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What is the likelihood that civilizational collapse would directly lead to human extinction (within decades)?

This is an upper bound for the number required to prevent extinction. Smaller groups would suffer more seriously from inbreeding, especially since our society's genome has a lot more deleterious mutations in it than a hunter gatherer one. But quite badly inbred humans could still survive, breed up to more survivable numbers and gradually fix their genome by natural selection. The real number is probably a good deal lower.