The NECSI results are summarized in this figure. The black line shows nominal food prices; the vertical red lines are incidents of political unrest, many of them concentrated in the "Arab Spring" of 2011. The paper develops a model and a price threshold at which political unrest is likely to occur. Based on current predictions of price increases (US corn prices reached record highs in August, but have retreated somewhat since then), the model predicts that another round of incidents will begin in the region in October, 2012.
What's driving the price increases? One large factor is the drought that spread across much of the US grain-growing regions this year (weekly maps showing the extent can be found here). The higher prices reflected a belief that US grain output would be significantly smaller (although today the USDA announced that the corn crop may not be quite as bad as has been previously feared). A second factor is the use of corn as a feedstock for producing ethanol for use as a transportation fuel in the US. The US has a renewable fuel standard that requires an increasing total amount of ethanol to be blended into gasoline supplies. While the overall situation regarding ethanol is complex , the ethanol industry will still purchase large amounts of the corn crop this year.
The NECSI work provides a nice formal mechanism quantifying something that I find myself saying too often: "Drought in the US means that Africa starves." To a lesser extent, you can replace the US in that statement with Argentina or Australia. The reduced US grain crop follows relatively poor harvests in both Argentina and Australia, two other major grain exporters. You can also replace drought with increased domestic demand and get the same result. US ethanol mandates may be fine domestic policy -- although there are lots of analysts who disagree with that -- but terrible global policy. And not just in terms of millions of starving people. The MENA countries produce and export a lot of oil. Political unrest generally disrupts activities like oil production (oil pipelines are easy targets for dissidents). High prices for global grain exports could conceivably lead to higher prices for global oil exports.
Aren't complex dynamic systems, filled with feedback loops and time delays, fun?
 The penalties for failure to meet renewable fuel standard requirements are fines; companies may choose to pay some fines rather than very high prices for ethanol. In previous years the oil industry blended more ethanol than required, accumulating credits that could be used to offset a shortfall and avoid fines this year. Blended ethanol raises the octane of the final gasoline product; there are minimum octane requirements; the alternatives to ethanol may be more expensive, which would cause the oil industry to continue to use ethanol even at higher prices. Based on the years I spent working for large corporations, I can guarantee that someone -- probably many someones -- is busily trying to solve an optimization problem that minimizes the costs of all the factors in aggregate.