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Plenty of food and water for millions

Cosmic ray protection

Only lights used are infrared, visible, UVA, and UVB

Monogamy

So first off the starting population is around 45,000. While some are subfertile, some are infertile, and some are fertile or super fertile(mainly the young ones like teens that are super fertile), the average pregnancy rate on the generation ship is 80% per year. Since there is a 1:1 sex ratio I am left with a total percentage of 40% of the population who are pregnant. That is the same as the 80% of women I calculated earlier.

Miscarriage rate is 15% on average. So per year that is 2,700 miscarriages. Stillbirth rate is 1% on average. This is a further 180 stillbirths. So only 64% of pregnancies would actually have a baby survive after birth. For simplification, I will ignore premature birth rates and assume on the generation ship, there is technology to keep the baby in until full term. So 15,120 full term babies.

The time breastfeeding is 2 years. Again, for simplification, I will assume no pregnancies for 2 years. Average generation length is 20 years, the youngest ideal age for pregnancy. Average age at menopause is 50 years so that is on average about 11 pregnancies per woman.

So next up is multiples. 3% of pregnancies would be twins(so 540 twin pregnancies every 2 years 9 months). Natural triplet pregnancies are .01%(so just 18 triplet pregnancies every 2 years 9 months)

Quad rates would be so low that I won't take them into consideration in annual birth rate(.02 quads every 2 years 9 months is low, that means that for a woman in the population to have quads, it would take on average 5.75 years or in other words that there would only be 5 quad pregnancies in 20 years)

Quintuplets, the same but even more extreme. This is the highest order multiples I could find a natural conception rate for. That rate is 1 in 55 million. Even with the 80% pregnancy rate, it is simply too low for a quintuplet pregnancy to occur within 1 generation. It would take 278 generations or more than 8000 years for there to be 1 quintuplet pregnancy. It simply isn't going to happen without inter-galactic travel at a reasonable generation ship speed or fertility treatment or just sheer luck.

With that out of the way, I have figured out that for the number of pregnancies that have at least 1 baby survive after birth in 1 generation, this would be the formula:

$Pregnancies=Populationi∗0.5∗0.8∗.64*11$

Now for the # of babies I would take that and divide it by percentage singletons, twins, triplets, and quads.

$Babies=(.96[8]*Pregnancies+(.03*Pregnancies*2)+(.001*Pregnancies*3)+20)=209,374$

So annual birth count would average to be 6,979 per year in the first generation.

But is all this complicated math correct assuming that all the rates and simplifications are true and no fertility treatment is done(in other words 100% natural conception)? Or did I make a mistake somewhere in the math? By the way, I put the 8 in brackets because it is the repeating part of a repeating decimal.