666 haplotypes

 because it would not have segregated, by chance, in one of the offspring. In this case, there are po- 6 # 6  36 tential two-locus haplotypes and po- 36 # 37/2  666 tential different genotypes for each unsampled individual. Therefore, in a family in which only full sibs are sampled, distinct parental ge- 666 # 667/2  222, 111 notype combinations are possible, and the compatibility of all of them must be tested against the offspring’s genotypes. In practice, a great many parental genotypes may be eliminated by a prior examination of single-locus incompatibilities between parental and offspring genotypes (e.g., for a description of a simple algorithm, see Lange and Boehnke 1983). Thus, since the complexity of the problem increases with approximately the eighth power of k, we have restricted ourselves to moderately