It takes a village. I'm sure there is some minimum population for the food density in any particular region which would be needed to collect and process enough for the entire group.

And then of course the leader owns it all, buys it for a set price and sells it for sexual favors or whatever artifacts the men could make in their spare time. And stores it hoping for a famine.

After all, without a healthy reserve how could the leader expand the area looking for new food? How else could he motivate his workers except by withholding the food they have collected and processed?

Serious management problems even back then.