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Okay so in my setting, long story short, it starts off with a group of humans escaping an alien fleet they were enslaved by and conscripted into, and they find an earth-like planet that's smaller than Earth (more like Mars sized, I guess!) to settle down on and try to restart humanity.

So, I'm trying to math out how much my human escapee population would grow over the course of 200 years with the following parameters: They have 8 people at first, 3 of which are adult women able to get pregnant, and they can conceive and give birth in a single month cause alien genetic modifications. Aside from the expedited gestation period they are ordinary human women. How do I put it all together and track a population growth over 200 years? What factors do I need to consider?

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    $\begingroup$ Computing... Computing... Error: insufficient data. Unmodified human females don't conceive while breastfeeding their babies; this lactational amenorrhea last for about 6 months to one year. Also, unmodified human females can sustain only a limited number of full-term pregnancies -- say about ten maximum. So, what are the real parameters? At what age do women become fertile? How quickly after giving birth can they conceive again? How many times can they do this? What percentage of baby girls survive to become fertile? $\endgroup$ – AlexP Jul 15 '18 at 21:28
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    $\begingroup$ @vessynessy20 Welcome to StackExchange! You will need to further refine your question for us to sufficiently answer your question. I made an attempt at improving the title. Keep in mind that asking a properly formed question is an integral part of SE. A resource can be found here: worldbuilding.stackexchange.com/help/closed-questions $\endgroup$ – Raznarok Jul 15 '18 at 21:39
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    $\begingroup$ Won't genetic defects emerge from inbreeding? Or is there an alien genetic modification that prevents or dulls it? $\endgroup$ – Starpilot Jul 15 '18 at 21:50
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    $\begingroup$ Vessynessy20, Welcome to Worldbuilding.SE. I'm not particularly happy with your reception here and I apologize for it. It takes everyone time to learn our rules and adjust to our culture, you should have been given that time. Population estimation is actually quite a complicated matter. This is what @AlexP was referring to. Along with his issues I can add the fact that if a woman literally could bear 12 babies a year, then in 5 years you have a max pop of 188 with only 8 adults. (*continued*) $\endgroup$ – JBH Jul 16 '18 at 1:47
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    $\begingroup$ I agree with the reopen nomination, but with reservation. The OP has refrained from addressing the comments with an edit to the question. If the question is reopened, it may be closed again for a different reason (too broad? unclear?). Regardless, this does appear to be a legitimate, on-topic question for the site. $\endgroup$ – Frostfyre Jul 16 '18 at 17:01
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Whatever number you like between 0 and 10,000,000

There are a number of unspecified variables:

  • Availability of resources - how many children can be supported per person by the previous generation?
  • Medical technology available - what will the infant mortality rate be? How treatable will genetic defects resulting from inbreeding be?
  • Reproductive age (social / medical restrictions) - how long is each generation?
  • Reproductive intent - are these people on a fanatical quest to repopulate humanity or are they having children when they are individually wanting to do so?
  • Alien genetic modification effects - what effect will these have on ratios of male / female births?
  • Effects of inbreeding

Let's look at a middle of the road scenario, in which each couple has 5 children who each survive to reproduce themselves, with 50% of births (rounded down) being female and 25 year generations:

  • Gen 0: 3 females (8 total)
  • Gen 1: 7 females (15 total)
  • Gen 2: 17 females (35 total)
  • Gen 3: 42 females (85 total)
  • Gen 4: 105 females (210 total)
  • Gen 5: 262 females (525 total)
  • Gen 6: 655 females (1310 total)
  • Gen 7: 1637 females (3275 total)
  • Gen 8: 4092 females (8185 total)

So, in this scenario there would be over 8,000 individuals in the most recent generation by the 200th year, with a total population of around 12,000 (assuming that most of generations 6 and 7 are still alive).

That is a "moderate" scenario. Looking at a high-population scenario - if there are no resource limitations, excellent medical technology salvaged from the ship and a population of women willing to go through childbirth an average of ten times each starting at an earlier age then the total population after 200 years could go up by a factor of 1000 or more. However, I suggest based on all the conversations I have had with mothers that telling women they have to go through childbirth 10 times each... may not be well received by the women. I also cannot see a situation of such abundant resources on an undeveloped planet that supporting such a population would be viable.

Now to the low population scenario - as quoted in Adam Kirkiewicz answer to this related question, the population may only be a hundred or so if the escapees / settlers decide to take it easy (on the reproductive front) as on Tristan da Cunha. This could also be a result of disaster/s in the middle generations killing a significant number of the breeding population or the resources they need to expand.

Finally - inbreeding is going to be a significant issue. Assuming that generation 0 are all unrelated to each other, generation 1 should, with luck, all be able to find partners that they are unrelated to. Generation 2 and onwards are going to be inbreeding. This will result in various deleterious effects, probably including significantly lowered intelligence. This is likely to make the later generations less able to deal with any problems they encounter, increasing both the total risk of extinction and increasing mortality rates among both infants and adults. I strongly suggest reading the question "Self-Fertilisation" on p158-167 in What If by Randall Munroe - unfortunately I cannot find a link to an electronic copy of this question on the XKCD What If archive page.

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    $\begingroup$ The simplistic bolded title belies the fact that the body of this is an excellent answer. It provides a realistic upper and lower bound for the OP to choose from based on the environmental conditions experienced by his people, and also highlights a few significant issues from the scenario. $\endgroup$ – Ynneadwraith Jul 18 '18 at 12:46
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Most likely zero.

