However, organic vegetables and cereal crops like maize and wheat had a lot lower yields compared to conventionally grown crops.

Ms. Seufert says the soil on organic farms holds water better, and that can reduce the yield difference. Also, organic farmers can improve their yields by making sure their crops get enough fertilizer. But increasing the nitrogen is harder to do organically, using just animal waste and crop rotations.

Organic farmers rotate food crops with plants that fertilize the soil. But while these "cover," or fertilizer, crops are growing, food crops have to be grown on other land. And if farmers use manure, they have to feed the animals that produce it, and that requires grazing land or crop land.

The United Nations predicts that world demand for food will grow seventy percent by the middle of the century. John Reganold is a soil scientist at Washington State University. He says no one should dismiss organic agriculture as part of the solution.

JOHN REGANOLD: "I think when people see these studies, their first reaction is, 'Well, my goodness, organic farming can't feed the world.' Guess what? Conventional farming cannot sustainably feed the world."

Mr. Reganold -- who was not part of the study -- says farming is increasingly a combination of organic and conventional methods.

JOHN REGANOLD: "And it's really going to be a blend of these, I think, more diverse systems that are going to save us."