Half of the world's population could face severe food shortages by the end of the century as rising temperatures take their toll on farmers' crops, scientists have warned.

    Harvests of staple food crops such as rice and maize could fall by between 20% and 40% as a result of higher temperatures during the growing season in the tropics and subtropics. Warmer temperatures in the region are also expected to increase the risk of drought, cutting crop losses further, according to a new study.

    The worst of the food shortages are expected to hit the poor, densely inhabited regions of the equatorial belt, where demand for food is already soaring because of a rapid growth in population.

    A study in the US journal Science found there was a 90% chance that by the end of the century, the coolest temperatures in the tropics during the crop growing season would exceed the hottest temperatures recorded between 1900 and 2006.

    More temperate regions such as Europe could expect to see previous record temperatures become the norm by 2100.

    "The stress on global food production from temperatures alone is going to be huge, and that doesn't take into account water supplies stressed by the higher temperatures," said David Battisti, at the University of Washington, who led the study.

    Battisti and Rosamond Naylor, at Stanford University in California, combined climate models from the Intergovernmental Panel on Climate Change (IPCC) and historical examples of the impact of heatwaves on agriculture, and found severe food shortages were likely to become more common.

    Among the periods they examined was the record heatwave across western Europe in 2003, which killed an estimated 52,000 people and also cut yields of wheat and fodder by a third. In 1972, a prolonged hot summer in south-east Ukraine and south-west Russia saw temperatures rise by between 2C and 4C above the norm, driving down wheat and coarse grain yields for the whole of the USSR by 13%. The disruption affected the global cereal market for two years.

    Naylor, who is director of food security and the environment at Stanford, said the study emphasised the need for countries to invest in adapting to a changing climate. To develop new crops to withstand higher temperatures could take decades, she added.

    "When we looked at our historical examples there were ways to address the problem within a given year," Naylor said. "People could always turn somewhere else to find food. But in the future there's not going to be any place to turn unless we rethink our food supplies."

    The tropics and subtropics, which stretch from the southern US to northern Argentina and southern Brazil, from northern India and southern China to southern Australia, and cover all of Africa, are currently home to 3 billion people. Future temperature rises are expected to have a greater impact in the tropics because the crops grown there are less resilient to changes in climate.

    According to the study, many local populations now live on less than £1.30 a day and depend on agriculture. The need for food is due to become more urgent as populations are expected to nearly double by the end of the century.

    "When all the signs point in the same direction, and in this case it's a bad direction, you pretty much know what's going to happen," Battisti said. "You're talking about hundreds of millions of additional people looking for food because they won't be able to find it where they find it now.

    "You can let it happen and painfully adapt, or you can plan for it. You could also mitigate [climate change] and not let it happen in the first place, but we're not doing a very good job of that."

    Naylor added: "We have to be rethinking agriculture systems as a whole, not only thinking about new varieties [of crops], but also recognising that many people will just move out of agriculture, and even move from the lands where they live now."

    In many countries, a combination of poor farming practices and deforestation, exacerbated by climate change, may steadily degrade soil fertility, leaving vast areas unsuitable for crops or grazing. In 2007, scientists warned that poor soil fertility meant a global food crisis was likely in the next half-century.

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