idk but if you would like more feed back on it, your question would be better on the main forum.
Your fish sigh?!! 
Please explain how you can tell?!
OTOH, my cats sigh quite a lot. Which is ironic considering they have no concerns at all other than which stair to sleep on in order to cause maximum danger…
Yeah, I wanna know about the fish sighing too.
My cat sighs a lot whenever he’s frustrated with me. Usually, it’s because his food bowl has been empty for maybe 30 minutes and he’s annoyed I haven’t leapt up to refill it. Despite the fact that he weighs over twenty freakin’ pounds and is obviously not gonna starve to death in any time period shorter than a month. (OK, got kinda derailed into an OT rant about my cat)
Hmmm, now I’m thinking about the differences between yawning and sighing. Seems like they both accomplish the same thing, a large intake of oxygen, but occur for different reasons and in different ways. With a sigh, I inhale through my nose and then forcibly exhale. With a yawn, I forcibly inhale through the mouth and slowly exhale…
Yep - a number of years ago, while tagging Loggerhead sea turtles off the coast of Georgia, I saw big females sigh while laying eggs. They’d drag themselves out of the water and up to a nesting spot on the beach and after digging a hole, lay upwards of 100 eggs. At times, during this effort, they’d respire in a way that can only be called a sigh. Made a very moving experience even more so. xo C.