How humans and primates choose their leaders is surprisingly similar.
However, whereas humans use the term "alpha" to denote assertiveness, aggression, or overly bullying behaviour, our evolutionary neighbours would not share this view.
In primates, alphas keep the peace, provide comfort and stabilise the group.
It's all about creating the environment - the culture - for the group's overall safety, security and prosperity.
Their longevity as a leader also relies on them being cooperative, empathetic and generous.
And this keeps them popular amongst the group, too.
It seems that psychological safety is not something unique to our species...
Further info:
Check out Frans de Waal's Ted Talk on "The surprising science of alpha males"