Mapping quantitative trait loci in outcross populations via residual maximum likelihood .1. Methodology

A residual maximum likelihood method, implemented with a derivative-free algorithm, was derived for estimating position and variance contribution of a single QTL together with additive polygenic and residual variance components. The method is based on a mixed linear model including random polygenic effects and random QTL effects, assumed to be normally distributed a priori. The method was developed for QTL mapping designs in livestock, where phenotypic and marker data are available on a final generation of offspring, and marker data are also available on the parents of the final offspring and on additional ancestors. The coefficient matrix of mixed model equations, required in the derivative-free algorithm, was derived from a reduced animal model linking single records of final offspring to parental polygenic and QTL effects. The variance-covariance matrix of QTL effects and its inverse were computed conditional on incomplete information from multiple Linked markers. The inverse is computed efficiently for designs where each final offspring has a different dam and sires of the final generation have many genotyped progeny such that their marker linkage phase can be determined with a high degree of certainty. Linkage phases of ancestors of sires do not need to be known. Testing for a QTL at any position in the marker linkage group is based on the ratio of the likelihood estimating QTL variance to that with QTL variance set to zero.