When breeding for the darkest brown eggs Is the cock the most important bird in the breeding trio for controlling and improving egg color in the future? If so would it be beneficial to keep breeding him back to his daughters?
Well he could be....but one cannot very easily see what egg colour genes he carries.
There may easily be much more recent knowledge........ when Prof Punnett investigated darker egg colour he came to the conclusion that there was more than one locus ( a few?) responsible for darker egg colour, one or some of which were sex linked.
I'd have thought there might be other possibilities other than keep breeding back males to their daughters/granddaughters etc etc.
A possible problem with breeding the cock back to his daughters is the reinforcement of other possibly undesirable traits.
I have seen this a lot in dogs. Breeding for the perfect show dog has introduced hip dysplasia in some large dog breeds. I have talked to a old timer OFA vets who say the the temperment of todays hip healthier GSD breed is different than those twenty or thirty years ago when hips were a real problem. The OFA healthy breeds temperment is still good, just different.
I think it is always good to maintain some genetic diversity. Reinforce desirable traits by tracking blood lines. Be careful how many places the lines cross in the last two or three generations. Unfortunately, this means knowing which hen laid which egg and what rooster fertilized it. Also have to keep records.
I also read that eggs laid early in the clutch cycle are darker than those later. So you'll have factor that in if it is true.
Good luck. I look forward to learning from your progress. I hope you'll keep us posted.