In 1922 Wright devised a mathematical model for the definition of the coefficient of inbreeding:
Fx is the inbreeding coefficient of the dog in question, Fa is the coefficient of the common ancestor, n1 is the intervening generations between the sire and the common ancestor, and n2 is the intervening generations between the dam and the common ancestor. Since I will make use of the degree of inbreeding notation (x,y:a,b) for listing common ancestors, which counts actual generations instead of intervening generations, we will be using n1+n2-1.
The degree of inbreeding notation works as follows. Each number in front of the : is the generation a common ancestor appears in the pedigree on the sire's side. The numbers after the : are the generations on the dam's side. For example, dog A has the following pedigree:
D C E B F E G D H K J F E G
For dog E, we would write 2,3:2
For dog D, we would write 3:3
Some Example Calculations
| Rover's pedigree | Degree of Inbreeding | Inbreeding Coefficient Calculation |
Fido King Fluffy Fido Queenie Princess |
Fido - 2:2 | 2+2-1 3 (1/2) = (1/2) =.125 = 12.5% |
So Rover's inbreeding coefficient is 12.5%, based on the information we have. If we knew the inbreeding coefficient of Fido, then we would multiply .125 by (1+<fido inbreeding coefficient>). So if Fido also had an inbreeding coefficient of 12.5, Rover's inbreeding coefficient would be .125 * 1.125 = .1406 = 14.06%
A more involved example would be the pedigree of Ralph.
| Ralph's pedigree | Degree of Inbreeding | Inbreeding Coefficient |
Eric Drake Jessie Balu Eric Cindra Frankie George Eric Heide Cindra George Frankie Intel |
Cindra 2:1 Eric 3,3:2 For Eric, the numbers |
2+1-1 2
Cindra - (1/2) =(1/2) =.25
3+2-1
Eric - (1/2) =(1/2) = .0625
Ralph's inbreeding coefficient is 31.35% |