Mating system you describe is a form of polygamy (multiple mates) known as polygyny (male mating with multiple females). Often easiest for those with housing resources limited (pretty much everybody). Closest records in that case based on male (patrilineage) which is how we used to track our polygyny mated games. We would have hen(s) numbering from 1 to 6 in with each brood cock. Even though chicks hen reared, hens cuckholded each others nest making knowledge of actual mother not known with confidence. Nonetheless, we had managed some control over that by having hens being full sisters to each other. I am now cheating by having rooster cover a hen once every three days and keeping hens penned separately. That requires work. Wanting to have hens tie-corded like done with game roosters and allow rooster to range among the ladies to ensure all are covered. Hens allowed only to lay in their own nest, making possible / practical the breeding hens of varied genetic backgrounds to same rooster at same time.
The matrilineage I track has known with certainty the mother, grandmother, greatmother, etc. for every individual. Males ancestors also known but much greater effort made to ensure no matrilineages go extinct. I select males extremely hard with only one from each matrilineage being allowed to breed. matrilineages are each repressented by several hens at any given time.
What are you trying to select for? What breed? How many breeders can you support?
It's one of those things that's been bugging my mind lately haha
