The Neo-Malthusian crowd is fond of biologism: that is the idea of comparing human beings to simplistic biological systems with the aim of forecasting the fate of humans from the fate of bacteria. That’s why this crowd see doomsdays and collapses all over the place.
It is of course correct, that if you put bacteria into a closed container with a limited amount of food, the bacteria will grow fast and exponentially in the start and after some time level of and finally crash by starving to death. But it is not correct to use this as an analogy to human population growth.
First of all the world is not a closed system. We receive a staggering amount of energy from the sun: 120.000 TW or 8.000 times the total existing energy demand of all industrious human beings. The Earth is not even a closed system from a material point of view, as we receive about 100 tons material pr. day as cosmic dust. This means, that in the Earth-Based first stage of human population growth, population is not limited by some finite “food” quantity on the earth, but only by our ability to use as much of the incoming energy as possible.
Furthermore, human beings are contrary to bacteria sentient creatures, which can plan and forecast and see their way around short term limitations. Collapse and sudden die out can happen for human populations, but only if stupidity and fundamentalist orthodoxy rules.
A second false analogy is the comparison of human population growth with the S-shaped logistic growth curve, which describes an initial exponential growth stage following by a leveling of to zero growth according to the limits caused by the carrying capacity of the biological system.
This is true for biological systems, but manifestly not for human beings, who can consciously change the carrying capacity by introducing technological change. The first two great technological revolutions: agriculture and industry changed the human population capacity two decades from less than 100 million in a gatherer/hunter society over 1 billion in pre-industrial agriculture to 10 billion in the industrial society. The knowledge technologies: bio, IT and nano is in the process of changing the capacity another decade to 100 billion people on Earth. And subsequently of course, space travel will ultimately increase the human population capacity many decades more.
The logistic growth analogy is additionally false, because it predicts zero-growth by mortality increasing to the level of reproduction. This is definitely not true for human beings. The modern zero-population-growth societies have obtained equilibrium state by decreasing reproduction rates as a consequence of rapidly decreasing mortality caused by increasing wealth.
The great demographic transition taking place in increasingly wealthy and enlightened countries is the consequence of rational decisions by thinking people, not of some primitive automated biological process.