Is an alpha male a take charge person in times of need. Accepting the consequences and saying to heck with them until the task is done?
Admittedly, this whole concept of an "alpha" and a "beta" male is subject to controversy. It is a convenient and popular analogy, but may be based upon some outdated theories. On some level, just as I have described in my previous posts, there is "something" to this theory within human and primate social structure, but it can get a bit nebulous. So, to accurately answer this question, it requires specific context with regards to the specific individuals and their relationships to each other, and not some general answer.
I know you like wolves. You might be interested in this:
Wolf packs don’t actually have alpha males and alpha females, the idea is based on a misunderstanding
https://wolf.org/headlines/caption-...es-traveling-through-snow-as-a-pack-is-false/