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I have a story set about five thousand years after a major disaster reduced the world population from billions down to... well, that's the question. How low could it have gone, and still provide the seeds for a genetically stable population able to grow and thrive?
It's an alternate planet, and the majority of the pre-disaster population was dispersed across one large continent. Post-disaster, small pockets of people were left in many different places on that continent. They lost almost all of their technology, and were knocked back to the level of hunter-gatherers and basic agriculture. But, the climate was very favorable, resources were plentiful, and the needed skills/knowledge were available.
They would have started out in small pockets, which eventually established contact with other such groups, sometimes within a generation or two and other times after a longer delay.
Five thousand years later, people have spread, settled, and developed. Ultimately they have reached a population of about 35 million, with tech levels varying by region from hunter-gatherer or base agricultural societies in the most distant , least advanced areas (wildernesses and undeveloped countries) to late medieval technology in the most advanced and heavily populated areas (developed countries).
So, to get from one position to the other, how many survivors of that initial disaster would there need to have been?
*Additional info: the aftermath of the disaster was removed from the equation. For example, there were not millions of dead bodies to be dealt with or to cause disease. There was also no infrastructure left behind, from roads to buildings to power grids; the survivors had to start from scratch, BUT they were given resources to obtain the knowledge and skills they needed to do so. It's complex, but suffice to say this whole thing was staged by very powerful non-humans, as if they hit a kind of "civilization reset button", and a small (compared to the size of the population before) number of people were left to rebuild.