Interesting question, I don't remember reading any studies about this. But I'll toss some things out for thought.
Breed and variety is a man-made thing. Every breed or even type of chicken has been developed by selective breeding. At some point after chickens were domesticated man realized they could breed larger size, better egg laying, or some really weird looking ornamental chickens like the Polish headdress or Silkie feathering. So they developed types. Breeds were developed when people decided to compete with each other in who could raise the best chickens so they had to write an SOP so the judge would know the criteria to judge by, other than the unwritten rule that the king always won. The SOP is what defines a breed, before an SOP they are types.
Each chicken, male and female, is an individual with its own personality. In a free ranging situation with several hens and several roosters, each rooster tends to set up his own territory with his own harem. I don't know which has more control over which hens go with which rooster, the hens or the rooster. I suspect it is some of both but think the hens have a fair about to say about it. The tid-bitting (finding them food and letting them eat first), dancing before mating, and other behavior indicates to me that the rooster needs to win her favor. Even though they split into harems all the hens or roosters are not particularly loyal, there is some mating going on across harem lines. Some hens will squat for anything in spurs but others are more selective.
Some hens tend to stick very close to their rooster, some tend to roam a lot on their own, though usually with certain select other hens. To a certain extent which hen the rooster chooses could be a matter of convenience, which one is closer. I have seen a rooster focus on one hen when he starts to dance and keep after her even if she runs away and another hen squats when he starts his dance for the other hen. I'm not sure how strong "convenience" is but I think it plays a part.
When she is laying a hen exhibits certain characteristics, such as bright red comb and wattles. Bright red combs and wattles tell a rooster that hen's eggs need to be fertilized. While some roosters will mate with any female even with pale yellow combs, many are more selective. I've seen a rooster come running when a hen lays an egg and sings the egg song. He normally mates with her and them escorts her back to the flock. That way a hen that is laying eggs gets fertilized. Not all roosters do that but some do. Not all hens sing the egg song. A hen that is laying will be more attractive to a rooster.
I'm not a strong believer in breeds and behaviors but breeds do have tendencies if you have enough chickens for averages to mean much. I think strain is stronger than breed for this. You can breed certain behaviors into a flock. Two different flocks of the same breed can have different behavioral tendencies depending on whether the person selecting which birds get to breed uses behavior as one of the criteria. Each chicken has its own personality. Chickens with a certain general personality might tend to hang together, regardless of color/pattern. But if they come from a flock with certain behaviors I can easily see them sorting themselves out by "breed".
Chickens that are raised together often form lifelong bonds, regardless of the color/pattern of the feathers. it doesn't always happen but it does a lot. If you get all of one breed and raise them together while you have other breeds it may look like they are separating because of breed but it may be more to do with them being raised together.
A lot of this assumes you have enough room for the different roosters to each carve out a territory and have their own harem. Or for the hens to break into their own sub-flocks. I'd think if they are crowded together so they cannot do this most of this breaks down and you really get random matings.
I've had flocks with one rooster and hens of different breeds. I've had flocks with one rooster and crossbreed hens that looked a lot different. Pretty much all the eggs were fertile. You might get some segregation in breeds mating more often than crossing, but I would not really expect it to be much. To experiment you would need two different breeds that you could tell which chicks were pure and which were crossed. you'd probably want to know which way that cross went. You would need to have a large enough flock and hatch enough eggs for averages to mean much. I have not done that so I can't speak from experience, just give my opinion.
Breed and variety is a man-made thing. Every breed or even type of chicken has been developed by selective breeding. At some point after chickens were domesticated man realized they could breed larger size, better egg laying, or some really weird looking ornamental chickens like the Polish headdress or Silkie feathering. So they developed types. Breeds were developed when people decided to compete with each other in who could raise the best chickens so they had to write an SOP so the judge would know the criteria to judge by, other than the unwritten rule that the king always won. The SOP is what defines a breed, before an SOP they are types.
Each chicken, male and female, is an individual with its own personality. In a free ranging situation with several hens and several roosters, each rooster tends to set up his own territory with his own harem. I don't know which has more control over which hens go with which rooster, the hens or the rooster. I suspect it is some of both but think the hens have a fair about to say about it. The tid-bitting (finding them food and letting them eat first), dancing before mating, and other behavior indicates to me that the rooster needs to win her favor. Even though they split into harems all the hens or roosters are not particularly loyal, there is some mating going on across harem lines. Some hens will squat for anything in spurs but others are more selective.
Some hens tend to stick very close to their rooster, some tend to roam a lot on their own, though usually with certain select other hens. To a certain extent which hen the rooster chooses could be a matter of convenience, which one is closer. I have seen a rooster focus on one hen when he starts to dance and keep after her even if she runs away and another hen squats when he starts his dance for the other hen. I'm not sure how strong "convenience" is but I think it plays a part.
When she is laying a hen exhibits certain characteristics, such as bright red comb and wattles. Bright red combs and wattles tell a rooster that hen's eggs need to be fertilized. While some roosters will mate with any female even with pale yellow combs, many are more selective. I've seen a rooster come running when a hen lays an egg and sings the egg song. He normally mates with her and them escorts her back to the flock. That way a hen that is laying eggs gets fertilized. Not all roosters do that but some do. Not all hens sing the egg song. A hen that is laying will be more attractive to a rooster.
I'm not a strong believer in breeds and behaviors but breeds do have tendencies if you have enough chickens for averages to mean much. I think strain is stronger than breed for this. You can breed certain behaviors into a flock. Two different flocks of the same breed can have different behavioral tendencies depending on whether the person selecting which birds get to breed uses behavior as one of the criteria. Each chicken has its own personality. Chickens with a certain general personality might tend to hang together, regardless of color/pattern. But if they come from a flock with certain behaviors I can easily see them sorting themselves out by "breed".
Chickens that are raised together often form lifelong bonds, regardless of the color/pattern of the feathers. it doesn't always happen but it does a lot. If you get all of one breed and raise them together while you have other breeds it may look like they are separating because of breed but it may be more to do with them being raised together.
A lot of this assumes you have enough room for the different roosters to each carve out a territory and have their own harem. Or for the hens to break into their own sub-flocks. I'd think if they are crowded together so they cannot do this most of this breaks down and you really get random matings.
I've had flocks with one rooster and hens of different breeds. I've had flocks with one rooster and crossbreed hens that looked a lot different. Pretty much all the eggs were fertile. You might get some segregation in breeds mating more often than crossing, but I would not really expect it to be much. To experiment you would need two different breeds that you could tell which chicks were pure and which were crossed. you'd probably want to know which way that cross went. You would need to have a large enough flock and hatch enough eggs for averages to mean much. I have not done that so I can't speak from experience, just give my opinion.