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Basicly it is breeding across the lines, siblings cousins etc. Line breeding is in a line as stated as in one generation to another down. It can be aunts uncles etc, but usually is more in mother, grandmother etc. You take a pair and breed them together. Then take a son and a daughter from the pairing that you are satisfied with. You then breed them back to the parents. Then take the son and daughter from that breeding and go through it all over again. After4/5 generations you breed the two offsprings together and then start all over agin. You bring in new blood when needed and when you need to improve in certain fields. Strick culling is needed. This is one way the champions are made in livestock etc. Unrelated stock breed vitality but you lose in comformation. Mostly in birds, color is about all we look to, except the ones that show them. Livestock we breed for fur density [or hide] bone structure, thickness, color formation etc. In Dutch rabbits, they color line should be as close to even on both sides and straight lines, an almost impossible task. It can be time consuming to try to figure out which way to go. My advice is not to try it unless you are into the genetics. Breed unrelated stock as much as possible to keep the stock as healthy as you can.

I'm no breeder, and I don't plan to be one! Certainly inexperienced people should stick with unrelated stock! What I hear most about linebreeding however, is that it's not impossible to see one animal repeated within the line say 3-4 times...

Yes that is how you lock in the traits. By doing so, you evenually make all offspring almost the same. Even a brother/sister is not 100% related, I would venture to say that around half brother/sisters are related with 50% of their genes. Others would vary. By breeding back to the same repeatedly, more genes are the same making them look more alike. Almost like cloning. But you do make the bad and good traits show up more. Inbreeding [across lines] is haphazard at best. It is usually done for testing for genes or to produce something that only they would have. When someone gets a good show animal say, they will breed it to several others to bring out the traits it carrys and by line-breeding it back several times, it brings more out. The process had to be done more than a few times to really see the difference. Animals produced that way carry genes strong enough that when bred to unrelated stock will still produce a good percent that carry it's traits. That is mostly cattle, they breed to champion bulls to upgrade their stock.