Consanguinity, Relatedness, & Inbreeding in pedigrees

    Consanguineous matings (marriages, if humans are under discussion) are those between related individuals, defined simply as those that share a common ancestor. In pedigree charts, these are indicated by double lines between symbols.

    The Relatedness (r) of two consanguineous individuals is the fraction of alleles they share at all loci. This can be estimated by analysis of any one locus. Any parent / offspring combination must share exactly 1/2 of their alleles at any locus: offspring inherit one or the other allele from each of two parents: (1/2)(1/2) + (1/2)(1/2) = 1/2. This is necessarily true for any single locus. Any two full siblings are also expected to share 1/2 of their alleles over all loci, but not necessarily at any single locus. For example, siblings #3 & #4 may each receive any of four allele pairs from the parents: A₁A₃, A₁A₄, A₂A₃, or A₂A₄. There are thus 16 possible allelic relationships between siblings at any one locus (see Table). In four of these, both alleles are identical (r = 1), in another four alleles all are distinct (r = 0), and in eight only allele is shared (r = 0.5). The expected r = [(4)(1.0) + (4)(0.0) + (8)(0.5)] / (16) = 8/16 = 1/2. For any finite sample of loci, measured r may deviate from its expectation, the expected deviation being greater with smaller samples.

    This is one reason estimations of genetic relatedness from commercial "DNA dot com" DNA tests can be ambiguous. For example, 4th & 5th cousins have r = 1/64 and 1/128, respectively, so that the expectation of allele sharing across 512 tested loci is 8 vs 4, respectively. Observed sharing of 3 ~ 9 alleles would not permit a statistical distinction to be be made between these degrees of relationship. Estimation of relatedness is further complicated when alleles are identical by state but not by descent (see below). In the example above, of the four alleles marked 1 2 3 & 4 in the P₁, only two may be distinguishable, such that both parents are A₁A₂. Then, six of their offspring will be genetically identical, eight related by 0.75, and only two distinct [HOMEWORK: show that this is true]. The sharing of these two alleles among individuals in subsequent generations overestimates relationship.

    The offspring of a consanguineous mating are described as inbred. The inbreeding coefficient (F) for an inbred individual is the expectation that the individual has two alleles identical by descent (IBD) at any given locus. Alleles are identical by descent if they are genetic copies of the same allele in the common ancestor of the consanguineous parents. These probabilities can be calculated by following each allele through several generations. The concept of IBD long antedates the discovery that genes are made of DNA, however IBD occurs as the result of a particular dsDNA molecule replicating itself along two separate lineages.

    For example, we can calculate the probability that individual #5, the product of a full-sib mating, has two alleles at the A locus that are identical by descent as F = 1/4 = 0.25. Other relatedness and inbreeding coefficients for typical consanguineous matings are shown below.

    Consanguinity and Inbreeding are often confused. Because many humans exist and marry in more or less closed, finite populations, any two marriage partners may have a more or less distant common ancestor, and are therefore consanguineous distant cousins. Their offspring would have (in principal) a calculable F. All finite populations are to some degree "inbred," as measured by the average F over all individuals in a population, and which is inversely proportional to its size N. "Inbreeding" becomes of special interest when the rate of marriages between closely-related individuals is higher than expected. This may occur in societies where sib-sib marriages are encouraged, as sometimes occurs for religious reasons, or to keep property in the same family. Western societies often discourage first-cousin marriages, but attach no onus to marriages between second- or higher-degree cousins; most people may be unaware of fourth- or fifth-degree cousins. (Recall that Queen Elizabeth II and HRH Philip were fourth cousins).

    HOMEWORK: Show graphically that individual #10, the product of a first-cousin marriage, has F = 1/16.