Not a short answer, but worth discussing:
1) Grains are to some extent substitutes. That is people will substitute rice or wheat for corn on occasion. Not a major driver but real.
2) A high percentage of corn is fed to animals. When corn prices rise, meat prices rise. We are getting a larger global "middle class" (defining middle class very broadly in a way that would be poverty level in the U.S. or France.) In Maxist terms, mostly a somewhat more prosperous segment of the working class combined with some actual growth in the middle class in the sense that Engels would probably have recognized. So even when meat prices rise meat consumption increases. But at the same time people who were just barely able to afford meat do drop back and start consuming more legumes and grains.
3) Soybeans, palm trees and other crops for biodiesel do displace other grains. Rice is a special case, but not all land where rice is grown are natural wetland; so rice fields can in many cases be reverted to other crops.
4) All this is well known. Anticipation of a rise in food prices is what led food commodities to be seen as a "safe" investment. So anticipation of rising food prices led to massive investment in various futures derivatives, which in turn led to massive rises in food prices. Maybe I should not have used the term "fundamental" in that context. It depends on whether you think the judgement would have been right in the absence of a speculative bubble. I I think it would have, but barely. In short it was about 90% speculation, but without the bubble we would still have seen modest increase of about 10% the size that actually occurred. Normal hedging might still have caused the increase to happen before the actual supply demand mismatch because of the fact that it was anticipated.
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