Assuming an average population, the most reasonable estimates I’ve seen for the “safe” margin are mostly around 1,000. It’s definitely possible to get by with fewer than that–there are isolated tribes with fewer than 100 members who have done just fine for long stretches–but it makes everything much riskier. Humans are k-strategists in terms of reproduction: we have small numbers of offspring, but invest a lot of resources into each one. Species like that tend to have higher thresholds for viable population size, because each instance of reproduction has more “significance” to the overall population, so a few suboptimal choices can have drastic impacts. However, unlike many other k-strategy species, we don’t tend to spread our populations out very thinly over vast distances, which helps ameliorate that somewhat. If your population were “optimal” (i.e. free of really bad recessive traits, all clustered together, very genetically diverse to start with, making “optimal” mate choices, etc.), you might be able to push the safe margin into the low hundreds. At that level, though, genetic drift starts to become a really big factor in evolution, so while it might be possible to sustain the species, the species might also get weird.
Assuming an average population, the most reasonable estimates I’ve seen for the “safe” margin are mostly around 1,000. It’s definitely possible to get by with fewer than that–there are isolated tribes with fewer than 100 members who have done just fine for long stretches–but it makes everything much riskier. Humans are k-strategists in terms of reproduction: we have small numbers of offspring, but invest a lot of resources into each one. Species like that tend to have higher thresholds for viable population size, because each instance of reproduction has more “significance” to the overall population, so a few suboptimal choices can have drastic impacts. However, unlike many other k-strategy species, we don’t tend to spread our populations out very thinly over vast distances, which helps ameliorate that somewhat. If your population were “optimal” (i.e. free of really bad recessive traits, all clustered together, very genetically diverse to start with, making “optimal” mate choices, etc.), you might be able to push the safe margin into the low hundreds. At that level, though, genetic drift starts to become a really big factor in evolution, so while it might be possible to sustain the species, the species might also get weird.