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I have always understood that below a certain number, the accumulation of recessive genes (inbreeding) would prevent a species from surviving, and that the larger the number the more likely spontaneous mutations would occur which would be beneficial (presumably most mutations would be non starters). Reading the contributors in Chuck's link shows it's more complicated than that, but assuming that the survivors don't practice selective breeding or eugenics, it still seems to me that the population would have to be of a reasonable size to survive, especially if resources were low, or conditions unfavourable, as a post apocalyptic period would probably be.