So this might be a slightly weird one, but I"ve seen answers to questions about minimum numbers for re-population and such, but what about a system where reproduction was controlled and coordinated, and the intent was zero population growth? The theory is, quite apart from sexual or romantic relationships, everyone in the group is the genetic parent of exactly two children (barring instances of twins/triplets/whatever), each with a different partner, so that everyone is genetically responsible for half of two children, and theoretically the closest relation anyone can have in their own generation is half-sibling, thus sharing on average only 25% of their DNA.
So how might a system like this impact the needed starting population size, assuming that eventual reintegration with a larger population was for practical purposes impossible? How many generations back does a common ancestor need to be to minimize the chances of undesirable effects of inbreeding? I know it would rely on a perfect, or near-perfect, 1:1 ratio of genetically female to genetically male, so I guess another question is how large a population do you need for the randomness of birth to reliably average out that way?