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Recent technological advances in genetics pose new§challenging problems to statistical methodology. The§genetic technique of QTL mapping deals with locating§genes that influence a quantitative character of an§organism. Within the statistical framework of model§selection, existing approaches are adapted and§modifed: The search for genetic effects is extended§to interactions between genes (i.e. epistatsis),§while taking computational performance into account.§Robust statistical methods are included in order to§cope with quantitative effects that have heavy-tailed§distribution or outliers. The performance and§applicability of all methods is assessed by extensive§simulation studies and the reanalysis of previously§published genetic data sets.