Estimates of world population growth come from:
http://faculty.plattsburgh.edu/david.curry/worldpop.htm
Essentially human for our first 2 million years of existence, human population worldwide went from about 10,000 to 4 million. Given that virtually all major models of long-run human population converge very closely, and they all assume a relatively steady growth rate, we're talking a doubling period of 250,000 years.
Malthus' estimates assume a doubling rate of 25 years, or a single human generation. The difference is a factor of 10,000. World population simply did not grow as fast as you're assuming, and humanity did not start outstripping local carrying capacities in a major, systematic way until we'd developed technologies that allowed us to make those sorts of population growth leaps.
According to Michael Kremer in "Population Growth and Technological Change: One Million BC to 1990", the base rate of technological change in human societies scales proportional to population -- small population, slow technological change. This equals very long inferential distances to the sorts of techniques and behaviors that make agriculture a viable prospect.
You need intermediate steps, in the form of settled horticulture or nomadic pastoralism, to really concentrate the population enough to have a chance at developing agriculture in the intensive sense. Those sorts of cultural developments took a long time to come into being, and it was a gradual process at that.
So, yes, it's true that if you grow certain grasses and just harvest their seeds reliably, grinding them into a fine powder and mixing that with water and then heating the whole mixture somehow without actually burning it in your fire directly, you can produce a food source that will unlock access to population-doubling intervals closer to the Malthusian assumption of one doubling per generation.
But that is a series of nested behaviors, NONE of which is intuitively obvious by itself from the perspective of a forager in a world full of nothing but other foragers. Which is why the entire chain took a long, long time to develop, and why agriculture was invented just a few times throughout human history.
This is not true. Humans are (more or less) the only species that practices agriculture, but the Malthusian trap happens to non-human animals too. As long as reproduction above the replacement rate is possible, it will happen until the resource limit is reached.
Termites, leafcutter ants, certain damselfish, ambrosia beetles, and certain marsh snails all practice agriculture. But yes, it's certainly an uncommon behavior.
What if reproduction above the replacement rate isn't possible for the period of human evolution we're talking about? What if the human population simply isn't reproducing fast enough for most of prehistory to reach the resource limit? Those are the conditions I'm suggesting here -- that reaching local resource limits was not the norm for much of our evolution, due to our inherent long gestation times and strong k-selection, the inherent metabolic requirements for fertility taking a long time to satisfy compared to modern conditions, the birth interval being very wide compared to Malthusian assumptions, and the techniques of food acquisition being of necessity limited by the the ease of satisfying everybody's requirements (if everyone has a fully tummy and all their kids do too, going out and gathering MORE food at the expense of one's kinsmen won't do you any good anyway).
What you get is abundance -- there's room to grow, but we can only do it so fast, and when we start to reach the point where we might overtax our resource base, we've moved on and there weren't enough of us using it in the first place to compromise it.
The defectors would not need to reproduce in blatantly extraordinary numbers. It would be enough to reproduce just slightly above the replacement rate, so slightly that it might be unnoticeable for all practical purposes.
That kind of statistical hackery might work in a large population, but not very well in a small one. In a group of 100 humans, ANY population gain is noticeable.
The exponential growth would nevertheless explode their population in not very many generations and lead to them overwhelming others
Except all evidence suggests it wasn't possible to have a population explosion, if you assume humans must have reproduced at the fastest allowable rate. Populations doubled in a quarter-million years, not 25.
How did this punishment mechanism evolve, and how did it > remain stable?
It didn't evolve genetically, it's a cultural punishment I'm talking about. Ju/'hoansi hunters are taken down a notch whenever they make a kill. Certain Australian aboriginal groups have meat-sharing customs where one hunter goes out and gets a kangaroo (say), and his share of the meat is the intestines or penis -- the choicer cuts get distributed according to a set of other rules. Except, then people invite the hunter over to dinner; he's not forced to actually eat crow every time he succeeds, but he's also socially aware that he depends upon the others for it (and he gets to receive a choicer share when some other hunter makes a kill).
World population simply did not grow as fast as you're assuming, and humanity did not start outstripping local carrying capacities in a major, systematic way until we'd developed technologies that allowed us to make those sorts of population growth leaps.
I don't understand your argument here at all. Earlier you said that growth to the Malthusian limit was prevented by a cooperative strategy of restraining reproduction. Now you say that lack of food production technology was limiting population growth. But if foragers did breed up to the limit where food...
From Mike Darwn's Chronopause, an essay titled "Would You Like Another Plate of This?", discussing people's attitudes to life:
Conclusion, graphs, and references in article. As usual, I recommend reading Chronopause.com as Darwin has many good articles; to quickly link a few: