Yes it is a part of natural selection in most species on the planet. Charles Darwin articulated the connection between sexual selection and natural selection. Please see the attached link to Sexual selection. There is a section in this link called "The Role of Male-Male Competition in Sexual Selection" which addresses your question.

[en.wikipedia.org]

I hear of it in women's dating profiles, ie, "seeking alpha male". And not just one or two. It is pervasive.

I think there are people who are more comfortable leading, and other following. Nothing to do with Alpha.

There's no such thing as an alpha male, female or wolf. The scientist who invented the term abandoned it.

In my experience, guys who claim to be alpha males are usually university students who aren't going to succeed, because of their drinking habits.

[businessinsider.com.au]

Alpha males and females are natural born leaders. They have an innate ability to organize large groups of people towards a positive common goal. They lead through quiet strength and intelligence and have a tendency to gather other strong and intelligent individuals around them.

They are not to be mistaken for Beta's, who are loud, brash, obnoxious and quite often violent. Beta's surround themselves with lost and the misbegotten souls in an attempt to disguise themselves as alpha's.

Sean McVay, head coach of the Los Angeles Rams is an alpha male. Aretha Franklin is an alpha female.

I think it has more to do with how men relate to men than how men relate to women, aside from the fact that some women are attracted to alpha males.

It seems to have worked for Genghis Khan. His descendants are estimated to be 0.5% of the earth's human population. He and the wife stayed together, however, and only her sons became "Khans" after his death.

It's more of an issue among men than it is among men and women. I'll give you a few examples:

LeBron James is the Alpha male of the Los Angeles Lakers.
Michael Jordan was the Alpha male of the Chicago Bulls.

They are the ones who call the shots on the basketball court and tell their teammates what to do.

It's also very important in the workplace. I worked as an engineer for many years in tech companies and you have two different flavors.

The true alpha male who sets the deadlines and drives the workers to meet the deadlines.
The "the alpha geek" who is not as aggressive as the alpha males but is widely acknowledged as the smartest guy in the room.

A successful tech company must have alpha males and alpha geeks.

From my own personal experience, most of the alpha males and alpha geeks I knew in the workplace had both career success and happy marriages.

I always used to think it was just something that was written in books about superheros.

It does for some, and not for others. This is what some women want, just like there are men who want a dominate woman. There are no absolutes when it comes to relationships and l am constantly amazed how many folks on this site seem to think there are.