(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?

I tried my hand at doing a bit of MVP for humans after discussing the issue with Robin. My estimates also ran in the thousands. The survival probability is roughly linear in initial population up to several thousand. To get 90% survival after 1000 years (more sensible than 100 for long-lived humans) with life tables corresponding to modern Sri Lanka I needed around 4500 people in the initial group. Adding occasional bad years (a 1/15 chance that a year had double mortality, and 1/150 that it had ten times mortality) reduced the survival probability to ~50% even with 5000 people. Running a low-mortality life table based on modern Sweden made things slightly better, ~60%.

My model did not take genetics into account, so it should be regarded as optimistic. I also had serious problems getting any survival with hunter-gatherer life tables, unless I tweaked them. Boosting average growth rate to 2% produced a MVP of a ~500 people – but that presupposes a very benign environment, not a likely occurence after a global disaster.

One interesting observation was that even a doomed population can linger for centuries. Conversely, small founder populations for isolated locations may be due to luck: we do not see any genetic traces of the unlucky ones, only the first population to by chance grow far enough to dominate the land.

If we are in the roughly linear survival probability range the chance of a population of size N surviving is kN. If we have N0 people divided into R refuges, each refuge has a chance kN0/R of succeeding. The probability that at least one refuge survives is 1-(1-kN0/R)^R. Given these curves a typical value for k is around 1/10000, I end up with a monotonously decreasing survival probability with R: it is smarter to have one big refuge than many small and vulnerable. However, a proper model would include the risk of local disasters which I think will improve the chances for distributed refuges. But in any case, this is a nice example of how even humans are vulnerable to habitat fragmentation.

You benefit if you put any value on humans other than yourself, or on anything that is preserved if humanity if preserved.

I don’t think the first one is necessarily true (except if you qualify it to be any and all humans) but I concede that the second one would be true.