The 100 is scientific nonsense that gets my blood boiling. 400 people is not a diverse enough genetic base to sustain a viable population. Even assuming they were evenly split down the middle and everyone was fertile and young enough to beget heirs...it's not flipping possible!
Battlestar Galactica had 39,000 and some change and even they were hanging over the precipice of extinction!
But we don't know the rest of the backstory yet. If the war was inevitable there's a possibility that frozen embryos, eggs and/or sperm were sent up to the stations and since this is the far future with 30-40 people per station, the age of female astronauts may significantly lower, like early 30s or even late 20s.
And we are only talking three generations here. 400 is a reasonably sized starting set, assuming the original crews were from all over the world, there should be enough genetic diversity along with some strict breeding guidelines to guarantee the surviving 4,000 don't end up like the Hapsburgs. Multiple partners from different stations, etc. Their problem now is the population capped at 4,000 with no room to grow further. You really need lots of children from lots of different pairings with as few common relatives as possible to create a diverse breeding population that can go at it with out restrictions.
I think it's doable, it's equivalent to a small isolated population groups we can find today but with better technology and planing.
