Two years ago, as the world's population surpassed the high mark of 6 billion, scientists were sounding alarm bells over unchecked population growth, especially in the developing world.
But now there is a growing consensus among demographers over a new forecast: that women in nations with 80 percent of the world's population will begin to limit their families to two children or fewer.
Before the century ends, the number of humans likely will start to shrink, reckons James Chamie, director of the United Nation's population division. That will be a "momentous" reversal in direction.
A combination of international family-planning programs, growing prosperity, and better education of women is widely credited with reducing fertility rates worldwide.
Last year, UN experts projected that the population would grow relentlessly until it reached 9.3 billion in 2050, and only in 2150 would it finally stabilize at about 10 billion. Many experts foresaw risks of overcrowding resulting in famine, spreading disease, other catastrophes, and political unrest.
For years, most parts of Europe and Japan have seen a declining birthrate. Now, demographers see this trend taking hold in some 74 "intermediate-fertility countries" where women now have about three children on average - not the five-to-six children common in many African nations.
Intermediate-fertility countries include Brazil, the Philippines, Syria, Israel, Malaysia, Indonesia, and Egypt.
The list includes India, with its more than 1 billion people.
"Total fertility is falling in virtually all of India's states," says Tim Dyson of the London School of Economics in a paper prepared for a UN conference of about 65 experts, starting today in New York, to discuss the new population projections.
The other population giant - China, with 1.2 billion people - already has a fertility rate below the replacement rate. Russia, another populous nation, has a declining population. So has Roman Catholic Poland.
Once fertility falls below the replacement rate, it takes a generation or two for the population to cease growing and then decline.
UN experts are not alone in their outlook for world population.
A study headed by Wolfgang Lutz of the International Institute for Applied Systems Analysis in Vienna puts the world's population peak at 9 billion in 2070.
Only four years ago, Dr. Lutz figured population would peak at 10.5 billion to 11 billion in 2075.
To Nicholas Eberstadt, an economist at the American Enterprise Institute in Washington, "expert opinion is jogging behind the reality" of falling fertility patterns, even in developing countries.
Some experts are concerned that the new population projections may discourage the financing of family planning in developing countries by the world's wealthy nations.
But 9 billion is still a 50 percent rise in world population, says Sally Ethelston, a spokeswoman for Population Action International in Washington. "The rationale for expanding family-planning access still exists."
Population projections far into the future are, to a considerable degree, guesswork. Nonetheless, views of demographers have shifted rapidly in the past few years.
Most maintain that as countries become more prosperous and women's literacy rates rise, women choose to have fewer children.
But even in some poor nations with high illiteracy, fertility rates have been falling. In Tunisia, with nearly 40 percent illiteracy among women, the fertility rate has fallen to the replacement level.
Women in such countries, perhaps influenced by family-planning information, also are deciding to have fewer children. "In most places of the world, family planning is the norm," says Mr. Sanderson, of State University of New York at Stony Brook. "The average Bangladeshi woman knows seven methods of contraception."
There are still nations in Africa and the Middle East where average fertility rates are still high. But their weight in global terms isn't great enough to prevent the world's population from gradually moving toward stabilization and perhaps even decline.
This decline has special significance, says economist Warren Anderson. "It really means that human beings are able to control their fertility before it reaches the carrying capacity of their environment."