Reduced flooding meant the arable land was not having its nutrients replenished, yet it was producing an extra two harvests each year.
As I said earlier, in Argentina, as elsewhere in Latin America, most of the arable land is privately owned by individual farmers and corporations.
Meanwhile, the arable land that we do currently have is becoming more damaged, with soil erosion now causing 40 percent of land degradation worldwide, the FAO says.
But the professor dismisses this, saying most of the arable land is cultivated already, while the rest supports indigenous woodland that is used for grazing cattle, or for wildlife, or both.
"On a per capita basis, China has half the arable land and a third to a quarter of the water than the global average, " says Merritt Cluff of the Food and Agriculture Organization in Rome.
Oscar Espinoza, an economist booted out of the central bank for reformist error, says state farms are still so inefficient that 85% of the produce at markets is grown by private farmers with 15% of the arable land.
The U.S., with the most arable land and developed agricultural production, stands to gain from these growing markets.
Too many Indians still rely on the land, and too much of the country's arable land depends on the vagaries of the monsoon.
The problem is, the amount of arable land per person is shrinking, says the FAO, from 0.38 hectares in 1970 to 0.23 in 2000, to 0.15 in 2050.
Madagascar may be a surprising example as it witnessed what is perhaps the most notorious land grab of all: a South Korean company was offered half the country's arable land a proposal that fuelled protests which eventually toppled the government who approved the deal.
In Britain the rental yield on arable land fell from 3.4% in the second half of 2003 to 1.75% in the first half of 2011, according to the Royal Institution of Chartered Surveyors.
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Second, Africa, with the world's most uncultivated arable land, has the potential to help end the global food security and nutrition crisis.
Expanding supply at the same rate will be difficult, because the amount of arable land under cultivation is growing by only a fraction of a percentage point each year.
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Which is a shame, because the U.S. has the largest federal water zone in the world, with more ocean area suitable for deep-water fish farming than the country has arable land area.
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In Madagascar this year popular hostility to a deal that would have leased 1.3m hectares half the island's arable land to Daewoo Logistics, a South Korean company, fanned the flames of opposition and contributed to the president's overthrow.
It suspects Kenya of using the EAC as a way of grabbing arable Tanzanian land on the cheap.
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China's Land Ministry has also warned that misappropriation of farmland has brought the country dangerously close to the so-called red line of 296 million acres of arable land that the government believes it needs to feed China's 1.34 billion people.
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By far the most ambitious of all the land deals in the past year was Daewoo Logistics' contract with the government of Madagascar to lease 1.3m hectares, almost half the country's arable land, to produce corn for Daewoo's home country, South Korea.
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Continuing wrangling has acted as a serious disincentive to further investment in the country's valuable arable land.
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Even today more than 80 per cent of arable land on the island is covered by cane fields.
With 60% of the world's unexploited arable land in Africa, Mr Conway says it needs to become more productive.
Nor is it just upon arable land that the bio-fuel industry is impacting.
We use the vast majority of our arable land to grow corn and soy commodity crops instead of actual food.
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China's demand for fertiliser is expected to be particularly buoyant as a result of its huge population and the poor quality of its arable land.
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James Janaway, who farms arable land in the Czech Republic and Romania as well as Hampshire, explains that farming in Eastern Europe is not plain sailing for Britons.
And while the FAO admits that some developing countries will be able to expand their arable land by as much as 12 percent, the downside is that a "considerable part" of this extra farmland will be a direct result of deforestation.
China faces an immense task to feed its population as breakneck industrial development has eaten into the country's supply of arable land.
Soil contamination has long been an issue in China, were rapid industrialization and lax enforcement of environmental-protection laws have resulted in the pollution of large swathes of arable land with a variety of heavy metals.
It means the 1939 kick seen in the nitrate "curve" above also incorporates some the delayed response from the land-use change brought about by the introduction of arable subsidies in 1917.
On the whole, only 3.5% of Africa's arable land is irrigated and about 9% of world fertilizer is used in the continent, according to the U.N.
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