Background: In the case of an autosomal locus, four transmission events from the parents to progeny are possible, specified by the grand parental origin of the alleles inherited by this individual. Computing the probabilities of these transmission events is essential to perform QTL detection methods.
Results: A fast algorithm for the estimation of these probabilities conditional to parental phases has been developed. It is adapted to classical QTL detection designs applied to outbred populations, in particular to designs composed of half and/or full sib families. It assumes the absence of interference.
Conclusion: The theory is fully developed and an example is given.