When you have first generation breeder stock on your farm from an outside supplier is this considered f1? Or, is that generations offspring f1? How about the same question, but when you cross breed?
F1 is the standard designation of a first generation hybrid. F2 is the hybrid's offspring. You'll see that also used on vegetable seeds. The parent stock are not hybrids but their offspring is. To be clear, if you cross a Delaware with a New Hampshire, the Delaware and New Hampshire are not F1, their offspring is.
When considering the cock for your mating program, should you use him to sire multiple generations? Do you breed a cock back to its offspring for back cross generation? Or do you need to introduce a new one?
There are lots of different ways to do this. When you cross a parent (male or female) back to their offspring it is called line breeding. Line breeding is a common technique to enhance certain traits when you are establishing your line. The downside to line breeding or any other type of inbreeding is that you lose genetic diversity each time you inbreed. You want to lose genetic diversity in the traits you are trying to enhance. For example, if you want a single combed bird you want to eliminate the diversity that gives you a pea or rose comb. But you want to retain the diversity that keeps the birds viable and productive. It can get kind if tricky.
There are also techniques to maintain genetic diversity while doing this. Hatcheries often use pen breeding. That's where you may have 20 roosters in a pen with 200 hens and you save your next breeders from them. It's not a good method to produce high quality birds since you are not controlling which ones mate, but you can maintain genetic diversity for decades i you have enough different birds in there.
Many breeders use the spiral breeding method to maintain genetic diversity. That's where you divide your flock into 3 families, say A, B, and C. All females stay in the same family but the best males are moved in a specific order, maybe A to B, B to C, and C to A to mate with the best hens. You do not rigidly stick with a specifically bird in each family, you use your best birds.
Another method that some breeders use is to bring in an outside bird, practically always a male, every four or five generations to renew genetic diversity. Say you have another breeder that is working toward the same goals that you trust, you might swap males every four or five generations. I've known breeders that are working toward developing a new color/pattern for a certain breed that do this. For thousands of years small farmers all over the world bring in a new rooster when they see a need to renew genetic diversity.
I'm sure there are other techniques. It's not one rigid system where you have to do it a certain way with certain birds. Some of it depends on your goals, some of it depends on where you are in your breeding program.
Are there inbreed mutations to consider when breeding a cock back through multiple generations?
It's not mutations, it's more a loss of genetic diversity. If you have recessive genes you don't want they can pair up and give you defective birds. Which ones are bad depends on your goals. Recessive genes can be a pain to get rid of since they hide under dominant genes. There is even a technique to tell which of your birds have a specific recessive gene hiding and which birds have eliminated it.
Another issue is that the less genetic diversity you have the more likely your flock is to lose vitality. The flock may lose fertility or production may decline. They become less thrifty. It's a general decline in the overall health and quality of your flock. That's where "hybrid vigor" comes from. If you cross two birds that are not closely related, even if they are the same breed, you usually get a boost to vigor. But that is a two-edged sword as you may be introducing genetics you don;t want back into your flock.
Every breed of chicken has been developed by inbreeding. Any breeder that consistently wins ribbons uses inbreeding. Inbreeding is not a bad thing, it is a way to improve your flock. But it needs to be managed.
I have played with genetics but I'm not that serious about it. I have a lot of respect for breeders that can manage this.
Good luck!
