There is a mathmatical equation for figuring out the level of relatedness between 2 individuals. This result is called the CoEfficient of Inbreeding.
The coefficient of inbreeding is defined as :
1. the probability that the progeny of a union will be homozygous for a specific autosomal allele derived from a common ancestor.
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If breeders kept records of the breedings of animals, the coeffiecient of inbreeding could be used to determine the level that animals are related. Then breeding projects could be chosen, (and outbreeding used) to lower the COI to a minimal level, which would then decrease the probability of inbreeding depression related problems, while still propagating the gene they are breeding for. There are many places online that explain how to compute the COI manually, however the equations become very complex when animals share more than 1 common ancestor. There is a free online program that I found called FSpeed (located here:
FSpeed - Fast Calculation of Inbreeding Coefficient ) that will compute the COI for you. Other breeding programs that compute this as well as keep records are easily a click away.