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Disasters that destroy all but a thousand humans are more likely than disasters that destroy all but a hundred humans. So this news says human extinction is more likely than we thought:
Conservation biologists may be deluding themselves. An analysis of the minimum number of individuals needed for a species to survive in the long term has found that current conservation practices underestimate the risk of extinction by not fully allowing for the dangers posed by the loss of genetic diversity. If correct, it means the number of individuals in endangered species are being allowed to dwindle too far.
Lochran Traill at the University of Adelaide, Australia, and colleagues found that for thousands of species the minimum viable population size (MVP) – where a species has a 90 per cent chance of surviving the next 100 years – comes in at thousands rather than hundreds of individuals. Many biologists, Traill says, work with lower numbers and so allow unacceptably high extinction risks.
Bad News On Human Extinction
It feels like that is missing a lot of post disaster environments(A), the possibility of a concerted human repopulation effort(B), and the dispersal of the remaining population(C).
(A) are we talking fast acting virus leaving the infrastructure largely intact, large scale eco-geologic disaster (earthquakes and volcanoes) or a climate change scenario that causes mass starvation (meteor strike, ice age, global warming induced wastelands, nuclear winter)
The resources left behind will drastically affect survival, as will the efficacy of further farming effects.
(B) Assuming that most people are dead and that rice/wheat/potatoes are still viable staple crops, there would likely be huge surpluses for the forseeable future. We aren't talking about hunter gatherers on marginal lands, we're talking about a group of people with their choice of the best soils in the world, along with an unprecidented repopulation of wildlife (game). Human intelligence being what it is, that surplus could be intelligently used to support ridiculously high breeding rates. (This also gets into the alpha/beta discussions. Doesn't MVP include basic assumptions on who's breeding with who in the wild? There wouldn't necessarily be any 'wild' in this scenario.)
(C) It's possible to put 4000 people on the planet such that none of them would ever see another living soul again. On the other hand, 4000 survivors of the apocalypse could all be in a single place (say, Cheyenne Mountain). The import thing is that the population needs to be close enough to interbreed. Either way, unless there are piles of bodies left, disease basically goes away, which is another problem with using modern hunter/gatherer lifespans.
In short, wouldn't genetics be all that mattered?
Great work; I hope you publish it when you think it ready. :)