Peak Farmland?

A recent study concludes that world food production will be able to be completed on fewer acres than is now farmed as crop yields increase and population growth rates decrease:

Our analysis encompasses the leverage on cropland exerted by parents, workers, consumers, and farmers. Since 1960, their combined behaviors havespared areas of land that are immense when compared with what continuation of birth rates, appetites, yields, and other factors might have led us to expect.  India and China alone have spared an area more than three times the size of France or a dozen times Iowa. Absent the slowing population growth, Evolving tastes, and improving agricultural practices, unimaginable destruction of nature would have occurred.
The past 50 years have already witnessed important peaks for environment and resources. The rate of increase of world population peaked arounnd 1970 and has slowed considerably since then. Peaks of forest destruction also have passed with a transition from less to more forests in many countries and regions. By the 1980s wooded areas in all major temperate and boreal forests were expanding. After 1990, growing stock expanded in many forested countries (Kauppi et al. 2006), and during 1990–2010 the density of forests grew in all world regions, albeit unevenly (rautiainen et al. 2011). Like farms and their crops, the productivity of forests providing wood products has risen. meanwhile consumption has fallen as e-readers replace paper and as demand for other wood products, such as railroad ties and telephone poles, has declined. As we hinted above, peaks of farmers’ use of nitrogen and water may also have passed.

Hopefully they are right.  I'm not as confident, and I'm also concerned that climate change may hurt our prime farm land.  This does serve as a warning that the current boom times won't last.  I've been expecting that.