The short answer is, it depends... However, putting some of these conditions aside and focusing on population size, the minimum number is likely very small compared with the approximately 7.8 billion people alive today. Smith's research into early human civilizations and space colonization gives him pretty good insight into our apocalypse survival hopes. He expects big cities would be most vulnerable if global civilization were to crumble, as they import almost all of their food and are heavily reliant on electricity. Surviving populations would, therefore, likely spread out to find resources. A surviving population of just a few hundred people...