> Not trying to be funny, either, but how could an isolated population, of a severely remote/xenophobic island, not just disappear due to the side effects of inbreeding?
Inbreeding is only a problem if it happens over many generations of closely related person (think your cousin or closer for many generations). A single brother-sister pair in a family tree is unlikely to do much harm beyond making family reunions a bit odd.
[Minimum viable population](https://en.wikipedia.org/wiki/Minimum_viable_population) studies use a rule of thumb called the “50/500” rule. Basically 50 individuals is the minimum population to prevent serious inbreeding issues, and 500 is the point where you are reasonably safe though of course this is an overgeneralization and not reliable for all species.
> Do secluded populations eventually become immune to the mutations?
That isn’t how it works. A mutation is either bad enough to prevent reproduction or it isn’t. If it isn’t then the mutation can carry on, if it is… then that’s the end. There’s no immunity, just the athematic of reproduction.
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