DERIVATION OF SINGLE-LOCUS RELATIONSHIP COEFFICIENTS CONDITIONAL ON MARKER INFORMATION

The coefficient of relationship is defined as the correlation between the additive genetic values of two individuals. This coefficient can b e defined specifically for a single quantitative trait locus (QTL) and may deviate considerably from the overall expectation if it is taken conditional on information from linked marker loci. Conditional halfsi b correlations are derived under a simple genetic model with a biallel ic QTL linked to a biallelic marker locus. The conditional relationshi p coefficients are shown to depend on the recombination rate between t he marker and the QTL and the population frequency of the marker allel es, but not on parameters of the QTL, i.e. number and frequency of QTL alleles, degree of dominance etc., nor on the (usually unknown) QTL g enotype of the sire. Extensions to less simplified cases (multiple all eles at the marker locus and the QTL, two marker loci flanking the QTL ) are given. For arbitrary pedigrees, conditional relationship coeffic ients can also be derived from the conditional gametic covariance matr ix suggested by Fernando and Grossman (1989). The connection of these two approaches is discussed. The conditional relationship coefficient can be used for marker-assisted genetic evaluation as well as for the detection of QTL and the estimation of their effects.