MAPPING QUANTITATIVE TRAIT LOCI IN OUTCROSS POPULATIONS VIA RESIDUAL MAXIMUM-LIKELIHOOD .1. METHODOLOGY

A residual maximum likelihood method, implemented with a derivative-fr ee algorithm, was derived for estimating position and variance contrib ution of a single QTL together with additive polygenic and residual va riance components. The method is based on a mixed linear model includi ng random polygenic effects and random QTL effects, assumed to be norm ally distributed a priori. The method was developed for QTL mapping de signs 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 c oefficient matrix of mixed model equations, required in the derivative -free algorithm, was derived from a reduced animal model linking singl e records of final offspring to parental polygenic and QTL effects. Th e variance-covariance matrix of QTL effects and its inverse were compu ted conditional on incomplete information from multiple Linked markers . The inverse is computed efficiently for designs where each final off spring has a different dam and sires of the final generation have many genotyped progeny such that their marker linkage phase can be determi ned with a high degree of certainty. Linkage phases of ancestors of si res 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 estimatin g QTL variance to that with QTL variance set to zero.