@ vineyridge (or anyone else who finds the history of this science interesting rather than intolerable, irrelevant and pedantic);
In the early 1920s, one of the founders of Theoretical Population Genetics, American student of physiological genetics, Sewall Wright wrote four papers about the pedigrees and populations of Shorthorn cattle. He used these animals because they had pedigrees stretching from his present back to the 1780s. Another interesting feature to note about Shorthorn cattle is that they went through some genetic bottlenecks with disastrous consequences for a few 19th-century fanciers who bought terribly inbred animals for the value of their pedigree. So in some parts of that breed (located in the US, I believe) there was a big and important genetic bottleneck.
Among other things, Wright used that rich pedigree information to calculate the degree of homogeneity for the breed at large. This kind of measurement doesn’t speak to the presence of individual alleles like the frequency of the recessive one we are talking about here. Rather, each animal is treated as a unit (with his full and more-or-less unknown compliment of alleles), and his percentage of shared ancestry with the average animal in the group, or with another one, is what was being discussed. I think that’s a pretty useful place to start.
It also means that when you choose an out-cross kind of a pairing, you might want to ask yourself just how far “out” or unrelated those two individuals are, even beyond that 5 generation pedigree. That’s a breed-level problem for the JC or WB registries to consider, IMO.
I know somebody did it and a lot of the owners were very upset about it…