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Let's say an isolated colony is established in an ideal environment with the goal of growing the inhabited human population as quickly as possible. Health care is provided for them by managers, or those that own the colony, and is roughly up to twenty-first century standards with improvement on gene technology. Those in the colony are not allowed to develop technology beyond that used in the nineteenth century to quell any possibility of a successful uprise against their managers, but they are given the means to be self-sufficient. They can grow their own food, they are allowed to be educated enough to read and have a trade, and have laws enforced by their managers to kepp them 'in line'.

How long would it take for one hundred couples in the colony (one hundred men, one hundred women) - all of good genes, with no genetic diseases - to make one million descendants? That is, if Generation A had two hundred people in it and started having children at the age of sixteen (and were allowed to have as many children as possible), and every generation started having children at the same age (and are also allowed to have as many children as possible), how many generations would it take for a generation to be made up of one million individuals?

It is illegal to have sex outside of marriage, and marriages are preapproved by managers to ensure there are no genetic issues - rather, only couples with low chances producing sickly children are allowed to marry and reproduce with each other. Assuming they keep genetics records of every individual, and then get samples from all of their children to have their genetics as well so they have on record who the parents are, I assume inbreeding would still be an issue at some point. How long would it be before inbreeding became a problem? Could they hit the one million mark before that?

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    $\begingroup$ "as many children as possible" part is problematic. I don't see enough details to figure out how much is that, and that's central part, rest is math. $\endgroup$ – Mołot Feb 1 '18 at 20:27
  • $\begingroup$ @Mołot Presumably as many children as possible would be however many children a woman can have in her life time multiplied by the number of women in the generation. $\endgroup$ – Bellerophon Feb 1 '18 at 21:51
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    $\begingroup$ @Bellerophon yes, but under our tech level (health care)? Medieval one? Futuristic? Fertility varies by race / ethnicity so what race are they? And so on. $\endgroup$ – Mołot Feb 1 '18 at 22:22
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    $\begingroup$ @Mołot The question states 21st century healthcare. It also says as many children as possible which is a biological limit and doesn't vary much between races. Fertility rate is a cultural limit and so doesn't come into account here. $\endgroup$ – Bellerophon Feb 2 '18 at 13:11
  • $\begingroup$ In a genetically healthy population with controlled breeding and regular genetic screenings, inbreeding will not be a problem at all. What you will see is the founder effect when the genetic diversity of the population is rather low. However, unlike inbreeding which is usually associated with negative effects like genetic deficiencies the founder effect in your population will result in stronger genes. However, you have to select your breeding pairs very carefully. $\endgroup$ – Olga Feb 2 '18 at 20:45
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Assuming 21st century health care so that women can survive birth and their children survive to adulthood and there's a social system to support the children, then look at modern countries, you could reasonably foresee a Total Fertility Rate of 6 or more (on average a woman gives birth to 6 children during her reproductive period). Combine that with an Infant Mortality Rate equal to the best around now, which is less than 1%.

Assume no dicking around with sex selection, so you get the rough 50/50 split in births you'd expect, with equal expectations of growing up. Assume you have only 3 generations alive at any one time. Each generation, we'll take of 1% or so of newborns to represent infant mortality. Each generation represents all the children born to women of the generation before.

So, Generation 0 has 50 men and 50 women, total population 100. Generation 1 has 149 men, 149 women (average 6 children from each Gen 0 couple, with a 1% or less infant mortality rate), total population 398 (Gen 0 + Gen 1).

Generation 2 has 443 men and 443 women, total population 1,284 (Gen 0 + 1 + 2).

Generation 3 has 1,316 men, 1,316 women, total population 3,816 (Gen 1 + 2 + 3).

Generation 4 has 3,909 men, 3,909 women, total population 11,236 (Gen 2 + 3 + 4).

And so on: here's the summary of total population:

  • Gen 0: 100
  • Gen 1: 398
  • Gen 2: 1,284
  • Gen 3: 3,816
  • Gen 4: 11,236
  • Gen 5: 33,172
  • Gen 6: 98,320
  • Gen 7: 291,908
  • Gen 8: 867,064
  • Gen 9: 2,575,480

So by the 9th generation born on the planet, the 10th generation overall, you've blown by the 1 million mark.

Now, for time. Assume women on average have their first child at age 20, their last at age 32 (giving two years per child). That gives an average generation length of 26 years, so you're looking at somewhere from 234 to 260 years after colonization to hit the million mark.

