From Fleeing Vesuvius. A history as big as they get.
I suppose we might call what is bound to happen at the beginning of the third millennium... a singularity.
E. O. Wilson spells it out as follows:
The global population is precariously large, and will become much more so before peaking some time after 2050. Humanity overall is improving per capita production, health, and longevity. But it is doing so by eating up the planet's capital, including natural resources and biological diversity millions of years old. Homo sapiens is approaching the limit of its food and water supply. Unlike any species that lived before, it is also changing the world's atmosphere and climate, lowering and polluting water tables, shrinking forests, and spreading deserts. Most of the stress originates directly or indirectly from a handful of industrialized countries. Their proven formulas for prosperity are being eagerly adopted by the rest of the world. The emulation cannot be sustained, not with the same levels of consumption and waste. Even if the industrialization of developing countries is only partly successful, the environmental aftershock will dwarf the population explosion that preceded it.
How many people can the world support for an indefinite period? Experts do not agree, but a majority put the number variously between 4 and 16 billion. the true number will depend on the quality of life that future generations are willing to accept. if everyone agreed to become vegetarian, leaving nothing for livestock, the present 1.4 billion hectares of arable land (3.5 billion acres) would supply about 10 billion people. If humans utilized as food all the energy captured by plant photosynthesis, some 40 trillion watts, Earth could support about 16 billion people. From such a fragile wold, almost all other life forms would have to be excluded.
Even if, by force majeure, the population levels off at well under 20 billion by mid-century, the relatively extravagant lifestyle now enjoyed by the middle classes of North America, Western Europe, and Japan cannot be attained by most of the rest of the world. The reason is that the impact of each country on the environment is multiplicative. It is dependent, in a complex manner, of the formula called PAT: population size times per capita affluence (hence consumption) times a measure of the voracity of the technology used in sustaining consumption. The magnitude of PAT can be usefully visualized by the "ecological footprint" of productive land needed to support each member of the society with existing technology. In Europe the footprint is 3.5 hectares (a hectare is 2.5 acres), in Canada 4.3 hectares, and in the United States 5 hectares. In most developing countries it is less than half a hectare. To raise the whole world to the U.S. level with existing technology would require two more planet Earths.
It matters little that North Dakota and Mongolia are mostly empty. It makes no difference that the 5.8 billion people in the world today could be logstacked out of sight in a corner of the Grand Canyon. The datum of interest is the average footprint on productive land, which must somehow be lowered if significantly more people are to achieve a decent standard of living. (Consilience 280-82).
But, voracious animals that we are, we will forever push to the borders of any margin that we achieve by eroding the environment and by developing technology. This will happen until we exhaust the oil reserves, and we are already at peak oil. Thereafter, the standard of living will decay for everyone, the available ecological footprint will shrink dramatically. Sudden and massive environmental decay will ensue, and then will follow the terrible wars and unprecedented catastrophes that are figured in the above diagram as an unnamable blank, as the missing peak of the story, before sustainable levels are reached in a post-Apocalyptic world. For the time being.
This unpleasant story has been rehearsed a number of times before it happens. It can be read, for instance, in Earth Abides, by George R. Stewart, with a difference. And with almost uncanny accuracy, in Jack London's The Scarlet Plague.