Thomas Malthus has a lot to answer for. As the young cleric performed birth and death rites at the end of the 18th century, he began to notice that there were far more christenings than funerals. The insight led him to write his "Essay on the Principles of Population", a dark warning against the perils of unchecked human reproduction. Overpopulation was a looming threat because the masses were on a treadmill of sex and procreation, he argued. Eventually, the world would run out of food. People would die of starvation. It was nature's way of keeping populations in check.

This "dark and terrible genius" may have been right to pinpoint the idea that population was a potent economic force, says Fred Pearce, but he was wrong about almost everything else. And yet Malthus's ideas persisted among the elites for hundreds of years, spreading a fear of population time bombs and seeding ideas for eugenics programmes up to the last half of the 20th century.

By the 1950s, "population controllers" were everywhere, wringing their hands in NGOs and United Nations agencies, worrying about the coming Malthusian population catastrophe, looking to the poorest parts of the world to curb the population growth. Mass US-funded family planning programmes were targeted at a number of countries, with foreign aid and even trade sometimes dependent on meeting western targets. In India, the government put pressure on citizens to get sterilised, while China's one-child policy led to brutal forced abortions.

But the population-controllers' predictions of world famine in the 1940s and the 1980s never came true. Why? As the numbers grew, so agricultural technology improved. Norman Borlaug won a Nobel prize for developing high-yielding varieties of dwarf wheat in the late 1960s which, if fed with water and fertiliser, would grow large heads without falling over. By the mid-1970s, wheat and maize yields had doubled in places such as India. Some environmentalists have questioned whether this green revolution was such a good thing, tying so many of the world's peasant farmers to mechanised, energy-guzzling farming practices, and Pearce sees their point. "But would they prefer billions starving?" he asks. Even today, whenever famines occur, the problem is rarely an absolute shortage of food but an inability to buy it.

Yet warnings about overpopulation and impending famine persist. Pearce doesn't buy it. The global population replacement level, the number of births required to keep population stable, is 2.3 babies per couple. But thanks to increased access to contraception and improving education for women, actual birth rates have been dropping around the world. In the 1950s, it was between five and six; by 2008 it was 2.6. At the current rate, the world's fertility rate will be below replacement level soon after 2020. "Future historians are likely to record two great social trends in the last half of the 20th century," writes Pearce. "The dramatic decline in fertility and the transformation of the role of women in society. These two events are clearly linked."

Pearce does not gloss over the potential environmental problems that could occur if the world were overpopulated. But, though an environmentalist to the core, he puts people before planet, pointing out that the poorest three billion, around 45% of the total, are currently responsible for 7% of carbon dioxide emissions, while the richest 7%, around half a billion, are responsible for 50% of emissions. "A rural woman in Ethiopia can have ten children and her family will still do less damage, and consume fewer resources, than the family of the average soccer mom in Minnesota or Manchester or Munich."

Overpopulation is not the problem, he argues, but over-consumption: more specifically, over-consumption in the west. Ever the optimist, Pearce thinks we can solve this crisis if we recognise its seriousness. Today's technology could enable us to reduce our carbon footprints by 80% by 2050 (as the British government has committed us to do).

There are a lot of statistics in this book, but Pearce's narrative is rescued by his stories of people, whether groups of women in Bangladesh, families buying their first televisions in the slums of Mumbai, ghost towns in eastern Germany or an unexpected Somali community in Ohio. At one point he marvels at the crucibles of New York and London, these growing cosmopolitan hubs of the world, with people finding ways to live despite the obstacles thrown at them. If this is the future, says Pearce, bring it on.