I just watched 28 Days Later for the second time last night, and I enjoyed it less than the first time I watched it -- but it inspired me to write some instructions on how to repopulate the earth, should it ever become necessary to do so. I'll focus purely on the technical requirements and ignore any questions of morality, pleading exigent circumstances.
If you've got more than 50 unrelated people and a decent mixture of men and women there shouldn't be any problems. Don't allow close intermarriages, and encourage later generations to have children with completely unrelated peers as much as possible. Genetic diversity could be strengthened by sterilizing children with serious defects, and this would probably be a wise move. Women should be encouraged to have as many children as possible, beginning at around ages 18 to 20. Women can have children at younger ages, but without proper medical facilities pregnancies for teenagers can be dangerous for both the mother and the child.
If your base population is smaller, your male/female ratio is badly skewed, or there are existing genetic relationships among your base population, things can become much more difficult. For example, in 28 Days the army platoon found by the heroes has nine men and zero women -- obviously a losing combination. Once the heroes arrive they add one man and two women to the pool, but would that be enough to start a self-sustaining population?
Not likely. If each of the two woman has a child by each of the ten men there will be 20 children, but two sets of ten half-siblings (and ten orthogonal pairs of half-siblings, one from each man). Each child would have nine unrelated potential mates. The real problems would arise later: everyone in the third generation would have four ancestors from the base population, and the same two grandfathers, making them all cousins. Even if distinct lines were kept genetically separated during the second generation the same problems would arise in the fourth generation. Inbreeding would eventually concentrate bad genes and it's doubtful that the population would survive.
The number of women would severely limit the number of children in each generation. Two women can only produce two children per year, and age differences among the children could limit the possible mating combinations among the second generation. Men can safely start having children as soon as they hit puberty, but given medical limitations it's not safe for women to do so -- and if a woman (particularly from the base population) dies (or is sterilized) while giving birth to a child her genetic uniqueness is lost. Far better to wait for the woman to fully mature than risk her health with an early pregnancy that could prevent future childbearing.
If the gender ratio were reversed -- if there were ten women and two men -- the population would still be unsustainable but it would grow more quickly. The best ratio for maintaining genetic variation is 1:1 for obvious reasons: five men and five women can have 25 distinct offspring, each with only two half-siblings; two men and eight women can only have 16 distinct offspring, each with eight half-siblings.
Update:
As raina pointed out in the comments, my math on the end there is wrong. Duh. Five men and five women can have 25 distinct offspring, each with eight half-siblings, leaving 16 (25 - 8 - 1) unrelated peers in their generation. Two men and eight women can have 16 distinct offspring, each with eight half-slibings, leaving seven (16 - 8 - 1) unrelated peers.
In fact, no matter what the gender ratio (as long as it's not 100% either way) a child will always have n - 2 half-siblings, where n is the total population. What makes close-to-even gender ratios better than skewed gender ratios is that they allow a greater total number of distinct genotypes for the child generation.
Here's a quandary - assuming this isn't the result of the Apocalypse (and there are still Christians around, and people of other religious principles), how do you get around the ethical implications of intentionally mothering and fathering children a) out of wedlock, and b) out of a loving relationship period?
Were I in that situation - barring the obvious "nudge nudge, say-no-more, say-no-more" advantages of having sex with several women - I would find it ethically, morally and religiously very difficult to do. Sex for some people is a personal relationship, and while sure it's necessary for the propogation of the species, do we toss out "Thou Shalt Not Commit Adultery" when even the future of the human race is at stake?
I don't know that it is as dire as you portray it. Inbreeding can be a problem, but I don't think that passing on bad genes will be a problem. With a lack of medical care, natural selection tends to weed those bad genes out prett effectively when they express.
B: The definition of marriage changes frequently with culture, and the Bible seems to recognize that the practical often varies from the ideal. For example, polygamy has been common for millenia, and King David had many wives and was commended for his godliness anyway.
P: Yes, but they will accumulate in a few generations and destroy the entire population. I'm not a geneticist, but I've taken several classes and my layman's understanding is that 50-100 unrelated people are near the minimum for a self-sustaining population.
I'm reminded of Marion Zimmer Bradley's Darkover books. The human population came from a crashed colony ship, and one of the later books (Darkover Landfall, I think) dealt with the crash and trying to keep genetic diversity in a small group of people.
True, but that was Old Testament, and before the New Covenant was established (I realize so was the 10 commandments). I'm going to see if I can find what the Gospels say about marriage...
I don't know that inbreeding is such a direct path to a situation where "bad genes" destroy the entire population. Farmers seem to do pretty well with a very limited genetic diversity.
Assuming an initial percentage of recessive bad genes (like 5%), I don't see why it matters if you have 100 or 100,000 people. Can you show me the math?
nobody: First, far fewer than 5% of genes are "bad" in the sense that they're deadly, alone or in combination. Animal farmers most certainly do need to be careful not to breed their animals too closely together, because the resulting offspring tend to be weak, small, infertile, and/or unhealthy.
The situation with plants is very different because they reproduce in an entirely different manner. Many plants even breed with themselves.
If you're interested in more details about inbreeding animals (and humans, I suppose), see here.
In the last scenario, with 5 men and 5 women, you said there could be 25 distinct offspring, each with only two half siblings. This confused me..I'm assuming the 25 offspring come from each male/female paring, so wouldn't each child have 8 half siblings: the four other children of his father, and the four other children of his mother? That would leave 16 unrelated members of his generation, and assuming a 1:1 male/female birth rate, 8 possible partners.
I have to say, considering all of this, that I really hope I don't have to repopulate the earth. Not only is there the adultury thing, but you'd practically have to consult a table to have sex, especially after a generation or two. Kind of takes the fun out of it.
raina: Let me think, did I screw up the math? Uh, yeah I did. Thanks. I'm updating.