Kidd et al. (1980) studied the allelic origins of a recessive trait in an extensive and complex genealogy. Due to computational limitations, the hypotheses they could consider were limited, and the dependencies in descent from alternative ancestors and to different sibships were not considered. Karigl (1981) developed a recursive algorithm for the computation of multiple kinship coefficients. Here we show that very similar algorithms apply to probabilities of the joint descent of multiple genes from specified ancestral genes. This makes possible a far more extensive analysis of hypotheses of allelic origins in a genealogy.