World Agriculture Limits

L. David Roper
4 April, 2016



There are limits to how world agriculture can produce food. The "Green Revolution" circa 1950 enabled world population to grow to over 7 billion in 2013. Since then the growth in cereal yield has been due to application of natural (phosphate rock) and and artificial fertilizers (ammonium manufactured using natural gas and air and potassium made from potash) Since natural gas, phosphate rock and potash are non-renewable resourse, they deplete with some maximum extraction rate in the year range of 2030-2060. Therefore, cereal yield will peak in the future.Tthe following curve shows a fit to the world cereal yield data with two Verhulst functions. The peak at ~2060 is assumed to be symmetrical.

Also, ammonia production follows natural-gas extraction:

Then the cereal-yield per capita is:

This assumes that population levels off at 10 billion.

World arable land has leveled off and slightly fallen over recent decades. It is expected that it will continue to fall as land is taken for urban development and, eventually, as fertilizer becomes less available. Assuming that it levels off to 15% by year 2100.:

This assumes that population levels off at 10 billion.


The impending decline in extraction of phosphate rock and natural gas for the world will cause cereal yields to reach a peak at about year 2025 and then fall rapidly. If world population continues to rise to an eventuall 10 billion, there will be progressivly less cereal food for each person. Also, arable land will probably fall to some lower lever, further decreasing the cereal per capita.

Perhaps genetically modified plants will alleviate the problem somewhat.

The world fish catch may also decline.

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L. David Roper interdisciplinary studies

L. David Roper,
4 April, 2016