Yields
Grain yields per acre (or hectare or square mile) have begun to plateau in major producers, starting shortly before 2000. In China, rice yields are poised to plateau.
A view across ALL cereal grains for ALL leading producers suggests a worldwide yield plateau from 2008 thru 2012. A 7% increase followed in 2013, 4/5 of it from a US rebound to a record harvest.
Perhaps total production can be sustained more by adding acres.
It is not clear how much of the yield plateau was due to climate change, how much to running out of more technical changes (the green revolution), how much to groundwater depletion, and how much to other factors. Groundwater depletion follows from warming, as farmers try to maintain irrigation.
The effects of the 2012 drought in the US and the 2010 drought in Russia are visible. (Both nations had record heat.) So are the effects of the 2012 floods in Britain. The reason for the 2012 drop in Bangladesh is not clear.
Note that yields for wheat top out at 8 kilograms per hectare (Britain, France, Germany graph above), while rice yields top out at 5 (China & Japan graph above).
Thus rice growers (Bangladesh, Vietnam, India, etc.) harvest fewer kg per acre than wheat growers (France, Germany, Britain, etc.). A change in a nation's mix of crops can also affect mean yield per acre.
Many studies have bee done on crop production as a function of temperature.
Section Map: Food Impacts