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  • $\begingroup$ I like this answer, but it is based on real world human behaviour, rather than the "race for numbers" scenario in the original question. I think the best answer is somewhere between this one and my own. $\endgroup$ – OhkaBaka Feb 1 '18 at 22:33
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    $\begingroup$ The "race for numbers" is pure nonsense because it overlooks the problem that humans don't just pump out children; children have to be cared for, and caring for children becomes harder when other children also have to be cared for and are too young to care for themselves even minimally. Not to mention the pure physical toil on the mother. There have been exceptions such as caused by the Great Stork Derby (4 women had 9 children in 10 years), but generally and historically a baby is a year old before conceiving the next (and the resulting 9 month pregnancy). $\endgroup$ – Keith Morrison Feb 1 '18 at 22:43
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    $\begingroup$ Except that you started at 50 couples instead of 100. I really like this answer. 3 generations is about right for mortality. $\endgroup$ – Necessity Feb 2 '18 at 3:48
  • $\begingroup$ Given an adequate food supply and a lack of contraception I think a total fertility rate of 6 is low. $\endgroup$ – Loren Pechtel Feb 2 '18 at 16:46
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    $\begingroup$ Not practical. Possible, but not practical. Among other things, the older a woman gets the higher the risk of problems in childbirth. The second is that it's going to be physically brutal on the women. Third, with 19th century technology, a great deal of the population is going to have to be farming to supply food, and removing half of the adult population from being able to work at anything other than childcare is going to be a disaster. Contrary to misogynistic myth, women were crucial for farming operations, and they can't do that while constantly pregnant. $\endgroup$ – Keith Morrison Feb 2 '18 at 20:54
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The Math

Assuming biologically humans can have one baby a year safely from 16 to 40, and that your 100 couples start at 16 years old on day 1 with 100% success rate... with no multiple births and perfect gender parity.... then my math (which is dubious) says about 115 years.

There are SO many factors though... assuming every woman is fertile for that whole period, healthy enough to bear children for 24 years... which is... ludicrous in real life, but theorhetically possible...

Honestly the men are bordering on irrelevant in this equation. Worse... detrimental... if you replaced 70 of your men with more women, you could get there sooner.

The Logistics

Ok I reread the original question to clarify something about HOUSING... where are all these rapidly spawned folks going to live. I realized these are real world colonists that are said to be self sufficient hunter-gatherers.

My calculation (and everyone elses so far) assumes these are people in a vacuum with their needs being met, etc. Requiring them to farm and ranch to sustain themselves, and their vast families, build homes and communities. Govern. etc...

The children and men can only do so much. I think it is unlikely in this scenario that humans can breed at this rate successfully. This would DRASTICALLY diminish the birth rate.

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  • $\begingroup$ I checked... the most I can find of single births is 23... but the woman with the most children gave birth 27 times (for a total of 69 children)... mad as it sounds, the above is apparently viable. $\endgroup$ – OhkaBaka Feb 1 '18 at 21:38
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    $\begingroup$ Was writing my answer at the same time, which was not an extreme but a first overview. 64 years seems a little bit short: did you wait for the children to reach 16 years old before breeding? But is is the same order of magnitude anyway... $\endgroup$ – Uriel Feb 1 '18 at 21:48
  • $\begingroup$ Yeah... that is the slowest part... it picks up at 16 years, and then explodes at 32 $\endgroup$ – OhkaBaka Feb 1 '18 at 21:49
  • $\begingroup$ OMG... but I didn't take into account the breeding pairs... crap... so yeah... longer than that... $\endgroup$ – OhkaBaka Feb 1 '18 at 21:50
  • $\begingroup$ Fixed the math. $\endgroup$ – OhkaBaka Feb 1 '18 at 22:11
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As Fast as Possible?

A human female will be able to give birth to a single child every 9 months. Across 450 months (37.5 years) you would expect to have roughly 5156 children (3% twin rate, 0.12% triplet plus rate). This puts each mother giving birth to approximately 50 children each, and if they start at 16 years old then 37.5 years conveniently puts the girls at the average age for menopause.

Therefore you produce the following data...

  • Generation 1 (of 200) produces 5156 children.
  • Generation 2 (of 5156) produces 132,922 children.
  • Generation 3 (of 132,922) produces 3,426,721 children.

The fullness Generation 3’s offspring would arrive in just under 112.5 years from the start. All of generation 1 would have passed away at this point, and most of generation 2 would have died as well. Thus, if 100 couples had as many children as possible and their descendants did the same, you would arrive at a population of at least 3,559,643 after 112.5 years. Generation 3 would need to have approximately 30% less children to arrive at a relatively stable population of 1,000,000.

Because of that Generation 3, instead of having the 50 children average of the previous generations, would have 15 children each. 15 children each as fast as possible would take 11.25 years. They would then need to be put on birth control and generation 4, 5, 6, etc would all have two children each and then be put on birth control. If each couple of Generation 3 has 15 children each as fast as possible then the population of roughly 1,000,000 would be achieved in 86.25 years from the starting point.

(Sidenote - The youngest of generation 3 would require an additional 16 years to reach "breeding age", but 1,000,000 would likely be hit before that point.)

