I'd like to have both options, if I was a bronze-age man. Farmers can still hunt and fish, if need be. Hunter-gatherers are SOL if their supply of game dries up.
Doubtfull that all forms of sustenance would leave an area unless that area became overpoplated or a comet struck it.
But in the past--when there was plenty of abundant hunting grounds to be had for free--if the game left a certain area, people just picked up and moved over the next hill.
But when your crops don't get rained on or the locusts eat them, you starve.
Unless you go over the next hill and kill the people already living there for their farmland--or if they starve, they come over the hill to kill you to take your land.
Thus was war born: episodic shortages of resources and no empty land to move to would drive people insane enough to call each other sub humans, and then murder members of their own species--of their own human family--in the name of war.
So I suppose the definition of overpopulation is when people fight because they are trapped by having no place to run.