I wonder if they discussed the problem with the shephard of the flock they studied. His insights may be be relevant. I think in some herds there is an alpha male that has a bell on his neck and sheep follow him.
The lead sheep is an ewe, and the other sheep follow her if I need to move them. She's dominant and will shove everyone out of the way if there's something she wants. They have a social ranking that changes slightly depending on a bunch of factors, but it's pretty much matriarchal. My lead sheep's daughters have high status, too.
My ram has a bell so I know where he is, because rams can be dangerous and the bell sound gives me warning if he decides to sneak up behind me.
Shepherds will put bells on their lead sheep so they can find them again if they're grazing in large pastures. Less dominant sheep will tend to stay close to lead sheep.
All of this is surprisingly variable depending on sheep breed. More domesticated sheep breeds tend to have stronger flocking instincts, which makes them easier to herd.
I think the bells have nothing to do with alpha male/flock leadership. It's more about the auditory alerts they provide the shepherd. Locating, startled flock, charging rams, etc. with the added benefit of making predators wary.
