Uhh, you can't get migrants, invaders or traders (or anything on the map at all) if its an island. If you are surrounded by water on all sides, don't bother playing, unless you plan on playing with only seven dwarfs and their offspring.
That's actually one of my forts at the moment. It's been incredibly fun, actually!
The only inhabitants of the island where a horde of elephants and a single tiger. After sectioning off a part of the island with choke points full of cage traps, I caught all the elephants (except for two, who I killed far later.) and had them in a room breeding like MAD. (Seriously, elephantsplosion.)
The tiger, in my efforts to ward her into my traps, killed my mayor and earned a name. Fortunately, the dwarf wasn't my single female, who is a miner and quickly fell in love with the other miner. So, after a bit more effort I caught the tiger and made a deep series of tunnels. Now she's allowed to prowl in my sacrificial chamber. Anyone caught unworthy will be dumped into the tiger's pit!
Yeah, they've been there for nearly a year now. I'm hoping my miners will hurry up and get married so they can pump out the kiddies. I removed [MULTIPLE_LITTER_RARE] and I might even lower the child age. Island dwarves have to grow up quick! I'm planning on building some cool shit around the place.
The island is completely isolated on all sides.