I watched this TED-Talk just now and had to post it:

It led to some very active criticism afterwards, but unfortunately with many false and unobjective arguments.

There are many posts to be found to point this out, for instance

this videothis documentthis open letter and this article.

In my opinion, this theory is sound and is proven many times. And it explains a mystery I lost sleep over: how on earth did the planet survive the plethora of grazing animals (among them masses of ruminants) and their GHG emissions before mankind came along? A cue to a solution I found in this study about nitrous oxide, but I could not harmonize that with the methane from the burping cattle or buffalo (not all grazing animals were horses back then).

But now more about the theory, that intelligently managed grazing can prevent the soil from degradation and the grassland from desertification, save the humus in the soil, which can store water and carbon dioxide, from erosion.