I have taken several things into account when it comes to population growth. First off, it is likely that on a generation ship it would be 100% natural conception so I need to take into consideration natural conception rates. I figured humans would be closer to linear than any other organism in terms of population growth.
So first off, average death rate of 8 per 1000 per year. With a starting population of 45,000 this means that every year around 360 people will die and by 20 years(length of generation(since 20 years is the youngest ideal age for pregnancy)), 7,200 people will have died. But birth will more than compensate for this within the same time period.
With a 1:1 sex ratio, I only have to take into consideration half the population when figuring out birth count. So instead of taking a complicated graph like this:
and estimating the fertility of every single age and how many people would be of each age, I just assume high fertility for most at an 80% pregnancy rate in the entire 22,500 women and since infertile couples make up an insignificant minority, this 80% is more likely to be true. I personally think this fertility graph is inaccurate. First off, it only takes into consideration ideal youngest age and average age of menopause. Plus, it doesn't take into consideration all this:
- Accidental pregnancy at an age younger than 20
- Hyper fertility which can lead to frequent miscarriages
- Reproductively sterile people
With a 15% miscarriage rate and a 1% stillbirth rate, only 64% of women will give birth to a baby who is alive. I am assuming the generation ship has technology like artificial amniotic sacks and a labor stopping injection for the case of preterm labor so that birth isn't preterm and the baby can continue developing.
Within 30 years, only 5 pregnancies per 22,500 on average will be quadruplets at a chance of 1 in 729,000. So there will be on average, 1 quadruplet pregnancy every 6 years, although this might be in several small bursts of quadruplets. Quintuplets would be so rare at 1 in 55 million that even within 1000 years, it is very unlikely that a single woman in a group of 22,500 women will have quintuplets.
Triplets and twins would both be a per year of conception average. Triplets would be the lower one at 18 pregnancies on average per year being triplets with a chance of 1 in 8,100. Twins would be way higher with 540 pregnancies per year of conception being twins or in other words a 3% chance of twins.
So this gives me 7,950 babies just from the multiple pregnancies and a further 101,931 babies from singleton pregnancies, all within 20 years.
So the population growth per 45,000 per generation would be 102,681 people or a rate of 128.18%
But is this accurate? I know linear would be what humans are closer to than the Fibonacci curve but is this too linear? I am assuming humans are selected for genetic diversity in every generation which is reasonable.