Linebreeding if used properly can vastly improve the strong traits in a herd. It can also double up on the bad things too, so it is suggested that breeders really know what they are looking for and cull HARD if they are using this practice.
Almost all of my juniors at this time are half siblings. I brought a pair of littermates in from Missouri. I have been working hard on incorporating them into my line, so, the buck was bred to all of my does, and the doe was bred to my other buck. Then, to really double up on the line, I recently bred the doe to her brother. I cannot wait to see how those babies look in another couple of weeks or so.
I have been culling super hard for the traits that I don't want in my herd. I think that my herd is improving at a faster rate than if I was not doing so. I have a little 3 month old doe that I am pretty certain will be my first homegrown GC.
These daughters of the buck will be bred back to him. At least one of the Sons of the doe will be bred back to her. I will also be breeding the half siblings to eachother, and eventually, my entire herd will go back one way or another to these two rabbits.
If you google rabbit line breeding, you will find a line breeding chart that explains it well.