In Nature, researchers disturbingly find that the yields of four major crops - corn, rice, wheat, soybeans- are slowing and even falling in various regions around the globe. From the abstract:

In the coming decades, continued population growth, rising meat and dairy consumption and expanding biofuel use will dramatically increase the pressure on global agriculture. Even as we face these future burdens, there have been scattered reports of yield stagnation in the world’s major cereal crops, including maize, rice and wheat. Here we study data from ~2.5 million census observations across the globe extending over the period 1961–2008. We examined the trends in crop yields for four key global crops: maize, rice, wheat and soybeans. Although yields continue to increase in many areas, we find that across 24–39% of maize-, rice-, wheat- and soybean-growing areas, yields either never improve, stagnate or collapse.

The Washington Post reports:

Study co-author Jonathan Foley, talking to Science Daily, suggests one possible explanation. “This finding is particularly troubling because it suggests that we have preferentially focused our crop improvement efforts on feeding animals and cars, as we have largely ignored investments in wheat and rice, crops that feed people and are the basis of food security in much of the world,” he said.

Consider the situation with corn around the globe. As the Nature study reports yields have stagnated or collapsed in several African countries. Currently African corn yields hover around 25 to 30 bushels per acre [PDF]. Even in 2012's bad drought year average U.S. corn yields were 122 bushels per acre [PDF]. Some researchers believe that it is possible to raise average corn yields in 20 years to 300 bushels per acre. This means that Malthusian starvation can be avoided if governments in poor countries allow their farmers to take advantage of modern crop technologies.