Fish,
It's Caulerpa prolifera. And the only sure way to eradicate it is manual removal.
Caulerpa sp. apparently release chemicals that allow their roots (holdfasts) to dissolve calcium...so it can grow in both sand and rock.
IME the only way to get rid of it completely is by manual removal...you just need to be persistent, and over the course of a couple of weeks, it will be gone.
HTH,
-R
|