What memes it triggers and what complexi are involved are culture-dependent, but the meme itself is not. I would suggest that what animals have is Behaviour. I would humbly suggest that all humans have is Behaviour. Its not the act we're concerned with, its the mechanism. Then we don't have memes.
Memes are the specific act.
You are the first person I have come across that has said this. Once you accept that they exhibit some kind of culture you've lost your footing and are headed to the slippery slope of culture as spectrum not binary. I still don't.