(Replying to PARENT post)
One of them, Teehuteatuaenoa, gave her account of the aftermath in an interview from Tahiti: http://www.fatefulvoyage.com/pitcairn/pitcairnDJenny.html
More on Teehuteatuaenoa and the history here: http://www.demtullpitcairn.com/teehuteatuaenoa.html
The island did suffer from lack of resources as the population grew. This lead to two migrations. One to Tahiti in 1831 and another to Norfolk Island in 1856. The latter is where many Norfolk Islanders can claim their ancestry from. Some islanders returned from Norfolk and re-settled Pitcairn soon after that migration.
With regards to genetic diversity, there have been many 'outsiders' that have settled and married with islanders. These were often the result of visiting whalers and shipwrecked sailors. You'll find most of the ancestral lines on Pitcairn have a mix of the initial mutineers, their Tahitian wives and outsiders giving genetic diversity.
(Replying to PARENT post)
Not quite the same, but there are islands in the St. Lawrence in Quebec that are similar backwaters. My father has been hunting snow geese on Ile-aux-Grues, just across from Montmane, Quebec. At this point, there are only about a dozen families on the island that stay there and continue doing the guiding/dairying lifestyle that is traditional year-round.