User blog:Skyzy/The Ark Population Equation

(I wrote this as a comment on another page but figured it should have its own page.)

"the population on The Ark was just over 400 when it formed yet when the show begins it is over 6 times that at nearly 2,700."

This has been in the back of my head for a while. Assuming that the Sky People continued to reproduce and give birth via normal methods (pregnant mothers vs. incubating wombs), I've been wanting to sit down and properly figure out how many potential children had to be born in each generation to reach 2700. That means in very broad terms, it took only ~57 years for a population of 400 to multiply to, let's say, 5400. Completely ignoring mortality rates and ballparking figures: For example, 150 women in the First generation give birth to 6 kids each.
 * The 1-child law has been in effect for at least Clarke's generation and perhaps even her parents' (do any of the adults have siblings?). So, subtract ~40 years (each generation being roughly 20 years).
 * When the 1-child law was passed, the population had to be greater than the 2700 because the following years would show a reduction in half of population numbers.
 * First generation of 400, we know that less than half were able to bear children (because at least half were males (again assuming they can't yet give birth in the future) and some of the women might be infertile/past child-bearing/uninterested). Let's toss 150 out there for simplicity's sake.
 * 150 women would have to give birth to at least 3 kids to keep the population stable (+50 extra to counteract mortality rates)
 * That booms the population up to 900 new people in the first 20 years. Out of those, let's say 400 couples reproduce in the Second generation and they have 5 kids a piece.
 * We're now at 2000 children born in the Third generation. 950 couples reproduce this time at a rate of 3 kids.
 * By the Fourth generation (Clarke's grandparents, Vera Kane) and 60 years in, the population is now at 2800 new children
 * They pass the 1-child law and only 1400 children will be born into the Fifth generation (Abby's).
 * This means Abby's generation would have produced roughly 700 children into the Sixth generation (of which 100 of them were sent to earth).
 * Every offense is a capital crime so they're killing off a lot of people on top of that. Let's pretend they just coincidentally kill off the same number of people that have survived from the previous generation(s) so by the time Clarke's generation is born (the Sixth), the population is down to the 2700 we see.
 * 6th gen: 700
 * 5th gen: 1000/1400 (lots of floating)
 * 4th gen: 1000/2800 (old age, sickness, lots of floating)
 * 3rd gen: 5/2000 (why not?)
 * 2nd gen: 0/900
 * 1st gen: 0/400

And that's just me playing around with scenarios because the only logical reason why the first generation would have 6 children each is fear of the human race becoming extinct.

Note: I have dyscalculia so I never trust my math. Please let me know if I screwed anything up.