Dogs aren't. You were talking about dog poop as equivalent to animal remains as fertilizer. You are totally wrong.
I would think that Anatolian sheep dogs killing predators would mediate that result. YMMV
Anatolian sheep dogs are equivalent to predators in terms of their effect on soil.
You were talking about the land management skills of Anatolian sheep herders. They have two choices. Live with the predators that will kill a percentage of their herbivore sheep or use dogs to prevent livestock loss. Either way there will be a canine species on the land. With the sheep dogs there will be more herbivores.