If our social formations were limited to what the human genetic code told us we could be, then we might expect the human species to follow the population pattern suggested in Darwin's Origin of Species, and reiterated by modern population biology in the form of the "J-curve."
According to this model, animal species which are too successful at adaptation to their habitats will overpopulate said habitats, and deplete them of their natural food sources. The population graph of such animal species takes on the shape of a "J-curve," with population increasing exponentially (the upward-curve of the "J") as species "success" is consolidated. Thus the name, "J-curve."
Animal species which are "too successful" will overpoulate themselves, say the population biologists, until the animal species breeds a quantity of individuals for which no food supply is available. At that point, the "J-curve" is finished, and the "too successful" animal species experiences massive dieoff as its members starve to death in great numbers until an ecological balance is restored and population limits are established.
Could human beings be such a "too successful" animal species? Certainly, we humans are versatile enough to adapt to any habitat niche the world has to offer, and so we can get around the "J-curve" problem by multiplying our habitat niches. A couple of million years ago, for instance, our distant ancestors managed to avoid extinction in Africa (the fate of the australopithecines) by migrating to Asia and Europe. But that solution could only go so far; humans have now invaded every habitat the world has to offer a land mammal. Our population, too, follows that natural "J-curve" -- the human population explosion of the last two centuries looks on a graph like the upward straight-line of the letter "J" when viewed against the background of the rest of human existence.
We are now at the point where we have begun to speculate as to the origins of an eventual mass human dieoff. Agriculture, of course, has multiplied our food supply; but we could destroy the Earth's soil fertility and make it incapable of generating plant habitat in the quantities necessary to produce food for many billions of people. Or the human race could catastrophically disrupt agricultural habitats through human-caused climate change. Using up our planet's cheap oil could place strict limits on the human race's adaptive resources. The human race can certainly be said to have overfished the oceans to the point of serious disruption of ocean ecologies. Planet-wide overexploitation of other resources has occurred for other reasons as well.
At any rate, if humans were just like other "too successful" animals, we could expect the fate of the J-curve to occur to us. The saving grace for the human race is its versatility; we have to hope that "our genetic code" (at least) will not prohibit us from creating social forms that do not result in the tragedy of the commons. We must, however, reorient our versatility -- instead of using it to amplify our domination of nature and of each other, we must use it to cope with the excesses of our success as a species.