a method to find genes governing quantitative traits. A QTL is a region in the genome harboring such a gene. QTL mapping can be applied to both plants and animals. Human diseases are often studied using the mouse a model.

These are pigs from a cross between wild boars and domestic pigs, and the coat colors illustrate the mix. Studying this cross can lead to detection of QTL influencing e.g. growth in the pigs. Picture and data sets provided by Leif Andersson.

An important step in QTL mapping is analyzing genetic data from animal studies using advanced statistics. This involves solving a multidimensional global optimization problem, which solution gives the most likely positions of the important genes. Using standard optimization methods it is slow to search for as few as two QTL simultaneously. We develop computational tools that are efficient enough to allow for simultaneous search for at least six QTL.

Mathematically the project concerns a multidimensional optimization problem where the objective function is some test statistic of how well a model fits the data set. One example of an objective is the residual of a least squares (LS) problem. For one experiment the optimization needs to be performed thousands of times. There are two natural parts to this project: to speed up the evaluation of the objective function and to improve the global optimization procedure.

In K. Ljungberg, S. Holmgren and Ö. Carlborg. Efficient algorithms for quantitative trait loci mapping problems. Journal of computational biology, Vol 9, pp. 793-804, 2002.
we present fast ways of evaluating the objective using updated QR factorizations. Depending on the type of model it is possible to save up to 90% of the arithmetic operations when using updating.

In K. Ljungberg, S. Holmgren and Ö. Carlborg.
Simultaneous search for multiple QTL using the global optimization algorithm DIRECT. Bioinformatics 2004 20: 1887-1895.

we successfully use the DIRECT algorithm, Jones et al 1993, for the global optimization problem. The algorithm quickly finds the global optimum in three-dimensional QTL searches many orders of magnitude faster than an exhaustive search.

Our methods have been incorporated into the publicly available and widely used WebQTL and R/qtl packages.

The local convergence of DIRECT is slow, and therefore more efficient local algorithms are explored.

Software page.

The project is a collaboration between Kajsa Ljungberg and Sverker Holmgren at the Department of Scientific Computing, Örjan Carlborg, Kateryna Mishchenko at Mälardalen university college , Leif Andersson at the Department of animal breeding and genetics at SLU, Martina Persson from the Department of Mathematics, Mathematical Statistics Group at Uppsala University, and Razaw AL-Sarraj and Dietrich von Rosen from the Department of biometrics and informatics at SLU.