Maybe not after 200 years -- there may still be a small group of humans struggling to survive at that precise point in time -- but sooner or later, all the evidence suggests that there is a substantial chance that there will be none left.

There is a concept called the minimum viable population. It says that if the number of individuals of a certain species in an area where they are isolated from others of that species drops below that number, then there is less than a 90% chance for the population to survive. The farther below the figure the population is, the smaller the chance.

Given average circumstances, and including problems caused by inbreeding, the current estimate of the threshold is around 4,000. Looking at the detailed figures in the paper the prospects are slightly better than average for larger animals, and slightly better for mammals, but both effects are fairly small.

Of course, because none of the studies involved included humans, specific advantages that humans may have could affect the results. Such advantages may include the fact that humans will be aware of the potential problem of extinction in a way that other animals are unlikely to be, and may be better able to come up with innovative solutions to problems they face in the environment. I'm not sure either of these is enough to counteract the very large discrepancy between 8 and 4,000, however.

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This depends on a multitude of factors. An important one is mortality. 8 people settling a planet will face many dangers from wild animals over natural desasters to bad crops. How many children survive, and how long they will be able to reproduce is of course crucial to population growth.

Also, the people will, at least at first, have to spend all of their energy just to survive and to build up a stable settlement, they won't have a lot of effort to "waste" on raising children so this wouldn't be a priority for them.

Then: do you want to use your women as baby factories or should they actually be treated as humans?

Depending on all of these and other factors, you can get wildly varying numbers: put your assumptions into http://www.wardricker.com/timegrowth.php to see for yourself:

If, as you have suggested, human beings have been on earth for 200 years and produced another generation each 20 years, that would mean that 10 generations have passed since humans first "arrived" on earth. If we started with 6 people, and each couple in each generation had produced 10 children, with 50 percent of those living long enough to in turn reproduce, the population of the earth for the current generation would be 57,220 people.

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If, as you have suggested, human beings have been on earth for 200 years and produced another generation each 15 years, that would mean that 13 generations have passed since humans first "arrived" on earth. If we started with 6 people, and each couple in each generation had produced 20 children, with 100 percent of those living long enough to in turn reproduce, the population of the earth for the current generation would be 60,000,000,000,000 people.

Note: i plugged in 6 people, because the males are unimportant, so 6=3 couples.

All of this, of course, ignores the problem of the reduced gene pool here. I'm not sure how bad that would affect the population in just 200 years, but it sure wouldn't be pretty.

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Interesting question.

There are some assumptions I've made from your original question that seem maybe reasonable.

  1. Females can start having babies at 15
  2. females stop having babies at 45
  3. Genetic failures are miscarried - therefore birth defects do not really show up as a serious problem. This does mean the female "loses" a month of baby making. I'm assuming a failure rate of 1 in 2. That means females give birth to 6 children per year
  4. there are NO resource constraints (Not realistic I know - that's where a lot of your conflict will come in)
  5. there is NO FORM of birth control practiced. In other words - every female gets pregnant every month from the age of 15 to 45 - and 1 out of every 2 of those pregnancies results in a live birth.
  6. there is no death other than by old age (You don't lose any productive females before they bear all possible children)
  7. 1 in 2 children are female
  8. People live to about 95

I played a bit in Excel - and came up with this much population in the year 200 AA (After Arrival) 93680145

Which is approximately 93 ½ million. I "Think" This is correct - but I could have messed up my logic in excel so maybe not...

(At first I got a ridiculously massive number in the trillions - but then I realised I hadn't allowed for male births, which cut the reproduction rate down immensely)

Thanks for the question - interesting thought experiment.

You may want to decide which of my assumptions are valid - and include them in your question to make it easier for others to come up with some variant on what I did. You may also not like some of my assumptions, in which case it'd be good to also edit in your question and rule them out...

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  • $\begingroup$ The main discrepancy here is that you haven't accounted for child mortality rates: in the scenario given, the escapees are unlikely to have the benefit of much if anything of modern medical knowledge, so mortality rates are likely to be quite high, at least to begin with. Human life expectancy at birth in pre-industrial civilizations is generally somewhere in the vicinity of 25, with most of the discrepancy between that figure and our own being accounted for by children who die before reaching adulthood. To account for this, I'd suggest decreasing new births in each generation by 50%. $\endgroup$ – Jules Jul 20 '18 at 9:07
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In the best case scenario you will have 117 people, in most scenarios you will have 0 people

If everything goes well, each woman has 5 children in each of their lifetimes that survives to the next generation. You have made the mistake of correlating the fact that the women can have 1 month pregnancies, with the idea that they can have considerably more children than they normally would.

If each woman has 60 children, who is going to feed and take care of all the children? How is each woman going to get the food and nutrients for the baby that would normally be spread out over 9 months in just 1 month? How is a woman's body going to survive so many pregnancies? And how are 8 people going to feed themselves and take care of 100s of defenseless babies?

Its not going to happen. One month pregnancies will be a liability not benefit. Most pregnancies will be miscarriages because the women won't have the energy and calories to make a baby in 1 month. If they babies do survive they will die beyond a certain limit (5 per woman is my estimate), because the 8 people cannot feed themselves, create shelter, feed the huge energy needs of the rapid pregnancy women, and look after all the children all at once.

So if everything goes well, assuming each generation is 25 years, after 200 years you will have:

3 X 2.5^4 people after 200 years => 117 people.

Much more likely is every pregnancy will be a miscarriage and everyone will be dead after 50 years. There is also the problem of inbreeding, which will almost certainly kill everyone down the line even if they survive a few generations.

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