Coefficient of Inbreeding

The coefficient of inbreeding, F, is a measure of the probability that two genes at any locus in an individual are identical by descent from the common ancestor(s) of the two parents. A corollary to this is that F also indicates the likelihood that an individual is homozygous, as opposed to heterozygous, at a given locus, above and beyond the likelihood of such an event occurring through random mating. Mathematically, the calculation of the coefficient of inbreeding can be traced to a method noted population geneticist Sewell Wright devised in 1922:

where F is the coefficient of inbreeding, FA is the in-breeding coefficient of the common ancestor, n1 is the number of generations from the father to the common ancestor, n2 is the number of generations from the mother to the common ancestor and the summation is over all hereditary lines involving a common ancestor. In societies where inbreeding is relatively uncommon, FA can generally be assumed to be zero (this is the case where the limit of F is calculated as n1 + n2 →∞). However, in cultures where inbreeding is common or within families where inbreeding is known or suspected, FA can have a significant impact on F.

Calculating a Coefficient of Inbreeding

One of the more common occurrences of inbreeding is the mating of first cousins. Such a pedigree would have two common ancestors (both of the great-grand-parents in this example). Following Wright's method for calculating F, the great-grandfather is two generations removed from both the mother and the father and the great-grandmother is similarly distant from [Page 423]the parents. If we assume that neither of the great-grandparents is inbred, then:

Suppose, however, that the great-grandfather in this family was himself the son of two half-siblings. In this case, FA for the great-grandfather is not zero. Half-siblings share a common parent (and that parent is not counted twice because it is the same parent). Thus, for the great-grandfather:

and