Surprisingly its just with random breeding. From what I’ve been reading the number of people alone can provide enough diversity to prevent too many issues from arising. no genetic screening, eugenics or breeding programs required. Though those would definitely be beneficial to such a population. But strictly speaking, more people is always better.
https://genetics.thetech.org/ask/ask113
Besides, I don’t think it would be necessary even if I had much fewer people, and no access to more, and here is why:
Genetically speaking, the only problem with inbreeding is that it can make harmful mutations and recessive traits become dominant in the offspring, reducing the viability of the population. If everyone is genetically sound, the problem is simply the social stigma. I have read in game documents stating Purifier Serum will cure harmful mutations and even remove pre-existing genetic defects. As long as everyone takes a hit of Purifier Serum before having children (I usually dose everyone I recruit, to give them a blank slate), then the issue of harmful recessive traits evaporates. You would eventually end up with a population whose appearances are rather homogenous, but in the very long run natural mutation/adaptation should remedy that. Humanity, as well as other species have experienced some pretty nasty genetic bottlenecks in the past and survived. We could do it again, and having something like Purifier Serum available would make survival even more likely.
On that note, regarding my game in particular, I already made a bunch of purifier serum to cure any survivors I find who have unpleasant mutations. IIRC I have a steel jerrycan full of it atm, or at least partially filled, and I definitely have the resources to make it in bulk if I wanted more. Making a 200L drum of it would not be out of the question for me. On top of that I’m also not actually finished recruiting yet, and never will be; I’m planning to recruit practically every single person I find. For all these reasons, I don’t think genetic diversity is going to be an issue for my particular group of survivors.
I’m also building my underground vault city like a fortress. The entire city’s architecture is being designed and constructed with redundancy and defense in mind. Defensive points, combination civil defense shelter/armories, turrets everwhere, steel security doors/airlocks, distributed storage of utilities and supplies, everything I can think of. Also, in addition to every single person being armed/armored to the teeth my army of military robots will be on guard and on constant patrol (if commanding them ever gets implemented). I am unconcerned with exterior threats other than something that could just outright destroy the planet or just immediately destroy everything. If a portal opened up in my city, or some other subterranian threat pops in for a visit, I have ten suits of power armor I’m saving for an emergency response team. They, along with the militia and defense systems, will kill any unwanted guests, or worst case keep it isolated until the area can be sealed off, likely with a controlled tunnel collapse of the section. Since my city is going to be more like a bunch of small self sufficient cities crammed together than a single big one, the loss of any given section will not compromise the survival of the whole.
Just because our old cities and towns were vulnerable to the phenomena of the cataclysm does not mean new ones need to be. You just need to build and plan carefully.
Also, in the very long term, this city will only be the first. Once the poulation hits about 600, I’m going to build another city in either another bunker or the necropolis I secured. And then I will build another, and another. One bastion may fall, but two shall take its place.
