IT IS spring and 100 censuses are in bloom. China, India and America all reported their 2010 results recently. Census-takers are in the field in Germany and Britain. These provide snapshots of current populations. Just as useful are demographic forecasts. These, too, have just appeared, from the United Nations' population division. Every two years, it updates its projections. For the first time, it has projected them as far ahead as 2100.

According to the UN, the world's population will surpass 7 billion at the end of October, a few months earlier than had been expected. The global total will continue to rise slowly until 2100, when it will flatten out at 10.1 billion. During the period of fastest growth, in the late 1980s, the world's population was rising by over 88m a year. Now annual growth is down to 75m and by 2050 it will be only 40m.

The engine of demographic change is fertility—the number of children a woman can expect to have, on average, during her lifetime. Fertility rates have been declining everywhere. This is why in previous projections the UN assumed fertility rates in all countries would eventually fall to 1.85. In 2008 it forecast that, by 2050, 111 nations would have rates between 1.85 and 2.1, the so-called “replacement rate” at which the population exactly reproduces itself.

The new projection uses a different method of calculating future rates, which takes better account of local trends. The UN now assumes more countries than before will be stuck either with high or persistently low fertility, reflecting, in part, the so-called “pause” in declining fertility taking place in Africa. As a result, the UN now says only 51 countries will have fertility rates between 1.85 and 2.1 by 2050.

This change does not affect global figures but has big implications for national ones. Today Nigeria is the world's seventh most populous country, with 158m people. If its fertility declines by no more than the UN assumes, by 2100 it will be the world's third-largest nation, with 730m people—the current population of Europe (see table). Rwanda's population would rise fourfold, to 42m, giving it a density five times that of Japan. China's population would fall by a staggering 450m from its peak in 2025, to 941m.

Some of these projections are incredible: they are warnings as much as predictions. Still, the general picture is probably right. Sub-Saharan Africa is by far the fastest-growing part of the world. Little larger than Europe or Latin America today, it will be bigger than either by the end of the century, and much more than half the size of Asia (it is now only a fifth). The consequences could be severe. The Sahel would be turned into a desert by the soaring population of west Africa. China's dependency ratio—the number of children and old people as a share of working-age adults—is rising faster than Europe's, which will surely require scrapping the one-child policy. And China and India will be riven by conflict if the sexual discrepancies the UN projects come to pass. In 2025 China will have 96m men in their 20s but only 80m women. India will have 126m men in that age group and just 115m women.

Overall, the world's population is increasingly stable. Below the surface, strains are growing.