Global warming has already harmed the world's food production and has driven up food prices by as much as 20% over recent decades, new research has revealed.

The drop in the productivity of crop plants around the world was not caused by changes in rainfall but was because higher temperatures can cause dehydration, prevent pollination and lead to slowed photosynthesis.

Lester Brown, president of the Earth Policy Institute, Washington DC, said the findings indicate a turning point: "Agriculture as it exists today evolved over 11,000 years of reasonably stable climate, but that climate system is no more." Adaptation is difficult because our knowledge of the future is not strong enough to drive new investments, he said, "so we just keep going, hoping for the best."

The scientists say their work shows how crucial it is to find ways to adapt farming to a warmer world, to ensure that rises in global population are matched by rising food production. "It is vital," said Wolfram Schlenker, at Columbia University in New York and one of the research team. "If we continue to have the same seed varieties and temperatures continue to rise, then food prices will rise further. [Addressing] that is the big question."

The new research joins a small number of studies in which the fingerprint of climate change has been separated from natural variations in weather and other factors, demonstrating that the effects of warming have already been felt in the world. Scientists have shown that the chance of the severe heatwave that killed thousands in Europe in 2003 was made twice as likely by global warming, while other work showed that the floods that caused £3.5bn of damage in England in 2000 were made two to three times more likely.

Food prices have reached new record highs this year, and have been implicated as a trigger for unrest in the Middle East and Africa. A rising appetite for meat is a critical factor, said Wolfram. "We actually have enough calories to feed the world quite comfortably, the problem is meat is really inefficient," as many kilogrammes of grain are needed to produce one kilogramme of meat, he said. "As countries get richer and have a preference for meat, which is more expensive, they price people in poorer countries out of the market."

"The research provides evidence of big shifts in wheat and maize production," commented Prof Tim Wheeler at the Walker Institute for Climate System Research, Reading University, UK, who added it had involved "heroic" statistical analysis. But he said that, while long-term climate change impacts were another pressure on food prices, short-term price spikes were linked to extreme weather events, such as the Russian heatwaves and wildfires in 2010.

The study, published in the journal Science, examined how rising temperatures affected the annual crop yields of all major producer nations between 1980 and 2008. Computer models were used to show how much grain would have been harvested in the absence of warming. Overall, yields have been rising over the last decades and the models took this into account. The scientists found that global wheat production was 33m tonnes (5.5%) lower than it would have been without warming and maize production was 23m tonnes (3.8%) lower. Specific countries fared worse than the average, with Russia losing 15% of its potential wheat crop, and Brazil, Mexico and Italy suffering above average losses. Some countries experienced lower production of rice and soybeans, although these drops were offset by gains in other countries.

The losses drove up food prices by as much as 18.9%, the team calculated, although the rise could be as low as 6.4% if the increased carbon dioxide in the atmosphere strongly boosts plant growth and yields - a factor that is not well understood by scientists.

Global food prices have risen by about 200% in recent years, says Schlenker. Other causes of the rise are the increased demand for meat and the diversion of food into biofuels. Nonetheless, the researchers conclude that the negative impact on crops overall is "likely to be incurring large economic and health costs".

The US, which has the world's largest share of overall production, stood out in the analysis because it appears to have lost no production to climate change as yet. Schlenker said this was because the rise in temperature there was very small compared to other parts of the world. This was perhaps due simply to luck with the weather, or the cooling influence of aerosol particles, such as soot, that blocks warming.

"US farmers are having a good time in the sense that their yields have not been impacted much and prices have been pretty high, so for them it has been pretty profitable," he said. "But most climate models predict that eventually the US will warm."

Adapting farming to climate change could involved moving to cooler areas as existing areas warm, said Schlenker, but often soils are poorer in the new locations. He highlighted the potential of biotechnology - genetic engineering - to develop new crop varieties that are more resistant to heat, but said the potential remains unproven. "What happens over the next 20 years depends on how optimistic you are about finding those extra ways of adapting."