Almost half of humanity now lives in countries where population growth is set to end over the next few decades. In many it may be even replaced by a decline - and in some has already begun to do so.
The shift to using contraception and having smaller families which has spread around the world during the past three decades is one of the most momentous developments in history and pre-history, ranking alongside the discovery of agriculture and writing.
"It is one of the greatest human achievements ever," said Joseph Chamie, director of the United Nations Population Division. "It has bought many poor countries time in which to address huge social, political and environmental problems."
Within 20 years, two-thirds of us are forecast to live in nations were the average woman has 2.1 children or less - the replacement fertility rate below which populations eventually start falling.
China, with more than one fifth of the world's population, is in this "under 2.1" club already, thanks to its drastic "one child" policy. So is the entire industrialised world.
The UN's Population Division forecasts that, by 2016, two other Third World giants, India and Indonesia, and several smaller ones, will also join the club.
The rate by which the Earth's total population is rising each year has also begun to fall. In the second half of the Eighties, the numbers rose by 87 million each passing year - the highest ever. In the Nineties, that dropped to 81 million a year (equivalent to an extra Germany), and this fall is set to continue in the next century.
This century opened with about 1.65 billion people on Earth. Population is expected to have almost quadrupled by the close, reaching 6.09 billion.
The last third of the 20th century has seen politicians and thinkers preoccupied with the threats posed by rapid population growth on a finite planet. The first third of the next will see more and more nations struggling with the consequences of stabilisation and decline. The most worrying of these is a rising proportion of people beyond retirement age, and the accompanying high pension and healthcare costs.
Decline has already begun in former Warsaw Pact countries, where economic collapse and uncertainty following the end of Communism has made many women postpone or abandon having children. In Russia, an abrupt jump in male death rates linked to alcoholism has made the situation worse.
The UN says the populations of Italy and Portugal are also starting to decline. Italy's fertility rate is the lowest at just 1.2 children per woman, and the UN forecasts its population will fall by 4 million by 2020.
The latest estimate from Britain's Government Actuary, published a few weeks ago, has the United Kingdom's population rising very slowly from the current 59 million to a peak of just under 63 million in 2031, before starting a slow fall. France's population is expected to overtake the UK's within two years, leaving Britain in third place in the European Union.
While decline may already have started in some European countries, recent big falls in fertility and population growth rates in developing countries are far more important in slowing a rising world population.
Even so, population will increase by almost as much in the next century as it has in this, according to the UN's "medium variant" forecast; its best guess. This is largely because of the long time lags - up to 40 years - involved in halting growth once fertility rates start to come down.
The other reason is that there are still 50 nations, nearly all in Africa and the Middle East, where families of at least six children are the norm and population growth is still over 2.5 per cent a year. At that rate, numbers double in just 28 years.
The UN is about to publish new long-range forecasts for global population. Under the medium variant, it will have reached 9.4 billion by 2050 and 10.4 billion by 2100. By then it will have virtually stabilised. Under its low variant projection, population will climb to 7.7 billion by 2050 then fall back to 5.6 billion by the end of the next century.
Professor Ian Diamond, head of population studies at Southampton University, said: "In some areas there have been spectacular declines in family size." In Bangladesh, the fertility rate is estimated to have fallen from 6.2 children per women to 3.4 between the early Eighties and the early Nineties.
But he and other leading British demographers pointed out that falling fertility need not be a one-way ticket. Fertility rates were very low in Western Europe between the two world wars. Afterwards they rose rapidly to produce the post-war baby boom, then sank again.
The American Professor Paul Ehrlich, whose 1968 book The Population Bomb ignited three decades of concern and debate, told The Independent: "We're not out of the woods yet. But this is cheering news in a world where we can't support today's population at a decent level, let alone billions more."Reuse content