it's a very simple equation: if as the head of a family you're working to feed 6 people: your two parents and spouse and three children. when your children become of working age (which will vary depending of the type of work you do) then you have 3 less mouths to feed, which in turn become productive and work to feed an x amount of mouths themselves.

The equation is not simple in real life. I don't which islands you worked on but there isn't an abundance of work to be had for people on them. The children of many families resort to panhandling or selling cheap goods to tourists to try to bring some income in for the family. Furthermore, fishing communities are not really thriving in general as of late and your equation says nothing about expensive medical treatments.

still, the people who i work with produce a little bit more than they can consume, usually to trade their goods for something else that they need, like clothes or shoes. though they are poor, they don't live with food insecurity.

Those communities might not but many poor people in third world countries live with massive food and housing insecurity (not to mention medical costs). Where exactly did you do your work?

i've witnessed, for instance, how in some farming communities, the household that produces the most throws a party for the rest of the town.

A farming community is not the same as a poor island fishing community.

i think it's hard to imagine because we've grown in communities where these sort of things are unheard of, but it still happens, and it works flawlessly.

The point of my comment was not to highlight the impossibility of communal living but to debunk the misguided notion Westerners commonly have that impoverished islanders lead carefree, blissful lives. There is a shocking amount of desperation and suffering in many poor island communities.