The Pompeii "Cave Canem" dog appears to be executing the "bow" behavior modern domestic dogs display when soliciting playtime. Was this likely an intended tongue-in-cheek joke, or simply a disconnect with our understanding of canine behavior today compared to how it was viewed in antiquity?
Your question goes a bit more in depth than mine, but I asked something very similar a few years ago. Hopefully we get some more answers because I think this is quite fascinating.