Wikipedia: Alpha Males

Nice "alpha male" definition in Wikipedia: I like the idea that you let the alpha animal EAT first. Check it out:

In social animals, the alpha male or alpha female is the individual in the community whom the others follow and defer to. Where one male and one female fulfill this role, they are referred to as the alpha pair.

Chimpanzees show deference to the alpha of the community by ritualised gestures such as bowing, allowing the alpha to walk first in a procession, or standing aside when the alpha challenges.

Canines also show deference to the alpha pair in their pack, by allowing them to be the first to eat and, usually, the only pair to mate; wolves are a good example of this.

The status of the alpha is generally achieved by means of superior physical prowess. However, in certain highly social species such as the bonobo, a contender can use more indirect methods, such as political alliances, to oust the ruling alpha and take his/her place.

And of course, they have an interesting comment on HUMAN alpha males:

In humans, the alpha male often refers to a man who is powerful or high on the social ladder, similar to hegemonic masculinity. In Western cultures, the term is sometimes pejorative and describes a man who is overly masculine to the point of arrogance.

Google the term "alpha male" ... the results are about 14,700,000 ... the first result is Wikipedia. The second result is mine.