The term comes from monkeydom - dominant male in hierarchy who basically runs things and gets what he wants. In monkey troop, there’s only one and one of his privileges is he’s often only one who gets to mate.
In a nutshell they’re domineering, intimidating, impatient with people and details, thrive on responsibility, driven, irascible, know (not “think”) they’re right, often left-brained, and difficult.
Is there an "alpha female"? Studies have shown that females are not as innately** threatening as males. Also, across-the-board, males test lower in empathy and social responsibility - two traits that contribute to this personality style. So, not really!
**Tests for innateness mean it's evident with newborns, and in every culture, therefore not something "learned".
How do you cope with one? Here are some suggestions.
1. Take a stand.
You won't get to hold it, but if you don't, you'll become irrelevant.
2. Learn their language.
This is helpful with anyone, learning how they speak, and essential with alpha male. Listen to alpha and parrot back, using his terminology. For instance, if you get an email saying, “You were wrong,” you can reply, “How do I do this right?”
3. Maintain your dignity and self-respect.
It may well be under assault, and it’s up to you. The alpha male isn’t looking out for you, your feelings, or sentiments, or often even your opinion. If you show he’s “getting to you,” you’ll likely get more of it. (To them it's a show of "weakness".) Learn to manage your nonverbal communication - facial expressions, position of hands, posture, etc.
4. Come in equipped with Emotional Intelligence.
You’re going to need it. They are results-driven, and this means they run rough-shod over people, whom they see as merely a means to their end. (You will be judged on how "useful" you are.) You will have to learn to protect yourself. Deal with facts and don’t take it personally. If you look around, it was just “your turn,” that’s all.