This provocative blog says “no.” I think Linus Blomqvist makes some good points about “crying wolf” (overstating the importance of wild-species diversity to some ecosystem services), but I think he over-states the extent to which “many wild animals, while priceless in the aesthetic and spiritual sense, might be dispensable in the material sense.”
Wildlife-related tourism provides major material benefits in many areas, but that’s not my main point.
Every wild species has evolved a bunch of sophisticated strategies to address the challenges its ancestors faced (navigation, defense, resource shortages, temperature extremes, etc., depending on the species). Sometimes these useful strategies can be transferred to crops, genetically. Biomimicry, which copies wild-species strategies rather than genes (often to solve engineering problems), may provide even greater benefits. Neither of these benefits necessarily require as many bison or whatever as the earth once had, but we at least need to maintain viable population sizes.
My book argues that past evolution has improved wild species more than it has improved natural ecosystems, so I’m skeptical of the idea that agricultural ecosystems should blindly copy natural ones. But we can’t analyze most strategies of wild species using DNA samples or populations in zoos. We need to study them out in the ecosystems where they evolved. For example, wild potatoes in a greenhouse might still release a particular chemical when wounded, but it took observation in the wild to see insect pests fleeing in terror (Nature 302:608-609).