here's what to take, not a bow.
View: https://www.youtube.com/watch?v=TnN1Qvw1HAU
then you have the option of using baked clay balls at targets that aren't worthy of an arrow. Rocks dont fly straight, so dont waste your time and energy stalking anything to shoot a rock at! Take 4 arrows with 4-tined fishing heads, and 2 broadheads. Given a modified Crunch multitool, you can convert 3 of those arrowheads into 24 fishhooks in a couple of hours. You'll then have 3 blunt arrows, which can be fitted with wooden barbed heads if you wish. Be nice if you could take Dave Canterbury's 3 pc takedown arrows, but the producers say that your arrows have to be made of wood. Keep one fishing headed arrow, and have slip on rubber fletching on all 6 shafts, due to the moisture problem on the island. This way, you dont need to waste a pick on the hooks and line.
Dont waste your time and bait on trotlines for fish. You'll just lose the bait or catch minnows. Instead, set the hooks, baited with fish guts and shredded, roasted cambium, on small log rafts for the 3 lb ducks and gulls. A drowning rock, tied about a foot from the hook, will end the fracas in one second flat. There's 30,000 bunny and tree huggers permanently living on the island, so dont set the hooks for coons or magpies! The fowl offer some fat, which you need desperately. Catch them asap, cause they will soon be migrating. You also have to very soon use the fishheads and guts to bait in a bear, and arrow it from your tree blind. THAT means 100 lbs of meat or more, and a lot of fat. But you'll have to extract the salt from a lot of water to adequate preseve that fatty meat.