A vestigial form of wolf behaviour in the domestic dog is present when they push their food bowl around, or as is demonstrated in the video on this page they push at it rather ineffectually with their noses. The behaviour in the video is at the very bottom end of vestigial behaviour. And the behaviour I am referring to is a wolf burying their food to come back to the next day if they have a surplus.
So if a pet dog is overfed there is a surplus for them and therefore they want to bury it and they end up with this vestigial, half-baked action which is pushing the food bowl around. It’s meant to cover up their food but of course it does not achieve this objective. The dog fairly quickly gives up. The dog is telling his owner that they have been given too much food.
Instinctively they are protecting the food from an imaginary scavenger and want to come back to it at a later date. Dog sometimes bury bones for the same reason. Domestic dogs can’t bury wet cat food as if they are carrying a chunk of flesh in their mouths but if given a bone instinctively it is big enough such that they can’t eat it all in one go and therefore they want to bury it to come back to it.
In the wild, wolves may engage in this burying action when they’ve eaten their fill on a big prey animal. They dig a hole with their front feet while clasping the meat in their jaws. When the hole is big enough they drop the meat into the hole and push the earth back over the food with their snouts. It is this last action which is replicated in the “food bowl pushing exercise” described above.