They used to have some big old Kaibab Mule Deer on Santa Rosa Island and when it became part of the Channel Islands Parks (don't remember if the owners sold it or if the govt took it or what) they decided to go in there and helicopter shoot them all. Before the island was taken over the owners had a hunting program for them. Catalina used to have pigs and goats too. They managed to eliminate them on Catalina also. An interesting table on the bottom of this page showing what "invasive" species they have and what has been eliminated.
http://www.californiaislands.net/eradication Funny thing is they don't mention goats on Catalina (they call it Santa Catalina, its "official" name on the table) one way or the other and I know they had them at one time because I had a friend, (long deceased), that went ashore from his boat on a do it yourself bow hunt (quite a while back, don't know if there were any laws covering that one way or the other back then) and brought back a nice goat that he had mounted.