Let's assume that normally 2/3 of the grain calories are fed to livestock. Then we get a massive crop failure and global yields are 1/3 of expected. Price of grain goes up, farmers can't afford to feed their cattle so slaughter their breeding stock and the price of meat goes down. In the short term meat consumption goes up to counter-act the loss of grain calories due to the failure. In the medium term the smaller amount of livestock eating grain means humans eat a higher percentage of the grain grown. In the long term it's a new harvest and cycles repeat...