You should never make the mistake that human females don't do dominance battles of their own with each other. We do. In every aspect of our lives. And sometimes, we don't even realize that we do it.
Even the weakest among us does it but in a much more subtle manner.
And it is a heck of a lot more complicated than any male's battle. They concentrate on just the physical beating of each other. You win the fight, and it was done. Everyone knows their place.
Oh no, like a fine wine, there were always different layers of complexity to females interacting with each other.
The first layer, like males, was physical. Who was bigger, and who was smaller. Who could win a physical fight, and who couldn't.
Then it went on to looks. Who had more desirable characteristics than the other. Hell, even the length of hair a female had was a matter of dominance.