It seems that groups of about seventy people colonized both Polynesia and the New World (Murray-McIntosh, Scrimshaw, Hatfield, & Penny, 1998; Hey, 2005). So let us assume, as a reference point for analysis, that the survival of humanity requires that one hundred humans remain, relatively close to one another, after a disruption and its resulting social collapse. With a healthy enough environment, one hundred connected humans might successfully adopt a hunter-gatherer lifestyle. If they were in close enough contact, and had enough resources to help them through a transition period, they might maintain a sufficiently diverse gene pool, and slowly increase their capabilities until they could support farming. Once they could communicate to share innovations and grow at the rate that our farming ancestors grew, humanity should return to our population and productivity level within twenty thousand years.
(Murray-McIntosh, Scrimshaw, Hatfield, & Penny, 1998; Hey, 2005)
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.
Do you have a citation for the 100-1000 figure?
Comes from here https://mason.gmu.edu/~rhanson/collapse.pdf and the papers it cites:
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.