I have bred American Pit Bull Terriers for a number of years and linebreeding has always been popular. I'm talking about the true gamebred animals, not those 85 lb. mostly bulldog blue things that are popular nowadays. Although we have never and will never fight our dogs, these animals are bred for the sport. My females rarely reach 40 lbs. while my males top out at about 50 lbs. The point is, these dogs' pedigrees are full of examples of linebreeding and even a number of knowledgeable and well thought out inbreedings. I personally have completed a triple-breeding (father to daughter, take a female pup from that litter and breed it back to the original male). There were mixed results. While linebreeding can strengthen many good characteristics, it can also do the same to not so desirable characteristics. I believe that regardless of the animal, linebreeding should only be done with top notch animals that are a solid example of their individual breed standard. My breedings produced litters of mostly beautiful, people-loving dogs with outstanding personalities and above average gameness. I say mostly because a number of the pups (too many for my preference) came out skittish. They weren't scared of any dog, but they were terrified of people. I had a momma dog with this trait, but it didn't show up in her pups until I began doubling up those genes. The good dogs were dang good, but the relatively small number of skittish pups led me to abandon this breeding. I still use the male, and he is a great example of the breed, but in his situation linebreeding didn't produce the number of good dogs that would have justified continuing to tighten the blood. Bottom line: start with top-notch animals, only breed top-notch individuals, and don't continue on with something just because of the investment you have in it. You may fatten your wallet, but you're helping to ruin animals that people spent their lives developing.
In my opinion line breeding/inbreeding can be a very powerful tool if done correctly. Moving from the 'rule of 10' to 1:2:1 is nearly always and advantage.
Most of my experience is with rabbits and horses. Horses have been the most predictable, mostly I think, because the pedigree info is so accurate. When you have 8 generations of pictures and descriptions, and the online pedigree computing power that is available now, gosh it's hard to make a bad pick if you are willing to put your time in doing the reserach. My rabbits, once I got 4-5 generations of my own breeding, bred very predicatably as well.
It takes time to learn the weaknesses and strengths and how both are inherited in your flock/breed. Once you get a handle on it though, linebreeding can help make huge leaps in quality.
Line breeding can "make" or "break" a good line.
Here is a good link by Robert Blosl on Rotational Line Breeding. ( It was written with White Rock Bantams in mind but will work for any poultry, just change the size of the pens as needed. ) http://bloslspoutlryfarm.tripod.com/id60.html
I line breed occasionally, but usually never double back again. The closest I go is individual back to a grandparent or uncle. I have not done brother sister of father daughter, mother son. I just don't think my lines are so "precious" that such extreme tight breeding is warranted. I also go to lengths to obtain the best outcross blood I can get when I outcross. I breed toy and miniature poodles, mostly parti and chocolate and black. I don't breed for show dogs, but for coat quality, soundness, free of health defects, easy care, less hyper type of a good family dog. I know that is not a really lofty breeding goal in a lot of peoples' eyes, but I try to breed dogs that I would only wish on my own grandmother, upkeep and vet bills and grooming wise, ease of getting along with the family, easy to train, nice to look at. matt resistant coats, but still with good poodle coat that will hold a cut and not break off and leave a mess too much. I have lines I am currently phasing out because they are too "shrill" when they bark. Otherwise they are my best dogs. I just can't take the pitch and I doubt other people could eithe. They came from some of the best red lines out of Texas, but I just don't think they make the cut for "liveability" because of their voices, so they are done (almost) I still have one male that is fair in that department. He will probably produce "shrill" in future litters, but his puppies are otherwise so spectacular I overlook it. I would NEVER close breed that dog. He is always outcrossed on quiet girls.
i think line breeding should only be used for lines or families of animals that are top of the line. This enhances the traits, and also lets recessive genes (that are desired) express themselves. A drawback of linebreeding is undesirable traits popping up now and again. I think that line breeding is a good tool but if you dont have really nice birds then i think your just getting no where you know what i mean.
In almost all of my breeders I have done linebreeding. Most of the time I start with a trio of sometimes related birds, they have to atleast be cousins or something, not full siblings. When I mate them I keep all the pullets and mate them back to the father and if there is a good enough cockerel he will get mated back to a mother hen. If no good cockerels are to be found I keep the trio plus pullets in the same pen and mate again.
Normally I just do this method but sometimes I have kept ok sons and mated them back when I have no other choice. Linebreeding is a must if you are working with great birds or making a new color. For example the dunlaced birds- they are all decendant from one silver laced cock and a couple dun hens, there might be some BLR in there too. Either way they all trace back to one rooster. I always kept the best pullets and mated them back to him then in the end I did some 1/2 sibling mating to get it just right.