666 haplotypes

Genotype Combinations in Family Pedigrees

Genotype Combinations for Unsampled Individuals:

1. • If some members of the parental generation are not sampled, the number of possible genotype combinations can be much larger.
   • This depends on the number of alleles (k) at each locus. For example, if k=5 among the sampled individuals, we need to account for a potential sixth allele present among the unsampled individuals.
   • Consider a two-locus haplotype (combination of alleles at two different loci). With 5 alleles at each locus, there are 6×6=36 potential two-locus haplotypes.
   • Each unsampled individual can have 36×37/2=666 potential different genotypes.

2. Total Parental Genotype Combinations:

   • In a family where only full siblings are sampled, we consider 666×667/2=222,111 distinct parental genotype combinations.
   • Each of these combinations must be tested against the offspring’s genotypes.

3. Simplifying the Problem:

   • To manage complexity, prior examination of single-locus incompatibilities between parental and offspring genotypes can eliminate many parental genotypes.
   • Algorithms can help identify compatible parental genotypes based on observed offspring genotypes.

4. Polymorphism Levels:

   • The complexity increases exponentially with the number of alleles (approximately the eighth power of k).
   • Researchers often restrict themselves to moderately low levels of polymorphism (k≤5) to handle the computational load.

Remember that this explanation simplifies the topic, but it captures the essential aspects of genotype combinations in family pedigrees. If you have any further questions or need clarification, feel free to ask

 The number of genotype combinations for each family is the product of the number of possible genotypes for each member of the family. If all independent individuals of the pedigree (the parents) are present in the sample, the total number of genotype combinations will be rather small and will depend mainly on the number of double heterozygotes in the sample. However, if some members of the parental generation are not sampled, then the number of possible genotype combinations may be very large, and this number will depend on the number of alleles (k) at each locus. For instance, consider the case in which k=5 among the sampled individuals. For each locus, we have to allow for the presence of a sixth allele that may be present among the unsampled individuals of the pedigree but that would have escaped detection because it would not have segregated, by chance, in one of the offspring. In this case, there are 6×6=36 potential two-locus haplotypes and 36×37/2=666 potential different genotypes for each unsampled individual. Therefore, in a family in which only full sibs are sampled, 666×667/2=222,111 distinct parental genotype 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 low levels of polymorphism at each locus, with k≤5.