What is a Coefficient of Inbreeding?

A coefficient of inbreeding is a measure of how much homozygosity we expect as a consequence of inbreeding. Genes are said to be heterozygous when an individual has two dissimilar genes for a trait; when the two genes are the same, the individual is homozygous for that trait (or that gene pair). We don’t have the technology to measure the actual gene combinations, but we can calculate the probability the genes will be the same by looking at the pedigree.

Each parent contributes 50% of their genes to their offspring. Thus, half-siblings like Ram B and Ewe C in the example below have 50% of their genes in common with Ram D, since they are both fathered by Ram D. But Ram B and Ewe C may have from 0 to 50% of their genes in common with each other – that is, of the 50% of the Ram D genes that Ram B received, somewhere between all or none of those genes may have also been sent on the his half-sibling Ewe C. On average, they will have received the same genes from Ram D half the time – so they should share 25% of their genes with each other.

Now, if the half-siblings are bred together, they each contribute half of their Ram D genes (25%) to their offspring. On average, their offspring are expected to get the same Ram D genes from Ram B and Ewe C half the time – so Sheep A is expected to be homozygous for 12.5% of its genes.

Table 1. Pedigree of sheep A (12.5 percent co-efficient of inbreeding)

Ram D
Ram B
Ewe E
Sheep A
Ram D
Ewe C
Ewe F

Table 2. Some possible relationships between a ewe and a ram, and the resulting coefficient of inbreeding for their offspring:

Relationship between the parents Coefficient of inbreeding for the offspring
Father-daughter, mother-son 25%
Half-siblings 12.5%
Grandparent-grandchild 6.25%
First cousins 6.25%


When multiple ancestors are found on both the sire and the dam’s pedigree, then the calculations for coefficient of inbreeding become more complicated. A thorough discussion of 2 different ways of calculating a COI, and the errors involved in using only 5 generations of data to do so (using Thoroughbred horse pedigrees), is Coefficients of Inbreeding: An Investigation into Wright’s Equation and Hardiman’s Method.

Some Sofware Options

It is much easier to use a software program to calculate coefficients of inbreeding than to calculate them by hand. There are various software programs available for this purpose, from free-ware to relatively expensive pedigree programs. A few are listed below.

Rapid Computation of Inbreeding Coefficients. FSpeed is a Windows program for calculating Wright’s coefficient of inbreeding very, very quickly. A free version is available.
Breedmate /Pedigree-X
The Breed Mate family of Pedigree Software Packages covers dogs, cats, horses and other animals. The software must be purchased.
FREE! pedigree software. Originally designed for use with Dalmation dogs, can be easily modified to keep track of sheep pedigrees. The Visible COI add-on software is very useful in calculating the relative contribution of each ancestor towards the overall breeding coefficient.