Historically, Allan explains, we have blamed the process of desertification on trying to extract too much from the land, and focused on resting it (in particular by protecting it from over-grazing). However, the ironic result of efforts to rest land (in climates that are not continuously humid, which is a large percentage of the earth) is that it actually accelerates desertification!
As he explains, we must recognize that plants developed alongside grazing animals, which developed alongside predators, and despite their apparent competition with one another, the cyclical interactions among them are effectively symbiotic, allowing them to all thrive together where none could alone. We humans have disrupted this process, and then foolishly tried to right it by entirely inadequate methods of human-engineered technology, disregarding the complexity of the processes involved. We have neglected what he says is our only remaining hope, which is to turn the problem over to natural (well, almost) processes in order to restore the balance.
Allan proposes, in his February 2013 TED Talk below, that what we need to do is use livestock, moved in ways that mimic their natural herding and grazing patterns (based in the context of predatory grasslands), to recreate the natural processes that allow plants to flourish. This involves periods of grazing which actually cause plants to go through important growth cycles (explained below in another TED talk by Tony Lovell) and encourages natural biological decay, with added animal waste fertilizer from the animals, as they trample the plants but then quickly move on (once their food source is covered in urine and dung!).
I also see this perspective echoed in the work of another individual who has worked extensively with Savory, Abe Collins. Collins is a soil-focused cattle grazier and sustainable farm designer who has seen impressive results with methods along the lines of Savory's. In his own talks, Collins relates the importance of topsoil development, dependent on biodiversity, as crucial to local economies, particularly with regard to water retention and the local watershed properties, and solar energy potential. You can also check out his work at the Soil Carbon Coalition website. They are promoting a new book, which I've purchased and is on my stack: Cows Save the Planet (and Other improbable Ways of Restoring Soil to Heal the Earth).
Who knew ethically raised grass-fed meat was more sustainable than vegetarianism??