The term "pecking order" literally comes from this behavior among chickens: the use of non-lethal force to exert dominance.
You've got animal behaviour a little too generalised here. Neat ploints, but chickens cannibalise the weakest one, so it's not exactly like nature's way for chickens to all get along.
And baboons too; nature is not really a place where everybody gets along. And the stakes are always life and death. What happens to the ousted alpha? He lives a shitty life and dies not extremely long afterward. Even Grettir the Strong died as an outlaw.
Anyway, fun talk about gun control lol. I don't have much of an opinion there; not my country.