Saying that the poop from a dog fed on animal remains was as good for the soil as the combination of turning in the remains directly is not even close to correct. That's why your suggestion that I was in error in discounting the droppings of an Anitolian dog as insignificant is plainly silly. When I offered supporting data, you ignored them.
The fact remains: predatory animals are nothing but a cost to a shepherd. More predators is worse. Dogs don't come free. That's why the shepherds of Anatolia are poor. 1080 baits work, and can be rigged to be highly selective for canine predators of the flock.
Higher predator counts are only useful where herbivores are overpopulated, which is extremely rare. Most overgrazing problems are more due to bad timing and distribution of herbivores than their actual numbers, which is more indicative to the lack of people to do the herding than it is herding animals. Asking a shepherd to allocate more resources to feed protective animals instead of getting rid of the source of predation and bringing in more people is in general counterproductive for the entire system, especially the soil. More dogs won't work economically against unmanaged predator populations.
By all credible technical accounts as exemplified by the increasing range and population density of coyotes, nationwide, hunting has failed to reduce their numbers. It may teach them to shun people and it may teach them to steer clear of their assets but it won't make them go away.
And you ignored the obvious fact, which I stated, that all the animal matter put together is negligible compared to decaying vegetation.
I think that Jeff was right when he cited Islam as the reason Anatolian sheep herders are poor. I suspect that the NAZIs and the Soviets didn't have a particularly good influence on Turkish infrastructure and prosperity either.