I remember reading about this whole concept of "alpha" and "beta" males/females and how misunderstood it was.

For example, we usually see alpha male as someone physically dominant in the group, while in fact it is not true - hierarchies that are supported only by physical dominance of "alpha male" fall apart very quickly, usually taken down by 2+ males.
Therefore, if you are an "alpha male" that only means you have slightly more authority in that narrow circle of people that help you maintain power (and of course more power outside of it).
It was proven by observing wolves and chimpanzees - alpha wolf walks last in pack to make sure everyone else is safe, fights with outsiders and in exchange eats first and gets to mate - but the personal risk is huge, as walking last makes you prone to being killed (no one is covering your back, if something happens to you probability of others noticing is lower) plus fights with outsiders come with obvious and quite severe risk.

So, we give leaders food and mate, because we want them to:
a) protect us (therefore we keep them well fed)
b) keep their genes in the pool (because, I assume, they were decent leaders and there is good chance their offspring will help us too)

The above is "servitude of leader" at its prime if you ask me - since "protection" is a very broad word and it includes internal and external dangers.

That have a very interesting consequences - we absolutely DESPISE people who accept perks of being a leader and don't provide the above.

And to warp things up: Females periods synchronize not to make "alpha male" couple with every single one of them, but to make sure when "alpha female" is out of the market, everyone is. :)

Cheers!