Why do we have to demonstrate the tribal leader personality? Do you always demonstrate the tribal leader personality in order to get girls?

Because a "tribal leader" is the one with the power. A man with power is attractive to women.

How do you convey/demonstrate that you're the tribal leader? How do you do that?

Now I am the tribal leader by default. I work in private security and competitive intelligence consulting and ride with a group of ex-military tough guy types. Also, in my office we work in a compartimentalized task force kind of way and I am one of the project managers, reporting directly to the executive board.

Before that I did it by adopting the kind of look that commands attention WITHOUT looking like a freak and taking power whenever I could. People have just the room you give them, the same way you have just the room others give you. Basically, when everyone is looking at each other thinking what to do, take initiative and say "let's do this". Do this with confidence, act like you are used to being in command. If you flinch, you're done. But don't be arrogant, be the kind of guy they look up to, not the guy they want to run away from. Do it as fast as possible so people are acostumed to you being in charge right from the beginning.

Conveying leadership/dominance depends on the context. Approaching women with lots of confidence and going direct without any hesitation can convey you're are a man who goes after what he wants which conveys leadership/testosteron.

Body language can convey leadership.

When you're setting up a date with a girl and you don't ask questions like, "When have you time?" "What do you want to do?", etc. But you ask questions like, "Is tuesday evening, fine?" That's how you lead a conversation which also demonstrates leadership.