The islands in question, range in size pretty dramatically.
On the smaller ones I can see not wanting rifle hunting. Perhaps, I could even understand not wanting shotgun hunting, but banning archery hunting is indefensible.
Once man decides to be the top predator on an island - he's got to step up to the plate, and do the job. Inaction only leads to environmental collapse and starvation.
Man has to take back the top-predator role on these islands.