Does a cow trade for the grass it eats, or a fox for lambs it takes...

Well, actually, yes. Grass, like all plants, requires carbon dioxide (which the cow breathes out) for photosynthesis. Also, the cow excretes nutrients vital to the continued existence of the grass and when it dies returns what it took from the grass (for the continued existence of the cow) to the grass by its decomposition -- just as you and I will.

You, me, and the fox are a bit more complicated, but carnivores (the fox) eat herbivores (the lamb). Ultimately, we all thrive on the grass, and we all "pay back" to the grass by our excretion and eventual decomposition.