It seems like Hydra Island is linked to The Island in some way.
When Ben moves the island, IIRC episodes later on still include Hydra Island being close by to the The Island (I'm a bit foggy on the timeline there). In the finale when Desmond pulls the plug and The Island starts to fall apart, so does Hydra Island where the pilot and team are trying to get the plane going.
Is the linkage between these islands ever explained in the show or in behind the scenes sources? Are they just two peaks of a single underwater mountain that is one unit?