I was reading up about this awhile back. Most of the sites I looked at say that inbreeding is breeding involving close relatives - including parent/offspring, brother/sister, half-brother/half-sister. Line breeding is more distant relatives breeding.
I wrote a geneticist friend of my husband's and got this e-mail back about it all. I hope it helps clear things up for you, it did for me:
When a mother and a father have a baby, that baby has two sets of genes
one from each. Let's play a little game and pretend that healthy genes
are capitalized and unhealthy (mutated or for other reasons) genes are
lower case. Say the mother has genes:
>>>> Aa
>>>> BB
>>>> Cc
>>>> Dd
>>>> EE
>>>> FF
>>>> GG
>>>> HH
And the father has the genes:
>>>> AA
>>>> BB
>>>> CC
>>>> DD
>>>> EE
>>>> Ff
>>>> Gg
>>>> HH
Then we know exactly what genes the baby, who gets one copy of one half of each, can have -- thogh there are already a lot of combinations (bear in mind this is a game, the real human genome has billions of these, and even though all combinations can be mathematically predicted, in reality no
one can ever do that).
>>>> AA
>>>> BB
>>>> CC
>>>> DD
>>>> EE
>>>> FF
>>>> GG
>>>> HH
or
>>>> AA
>>>> BB
>>>> CC
>>>> DD
>>>> EE
>>>> Ff
>>>> Gg
>>>> HH
or
>>>> aA
>>>> BB
>>>> cC
>>>> dD
>>>> EE
>>>> FF
>>>> GG
>>>> HH
or
>>>> aA
>>>> BB
>>>> cC
>>>> dD
>>>> EE
>>>> Ff
>>>> Gg
>>>> HH
You'll notice that some of these are exactly the same encodings, but that doesn't matter to us, it only doubles the probability that the baby will inherit those copies. All that matters to us is that the baby never got two copies of a bad gene. Also notice that 1 in 4 babies managed to get away without any latent problems at all and is perfect!
Now, genes encode both materials and processes within the body, and as long as one copy of a gene is good you're fine. But look what happens if the mother and father are actually
brother and sister:
Now the mother has genes:
>>>> Aa
>>>> BB
>>>> Cc
>>>> Dd
>>>> EE
>>>> FF
>>>> GG
>>>> HH
But the father, her brother, has the genes:
>>>> Aa
>>>> BB
>>>> Cc
>>>> DD
>>>> Ee
>>>> FF
>>>> GG
>>>> HH
Notice that since they are closely related they have similar encodings. Here're the baby's odds:
>>>> AA
>>>> BB
>>>> CC
>>>> DD
>>>> EE
>>>> FF
>>>> GG
>>>> HH
or
>>>> Aa
>>>> BB
>>>> Cc
>>>> DD
>>>> Ee
>>>> FF
>>>> GG
>>>> HH
or
>>>> aA
>>>> BB
>>>> cC
>>>> dD
>>>> EE
>>>> FF
>>>> GG
>>>> HH
or
>>>> aa
>>>> BB
>>>> cc
>>>> dD
>>>> Ee
>>>> FF
>>>> GG
>>>> HH
Notice the fourth combination, which has a 1 in 4 chance of occuring. While the baby got lucky with a working copy of genes D and E, it does not have a and c, and will probably die or worse. This happens to 1 in 4 babies.
On the other hand notice that now the odds of having a perfect baby has gone up to 1 in 3 (only because one in 4 don't make it).
So the Egyptian royal family, after thousands of years of marrying brother and sister, were thought to have the cleanest and most perfect genes in the history of the world, but they paid a terrible price for it.
And this will happen to cows. The closer you breed them, the more problems will come out, but the ones that make it may end up cleaner in the end.
There is no math here, you have to see what others have done, and if you want to try it, expect a lot of tragedies. Hope that helps.