Can Invisibility Evolve?

A reflection on the possible evolution of invisibility

When I was listening to the song Invisible Kid by Metallica in the car, a question popped up: Can real invisibility evolve? And I am not talking about camouflage or an invisibility cloack à la Harry Potter. No, I am thinking about real invisibility: there is nothing to see, but still something is there... (actually sounds a bit scary)

The benefits of pure invisibility are quite obvious. Predators can easily hunt for prey, they don't have to sneak up to them or wait patiently for hours in an ambush. For prey species, the same goes to other way. They don't have to worry about being seen by predators.

But for invisibility to evolve, individuals with this trait need to reproduce. Depending on the mating system, invisibility can be beneficial or a serious problem. For example, some fish species have smalle sneaky males that quickly deposit their sperm while two other fish are getting it on (well, they just spray eggs and sperm into the water). If these males are invisible, they would be more successful.
However, species that actively look for a mate can be faced with some challenges. How can you find something that you cannot see? Sound, smell, or certain cues might be helpful.

A big normal male and a small sneaky one.

There are off course some animals that have evolved a kind of invisibility, by becoming transparant. But pure invisibility has never been observed, which is actually quite logical. I am not sure whether purely invisible organisms can arise by natural selection. Or they have and we just haven't found them yet...

A transparant fish