An animal conservation there’s something called the rule of 5s, or the 50/500 rule. It’s a rule of thumb used to tell whether a population can support itself. The minimal viable population to avoid the harmful effects of inbreeding is only 50 individuals by this rule. 500 is the minimum to avoid intense amounts of genetic drift.
While this isn’t a conservation case (by God, by most metrics we have too many people) most human populations have much more than 50 people.
As for the Pitcairn islands in particular, their population isn’t even growing much. Iirc they had one child birthed in 2003. It was the first person born there in 17 years. Suffice it to say, they’re not gonna have enough time for inbreeding to take place.
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