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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:

enter image description here

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
  • etc.

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.

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    $\begingroup$ I don't think it's accurate. Human reproduction rates are hugely influenced by cultural factors, much more than, say, miscarriage rates. Example: If you want fewer children, then arrange your ship society so more women are in advanced schooling and the workforce. If you want more children, then lower the cost of housing and reduce barriers to re-entering the workforce. Remember that one purpose of a generation ship is to keep a large number of skills active and handed on until the destination is reached, so a fairly high starting population might be desirable. $\endgroup$ – user535733 Jun 4 '18 at 2:08
  • $\begingroup$ But they would get assimilated into 1 culture most likely so cultural factors wouldn't matter and miscarriage and stillbirth rates would be more important. And have a starting population of 45,000 because that is what is needed to prevent inbreeding without massive reproductive control. $\endgroup$ – Caters Jun 4 '18 at 3:09
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    $\begingroup$ You would design the operation and social conditions of such a ship very carefully and keep them controlled. In this way you would effectively program the social system of the ship to produce the required growth rate (i.e. whatever you aim for). You would not leave this to chance. $\endgroup$ – StephenG Jun 4 '18 at 4:32
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    $\begingroup$ "Natural conception rates" vary wildly depending on whether the women want to get pregnant or not; see for example the fertility rates in India and Japan. I would think that on a generation ship the social rules would aim for a stable population, because the available resources are at best stable. $\endgroup$ – AlexP Jun 4 '18 at 9:01
  • $\begingroup$ I honestly think it would aim for a population to grow to maximum capacity and then stabilize. Linear growth is best for this. And of course the women will want to become pregnant and if not they would still be forced to so still 100% natural conception and the chances of having multiples or a miscarriage are very hard to change with natural conception. I mean there is no anti-miscarriage treatment that works in early pregnancy. And only a few conditions like PCOS and a phytoestrogen rich diet can change the chance of multiples to be higher regardless of genetics. $\endgroup$ – Caters Jun 4 '18 at 16:10
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Maybe I'm looking at this the wrong way but given the technological advances to produce a generational ship in the first place and the extreme selection process that would occur to pick your first 45,000. I think the rules on the ship would naturally be for every women to conceive 2 children if a stable population is desired. You can of course increase this to account for any infertility or growth rate if desired. The options for anything else would be very limited.

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