First of all, the tragedy of the commons has been totally disputed by Elenor Ostram.
Secondly, anon, it's not a tragedy of the commons it's a tragedy of the mechanisms of capital. It's private ownership doing this not common ownership.
Thirdly, this is for everyone, why do we think a communist mode of production would change this in anyway? You simply aren't going to be able to feed people in the modern world on a meat diet of any kind. Maybe on occasion, but, obviously, most of the world will need to move towards a plant-based diet. It's not just a mechanism of capital in this case. You could have a rational planned economy that does not see fishing to feed people as irrational. You are still going to have a level of demand that our ecosystem cannot sustain on even under a communist mode of production.