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The genetic control of a complex trait can be studied by testing and mapping the genotypes of the underlying quantitative trait loci (QTLs) through their associations with observable marker genotypes. All existing statistical methods for QTL mapping assume an equilibrium population, allowing marker-QTL associations to be simply described at the gametic level. However, many mapping populations in practice may deviate from equilibrium; thus, gametic associations cannot reflect marker-QTL associations at the genotype level. We develop a robust model for mapping QTLs in a non-equilibrium natural population in which individuals are not necessarily randomly mating due to various evolutionary forces. Without use of Hardy-Weinberg equilibrium, the new model founds marker-QTL associations directly on the genotypes, specified by a group of disequilibrium parameters. Simulation studies were performed to test the statistical properties of the model, which suggests that the new model covers current mapping models and can be safely used for any data set.

Mapping Quantitative Trait Loci in a Non-Equilibrium Population