I'm inclined to believe they do. I had only two large Koi in my fishpond that had been together for at least 4 or 5 years and one (the smaller of the two) just up and died a couple of weeks ago. The remaining fish was continuously nudging it's dead mate in attempt to try and revive it perhaps, until we removed it. Now the last fish refuses to eat and I can only assume it's heartbroken and lonely. What do you think?