Sexual reproduction being a physically binary process, it is not surprising that a Malthusian law follows. The demographic philosopher, Thomas Malthus, at the age of 23 (mmm... I had just got my first degree by then; Ph.D at 26! Higher Doctorate, D.Sc, at 43!) predicted that the human numbers would increase geometrically by a series of 2^n, i.e. 1, 2, 4, 8, 16 etc., whereas food supply can increase arithmetically, i.e. 1, 2, 3, 4, 5 etc. Put another way, we are more productive in reproducing ourselves than in feeding ourselves. Malthus predicted that crops would fail, that there would be a very poor harvest, the cost of food would soar and some would starve.
Indeed, in 1789, the cost of bread almost doubled as a consequence of the kind of awful British weather we saw in the last summer and nine years later Malthus published his "Essay on the Principle of Population", in which he came to the conclusion that "misery" (famines and epidemics of disease) and "vice" (contraception, abortion and alcohol abuse) would provide a check on the rise in population.
The population of the world is close to 6.5 billion now, or about 6 times what it was when Multhus was writing, and so there was not a huge die-off as he anticipated. Not only that but the number of daily calories we are all getting per capita were 2,700 in the 1990's, up from 1,848 during the French Revolution. The mean income per capita too has risen by a factor of eight, life expectancy has increased on a worldwide basis from 28 to 67, and while in the late 18th Century, the average British man was 5 feet 5 inches tall, now he stands at an average five feet nine inches. So abundant is our food supply now that a fifth of all Americans can be classified as obese, and with the European nations such as the UK following a close suit.
The usual reason given for the failure of Malthus' prediction of a calamitous collapse of food and population is the "Green Revolution" characterised by a succession of agricultural advances which led to greater and more efficient production, and now the current generation of GM crops. Despite the forces of "vice" which have as Malthus predicted kept population growth at a roughly arithmetic rather than a geometric rate, and at a level where food production could keep pace with its increase, the question remains of whether we will be able to feed the world by 2050, when it is thought there may be 9 billion of us on the planet. The term "peak oil" comes to mind, since modern agriculture is underpinned in large measure by resources of oil. As the oil becomes more expensive and there is less of it on the world markets, food production could be hit hard, with according food shortages.
There might be a shortage of grain especially, especially, as more of it is grown for the ethanol industry, and we are approaching a situation where the production of fuel crops is coming into direct competition with growing crops for food, since, certainly in Europe, the amount of arable land is limited. The UK produces only about two thirds of its own food and surely, as transportation is curbed by the lack of oil to run planes and ships, becoming as self-sufficient on food production for each nation within that nation, must be a priority. World food prices have soared of late, and it appears that capital cereal production has passed its peak (in the mid 1980's); it is noteworthy too that the International Monetary Fund has recorded a 23% hike in food prices during the last 18 months. In Britain food inflation now runs at 4.8%, while national inflation is 2.4%. It is worse than this for some kinds of food, and for example, the inflation rate for fish is nearer 11% and for potatoes it is about 10% - good that our national dish is no longer fish and chips but chicken tikka masalla!
We may well struggle to maintain the arithmetic growth in world population to 9 billion by 2050, as a combination of food shortages per se and the competition between food and fuel crops, the lack of oil to run farms and indeed gas from which chemical fertilisers are made to increase agricultural yields per hectare of land. Malthus may have been fundamentally correct in asking 200 years back, the question: "whether man shall henceforth start to shift with an accelerated velocity towards illimitable, and hitherto unconceived improvement, or be condemned to a perpetual oscillation between happiness and misery."
I guess something has to give eventually, since resources of food, fuel and indeed water are not limitless.
"Worry about bread, not oil," By Niall Ferguson: http://www.telegraph.co.uk/opinion/main.jhtml?xml=/opinion/2007/07/29/do2901.xml