[ummwhat]

You've demonstrated that you've fallen for the popular misconception of Malthusian theory. It's not that food is "depleted at the margin" as in people starve until death rates go up. What actually happens at the margin is, lacking in sufficient resources to comfortably do so, people forego having kids. Perhaps, in olden times, lacking the prosperity to get the fathers permission in marriage.

[throw123123123]

It is not true, as both societies with no food have kids and societes with plenty of food don't have kids.

They have only a tenuous correlation at best.