Guys, <biologist hat on>, halo is basically
right. (Not surprisingly, since breeding chickens is not entirely different from breeding racehorses
)
Brother-sister, parent-offspring... either way, you have a similar chance of pairing up deleterious recessives.
(Mind, that is sometimes WANTED in a breeding program, so you can find out which animals are carrying that hidden allele and remove them from your program. One argument for inbreeding and linebreeding is that they "force" unwanted traits to surface so that you can actively cull individuals that are carriers.)
I realize that it is not TRADITIONAL in poultry breeding to use brother-sister pairings. But I wonder how much of that may be due to the apparent preference to use cockerels on hens, and roosters on pullets; I can imagine that double breeding (separate lines for breeding SQ males and females) could in some circumstances also argue for not using brother-sister matings.
In lab mice, you often have a lot better idea of the genotype of the parent than you do of the offspring (at least at first) so again there can be special-case reasons for using parent-offspring pairings in preference to brother-sister. Well actually this may be true to some extent in chickens as well. Plus older generations are more 'progeny tested', hence an additional value to breeding back to a parent or grandparent sometimes.
But from a simple GENETIC standpoint, they are both inbreeding and they both have the same effects.
<biologist hat off>
As far as the original question, basic animal breeding practice is to ruthlessly (er, as ruthlessly as you can bring yourself to manage) remove from your breeding population all individuals that have genetically-caused defects that you don't want to perpetuate. If you are a show breeder this could be as subtle as 'wrong number of points on comb'; if you are a homesteader it might be 'didn't start laying til age 1' or 'catches every disease coming down the pike' or 'produces unthrifty chicks'; if you are just sort of a hobbyist, it's really any ole thing that you dislike as long as it can be presumed to have some degree of genetic basis.
Also you may want to inject new blood every few generations, to improve general vigor and egglaying. One option is to introduce an outside rooster to the flock (preferably pretty closely related to your existing birds, unless you want to undo all your previous work at selective breeding); another way is to maintain two or more lines that you mostly breed among themselves but every generation or two swap a bird or two to the other group. (There are much much more systematic ways of doing it, but that's the general concept)
Have fun,
Pat
