Identity by descent

DNA at the same locus on two homologous chromosomes is said to be identical by descent (IBD) if it originated from the same ancestral chromosome. If two homologous chromosomes from different people are IBD at some locus, the people are related. If two homologous chromosomes from the same person are IBD at some locus, this person is inbred, i.e. has related parents. Two people, neither of whom is inbred, can share DNA IBD at a particular locus on either 0, 1, or 2 chromosomes.

Inheritance patterns in pedigrees are summarized by inheritance vectors. Consider a sib-pair and suppose we wish to identify the parental origin of the DNA inherited by each sib at a particular locus, say. Label the paternal chromosomes containing the locus of interest by (1,2), and similarly label the maternal chromosomes by (3,4). The inheritance vector of the sib-pair at the locus is the vector

Note that the labels 1, 2, 3 and 4 for the parental chromosomes are only meaningful within a sibship and may correspond to different DNA sequences in different sibships. Hence, these ``alleles'' are neither transportable across families nor functional. In practice, the inheritance vector of a sibship is determined by finding enough polymorphism in the parents to be able to identify the chromosomal fragments transmitted to individuals in the sibship. When IBD information is incomplete, partial information extracted from marker data may be summarized by the inheritance distribution, a conditional probability distribution over the possible inheritance vectors at the marker locus (Kruglyak and Lander [18], Kruglyak et al. [17]).

For sib-pairs, there are 16 inheritance vectors, however these are usually grouped into three distinct IBD configurations corresponding to the number of chromosomes sharing DNA IBD at the locus. In some situations (e.g. parental imprinting, cf. Section ) it is preferable to distinguish between sharing of paternal and maternal DNA and consider 4 IBD configurations.

  
Table 1: Sib-pair IBD configurations

Under Mendel's first law, all 16 inheritance patterns (inheritance vectors) are equally likely, hence the probabilities that two sibs share DNA IBD on 0, 1 and 2 chromosomes are , and , respectively.