> a mutation in wolves may be the beginning of dog breeding

It is (dog breeding is better called "unnatural selection"), but needs to be backed up by training. A domestic dog is something like three meals away from reverting to wolf, or less in the case of carnivorous penis extensions carefully mishandled macho dogs. It's a complicity, where humans selected domestic wolves, amongst other things, for susceptibility to training, while domestic wolves initially selected humans for the ability to train by granting them better hunting success.