Licentiate thesis 2003-014

Numerical Methods for Mapping of Multiple QTL

Kajsa Ljungberg

November 2003

This thesis concerns numerical methods for mapping of multiple quantitative trait loci, QTL. Interactions between multiple genetic loci influencing important traits, such as growth rate in farm animals and predisposition to cancer in humans, make it necessary to search for several QTL simultaneously. Simultaneous search for n QTL involves solving an n-dimensional global optimization problem, where each evaluation of the objective function consists of solving a generalized least squares problem. In Paper A we present efficient algorithms, mainly based on updated QR factorizations, for evaluating the objective functions of different parametric QTL mapping methods. One of these algorithms reduces the computational work required for an important function class by one order of magnitude compared with the best of the methods used by other authors. In Paper B previously utilized techniques for finding the global optimum of the objective function are compared with a new approach based on the DIRECT algorithm of Jones et al. The new method gives accurate results in one order of magnitude less time than the best of the formerly employed algorithms. Using the algorithms presented in Papers A and B, simultaneous search for at least three QTL, including computation of the relevant empirical significance thresholds, can be performed routinely.

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