Coefficient of inbreeding

The coefficient of inbreeding (COI) is a number measuring how inbred an individual is.

Specifically, it is the probability that two alleles at any locus in an individual are identical by descent from a common ancestor of the two parents.

[1][2][3][4] A higher COI will make the traits of the offspring more predictable, but also increases the risk of health issues.

[5] An individual is said to be inbred if there is a loop in its pedigree chart.

If an individual is inbred, the coefficient of inbreeding is calculated by summing all the probabilities that an individual receives the same allele from its father's side and mother's side.

As every individual has a 50% chance of passing on an allele to the next generation, the formula depends on 0.5 raised to the power of however many generations separate the individual from the common ancestor of its parents, on both the father's side and mother's side.

This number of generations can be calculated by counting how many individuals lie in the loop defined earlier.

Thus, the coefficient of inbreeding (f) of an individual X can be calculated with the following formula:[6][1]

In this pedigree chart, G is the progeny of C and F, and C is the biological uncle of F. To find the coefficient of inbreeding of G, first locate a loop that leads from G to the common ancestor through one parent and back down to the other parent without going through the same individual twice.

This can be verified in the previous example, as 12.5% is one-half of 25%, the coefficient of relationship between an uncle and a niece.