# Population formula part 1: Birth

#### caters

##### New member
I need my formula checked. It involves pregnancy rate, miscarriage rate, stillbirth rate, time breastfeeding, average generation length, multiples, and average number of pregnancies. So let's start off with the conditions:

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.

#### tkhunny

##### Well-known member
MHB Math Helper
A few thoughts.

1) This is a very simplistic model. No "complicated math".
2) Your attention to some details and not to others exposes the lack of sophistication in the mathematics, itself. (Number of decimal places, excessive precision, just to name two.)
3) A linear model of any concoction is unlikely to represent the generation model of any species I'm aware of.

Having said that, we must remember the great statistical mantra, "All models are wrong, but some are useful." Give this a good read: https://en.wikipedia.org/wiki/All_models_are_wrong

#### caters

##### New member
A few thoughts.

1) This is a very simplistic model. No "complicated math".
2) Your attention to some details and not to others exposes the lack of sophistication in the mathematics, itself. (Number of decimal places, excessive precision, just to name two.)
3) A linear model of any concoction is unlikely to represent the generation model of any species I'm aware of.

Having said that, we must remember the great statistical mantra, "All models are wrong, but some are useful." Give this a good read: https://en.wikipedia.org/wiki/All_models_are_wrong
Well it may be that it is non-linear. But humans would be the closest to linear. And it is complicated in a way. All the factors I took into it. And no that precision is not excessive and no the number of decimal places is not wrong. But with these numbers, I find scientific notation just makes the whole thing a lot more confusing than it is worth. I mean saying $1*10^-5$ just to say .001%? It's not worth it. And I justified all my simplifications, namely that assuming there is technology to keep the baby in until full term and assuming that becoming pregnant while breastfeeding is wrong on so many levels(which I really think it is, thus the 2 years 9 months between pregnancies).

And again, the details that I paid attention to are super important. Like miscarriages and stillbirths. Women with these would likely be too upset to have another baby for a long time. Multiples can significantly change the population within 30 years compared to assuming 100% singletons and makes it more realistic. Ones I didn't pay attention to either aren't important for these formulas or are so insignificant across the time scale that I might as well not add that complexity.

Infant mortality is 1 of those. So insignificant on a generation ship with futuristic technology and the ability to grow limbs and organs, all from iPS cells with the patient's DNA and self-antigens, that it might as well be non-existent. Difference between infertile, fertile, and super fertile is again another insignificant factor because only 1% of the initial population are infertile and teens(the most likely age group to be super fertile) also make up a minority in the initial population. So they aren't nearly as important as the average pregnancy rate of 80% of women or 40% of the population.