From the article:

Reaching "peak agricultural land" does not mean the problem of deforestation is solved. Growing demand for products like beef, soy, cocoa and palm oil has put increasing pressure on land across South America, South East Asia and Africa. In the last decade, the world lost an area of tropical forest twice the size of Spain.

Still, acre-for-acre across the world there has been yet more farmland abandonment, driven by reforestation in Europe and North America and the abandonment of pastures in Australia and Central Asia.

There are a few different reasons for this. Firstly, farming has become more efficient. The use of improved seeds, fertilisers, pesticides and irrigation has in recent decades vastly increased how productive the land we farm is, doubling, tripling and even quadrupling yields depending on the crop and country. Since 1961, FAO data shows that productivity increases have spared 1.8 billion hectares (4.4 billion acres, or around 35 Spains) of land from being brought into cultivation.

We've also squeezed more efficiency improvements in animal agriculture through intensive farming, productive animal strains and optimised feeding regimes. As these systems intensified, lower productivity lands have been abandoned in many countries.

But it's not all about intensification. We have also replaced some land-hungry crops with near-landless alternatives: wool and cotton have been to a major extent replaced by synthetic fibres; tobacco is rapidly being replaced by synthetic nicotine; flavourings in food such as vanilla are now largely synthetic; the global caffeine (although not coffee) market is dominated by production in labs; synthetic sweeteners have replaced substantial amounts of sugar cane and sugar beet. We estimate that these synthetic substitutes have spared over 110 million hectares (two Spains) of land from farming.

One particularly striking example is the shrinkage of the global wool industry. Production has fallen by around 50% from its peak in 1990. Grazing lands in Australia, New Zealand and Argentina – countries that use to be amongst the largest wool producers – have declined by 25%. Large areas of pasture have returned to nature, some of which is actively protected and home to unique species. For example, the huge 70,000 hectare (173,000 acre) White Wells sheep farm in Australia is now the Charles Darwin Reserve, home to 700 species of plant and 230 animals. Another 70,000 hectare (173,000 acre) area in Argentina, previously the Chacabuco sheep ranch, is now a nature reserve and home to the rhea or ñandú, an uncommon bird related to ostriches and emus. There are many similar examples worldwide.

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Based on historical trends and future forecasts, it is likely that crop yields will continue to increase globally on average. In 1961, we produced just over one tonne of grain per hectare (0.4 tonnes per acre). We now produce over four tonnes per hectare (1.6 tonnes per acre).

Yields are still increasing in most crops and countries, with more food grown each year on the same land, while fallow periods (time where land is left bare) are decreasing. However, a critical unknown is climate change: depending on how much climate action we take, warmer, wetter and more extreme climates could negatively affect yield growth, particularly if we don't adapt and develop more climate-resilient crops.

While global meat consumption is rising rapidly, driving increased demand for land, we are seeing evidence of consumers swapping from beef and lamb – which use substantial amounts of land per kilogram – to pork and poultry, which use a lot less land. In Europe we have seen a 20% reduction in beef and lamb and a 20% increase in poultry and pork since 2000, sparing around 20 million hectares (49 million acres - around one Spain) of land.

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New technologies in farming could also make food production yet more efficient. Globally, food grown in greenhouses, for example, is rapidly expanding. Greenhouses can produce much more food than open fields: Dutch greenhouses, for example, can produce around 500 tonnes of tomatoes per hectare (200 tonnes per acre), compared with 30 tonnes per hectare (12 tonnes per acre) in open fields.

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However, as we free up land, other competing land uses may take its place. Urban land represents around 1% of global area, and it seems unlikely this will replace farmland at scale (although in areas with high demand for housing and infrastructure it could). A major risk however is that plantation forestry and biofuels will further increase in area. Historical environmental policies have created demand for biofuels and wood-based products as sustainable alternatives, but much scientific research has called for better solutions. For sustainable change, new solutions should not carry these trade-offs. Electric cars, for example, are a better alternative to biofuel-based cars