There have been many famines throughout history. However, until the era of modern large scale transportation there was never the possibility of universal famine. But now with supertankers and huge container ships it becomes possible to move enormous quantities of food at very little cost per calorie of food; therefore, now it is a question of who has the money to purchase the food, as that is who will get to eat it rather than the local person who farmed the food. That farmer may not have enough money to purchase the food which he created. The farmers of the world no longer own the farms they work upon but are now largely paid workers and in a poor country they are paid very little. So little in fact that during a true world shortage where prices go very high the worker may not earn enough to feed himself. Seed companies have managed to create super seeds which are sterile and thus they prevent individual farmers from replanting what ever seeds may come their way. The local farmers may be living in small company towns and have no access to land upon which to grow food even if they had the seed, which they don’t.
With the exploding population and the degradation of the unfertilized land there will come a time when there must be a rebalancing of the humans to their resource base. This will be very painful socially and deadly to large numbers of people. Famines are nothing new. I came across this interesting quote about one famine on the Rhine river in Germany:
Hatto, in the time of the great famine of 914, when he saw the poor exceedingly oppressed by famine, assembled a great company of them together into a barn at Kaub and burnt them . . . because he thought the famine would sooner cease if those poor folks were despatched out of the world. . . . But God . . . sent against him a plague of mice . . . and the prelate retreated to a tower in the Rhine . . . but the mice chased him continually . . . and at last he was most miserably devoured. — Thomas Coryat: Crudities  from Bartlett’s Familiar Quotations p 426
There have been many other famines! One interesting statement by a Chinese emperor, (I have no idea where I read this) said the worst thing about being emperor was deciding during a famine who was to live and who was to die. There might be whole provinces of perfectly good people but there simply wasn’t enough food to go around and so whole groups of people must perish.
The modern Chinese government is aware of this coming famine and so they are purchasing up valuable farm land and legal rights to the food production of vast areas even here in the United States. Therefore there may come a time when there is famine here in the US even while food is being exported to China. This kind of export happened even during the Irish potato famine where the Ireland was exporting food to England where those people could afford to purchase it.
Periods of political unrest are likely to precipitate famines. This problem will become acute when the world consumption gets very close to the world production so there is little buffer. In that condition a little extra stress could trigger a lot of response which could and possibly would develop into a positive feedback situation. When that happened all sorts of protectionist things would happen and probably some of that would develop into high seas piracy and open warfare. At present cargo ships with hugely valuable cargoes traverse the seas unprotected, at least in a local way. They are presently protected by laws and by a sprinkling of combat ships to enforce the laws. However, when the true short supply comes to pass things will suddenly become much more difficult and world trade will suffer. Those localities which cannot defend themselves and produce sufficient food will suffer greatly. See Famine Early Warning Systems Network (FEWS NET). At present, while there is food available, the quickest way to ease a famine is to give people money and let them allocate it to maximize their access to food. This is obviously a very short term local policy and will quickly lead to political corruption. That policy probably can’t be implemented on a worldwide scale.
Perhaps a guess as to when the serious worldwide famine will hit is when about half of the money spent by the world’s population is spent on food. When food prices reach about that level many people will be unable to compete in the open market for food and serious food battles will ensue. I suspect that there will be little reduction in population or the fertility of humanity as a whole until that occurs. And when food becomes available again, if it does, there will be an immediate restoration of fertility to make up for lost lives.