Preposterous analogy. Surnames are not a proxy for genetics and Pitcairn is hardly a proxy for general population.
A person receives only his father's surname, while he receives both his mother and father's heritage.
And Pitcairn's population and genetic diversity is dwindling because the more resourceful young Islanders leave the Island never to return.
They most certainly are, as they are inherited too. Whole lines die out, leaving only a few to continue on.