"You look at these numbers and think 'that's impossible'," said Carl Haub, senior demographer at the US-based Population Reference Bureau, whose latest global projections show Uganda as the fastest growing country in the world. Midway through the 21st century Uganda will be the world's 12th most populous country with 130 million people - more than Russia or Japan.

Startling as they are, the projections are feasible, and a glance at some of the variables shows why. A typical Ugandan woman gives birth to seven children - an extraordinarily high fertility rate that has remained largely unchanged for more than 30 years. Half the population is under 15, and will soon move into childbearing age. Fewer than one in five married women has access to contraception.

Taken together, the factors point to a population explosion that has demographers and family planning experts warning that efforts to cut poverty are doomed unless urgent measures are taken.

And not just in Uganda. Across much of sub-Saharan Africa the population is expanding so quickly that the demographic map of the earth is changing.

In the rest of world, including developing nations in Asia and South America, fertility rates have steadily declined to an average of 2.3 children to each mother. Most will experience only modest population growth in coming decades. Some countries, particularly in eastern Europe, will see their numbers decline.

But by 2050 Chad, Mali, Guinea Bissau, Liberia, Niger, Burundi and Malawi - all among the poorest nations in the world - are projected to triple in size. Nigeria will have become the world's fourth biggest country. Democratic Republic of Congo and Ethiopia will have vaulted into the top 10 for the first time. Nearly a quarter of the world's population will come from Africa - up from one in seven today.

"What's happening is alarming and depressing," said Jotham Musinguzi, director of the population secretariat in Uganda's ministry of finance, pointing out the clear correlation between high fertility levels and poverty. "Are we really going to be able to give these extra people jobs, homes, healthcare and education?"

Development may not be the only casualty of the population boom. With increased competition for scarce resources such as land, conflict is likely to increase. Consequences will be felt far beyond Africa: pressure to migrate abroad - already great - can only grow, experts say.

It is not yet a lost cause. Experience has shown that with strong political will population growth can be tackled in Africa. Southern Africa's population is expected to remain stable thanks to sustained efforts to cut fertility rates, although Aids-related deaths are also a factor. In 1978 Uganda's neighbour Kenya had the world's highest fertility rate - more than eight children per mother. The government made family planning a national priority and by the mid-1990s the figure was less than five.

But a number of African leaders, including Uganda's president, Yoweri Museveni, believe that their countries are under-populated, and that a bigger internal market and workforce will boost their economic prospects. In a speech to MPs in July Mr Museveni said: "I am not one of those worried about the 'population explosion'. This is a great resource."

Studies across Africa have shown that the desire for large families remains powerful. In Nigeria a recent survey revealed that just 4% of women with two children said they wanted no more.

Part of the reason is cultural, with bigger families seen as a sign of security. It is also because of fears of high levels of infant mortality.

Stigmas about birth control are another factor. Reproductive health experts say that a lack of information and of availability of female contraceptives plays a major role. In Ethiopia just 8% of married women use contraceptives. In Uganda more than a third of all women say they would like to stop - or at least stall - having children.

For that, donors must share in the blame, said Steven Sinding, director-general of the International Planned Parenthood Federation. He said the world had declared premature victory in the battle to cut fertility rates. Curbing population growth is not one of the UN's Millennium Development Goals, which aim to halve poverty by 2015, and barely features in the Commission for Africa report championed by Tony Blair.

"In sub-Saharan Africa population remains a very serious problem," said Mr Sinding. "Yet donors have completely shifted their focus to HIV/Aids and nobody is talking about it any more. Population is off the development agenda and that's a tragedy for Africa."

Elly Mugumya, head of the Family Planning Association of Uganda, agreed. In a tiny clinic in Kampala's Owino market, one of the biggest food and clothing bazaars in east Africa, he watched as six women - and two men - crammed into a tiny clinic to receive information about contraception.

Cost is not the problem in Uganda, he explained: a three-month supply of birth-control pills costs 15p; condoms are free for the men. It is access - in most parts of Uganda clinics like this simply do not exist.