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I tried to put some calculation in a spreadsheet:

enter image description here

And with values:

enter image description here

So the million is reached between generation 7 and 8. Which is 7.5 * 16 = 120 years

But you could use a more "realistic" scenario, like not all the women have children, some children die before reaching reproduction age, some grandparents die early, and "only" 4 children by woman:

enter image description here

Then you'll get 1 million between gen 10 and 11: 10.5*20 (reasonable reprod age) = 210 years

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  • $\begingroup$ That was my original number too, though my math was broken and I had to correct for breeding pairs rather than individuals... did you take into account the 16 years of lag time before the second generation can breed? $\endgroup$ – OhkaBaka Feb 1 '18 at 22:14
  • $\begingroup$ I used excel as well, but ended up doing a year by year simulation. And you select your breeding population as the sum of birth between 20 and 40 lines above (considering they breed between 20y and 40y old). Not sure I am very clear here ;) $\endgroup$ – Uriel Feb 1 '18 at 22:25
  • $\begingroup$ Why did you divide children of 0-gen by 2 to make 1-gen couples and not repeat for the others? Also D2 should be B2*2+C2, not the other way around. $\endgroup$ – Necessity Feb 1 '18 at 22:49
  • $\begingroup$ @Necessity you're right, corrected the math $\endgroup$ – Legisey Feb 2 '18 at 7:50
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My best, very rough guess: about 40 years for a low estimate, a few extra decades for something more realistic

According to this Biology StackExchange question, as few as 25 couples can avoid inbreeding if the pairings are strictly monitored, so inbreeding shouldn't be much of a problem for your 100-couple colony, especially since they seem to start out healthy. However, this is still a pretty small gene pool, so any genetic problems that do develop while on the planet could easily affect a large part of the population.

As for the time to reach a population of 1 million from 200, here's a rough estimate:

Assuming they can get busy from the start and there are no problems or twins/triplets/etc., 100 women will produce 100 babies every 9 months; 1,000,000/100 = 10,000 9-month iterations, so that means 90,000 months or 7,500 years is the upper bound to reach 1 million people from only those first 100 couples.

However, as you said at the age of 16 the descendants of the original couples can start aiding the colony. Assuming 50-50 boy/girl ration, after 16 years and about 21 kids per original colonist, the next generation, consisting of 50 women, can start bringing bundles of joy into the colony. Using the same math above, 150 women can reach 1,000,000 in 5000 years. 9 months later there would be 200 women who could 1,000,000 in 3750 years, then 250 women do it in 3000 years, ever decreasing in smaller increments.

There is probably an equation to plot the above and get a more accurate, however since I don't remember much of my college calculus classes. From some trial-and-error diminishing returns really seem to kick in around 75 years(10,000 women), so my best guess to reach 1,000,000 people is around 20-50 years, if they're doing nothing but making sweet, sweet love. The upper bound is probably a better guess, since birth complications, recovery time, time taking care of the children, women passing child-bearing age, etc. will all contribute to the growth time.

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  • $\begingroup$ You got the math wrong somewhere. From the original pool, 100 babies every 9 month indeed require 10.000 month. But that is 833 years, not 246. If you used the same math thereafter... $\endgroup$ – Uriel Feb 1 '18 at 22:06
  • $\begingroup$ Thanks for pointing that out, I accidentally divided by days instead of months. It's even worse than your math: 10,000 9-month iterations is 90,000 months as I thought, but divided by 12 months in a year: 7500 years is the upper bound. I'll edit the math. $\endgroup$ – Giter Feb 1 '18 at 22:14
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Let's start with the math: consider that couples settle at 20 years and have 10 children between their 20 and 30's. So you roughly multiply by 5 your breeding population every 25 years. If you start with 200, you reach the 625000 after 5 generation (125y) and more than 3 million after 6 generations (150y). With optimization, you can do it within one century.

However, you need diversity to avoid genetic issues. 200 people are unlikely to avoid them without medical aid and/or genetic engineering. The concept of Minimum viable population applies here...

(update)

Here is a simulation showing only the breeding population (age 20 to 40).The initial glitch at year 21 is because at year 20, the first children breed and their parents are still breeding too. Year 21 is when the 100 children born 20 years before breed alone, quickly followed by all this generation. Year 41 you see the same phenomena. Year 115 is when you reach the million.

  • If you use a 16y-42y breeding age, you reach the million at year 95.
  • If instead of years, you breed non-stop (I doubt this is biologically sustainable), then years become 9-months periods, breeding start at 12 (yiks!), and you reach the million breeding population in quick 72 years
  • If you the take into account the non-breeding population, you reach the million total population in 59 years. This is the mathematical absolute without hacks (like breeding only girls for the first generation, as they are on the critical path, not like males).

Here is a view of the population (logarithmic scale): enter image description here

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  • $\begingroup$ Are you assuming people can't die of old age? $\endgroup$ – Samuel Feb 1 '18 at 21:49
  • $\begingroup$ No, but death are negligeable as the population growth is exponential. if you consider a 75y lifespan, the death represent 1/(5*5*5) = less than 1% of the population. $\endgroup$ – Uriel Feb 1 '18 at 22:02
  • $\begingroup$ Death is irrelevant... OP asked about descendants, not population $\endgroup$ – OhkaBaka Feb 1 '18 at 22:34
  • $\begingroup$ @OhkaBaka: good point ! Even if it does not improve the best-case scenario, which fits in human lifespan. $\endgroup$ – Uriel Feb 1 '18 at 22:42
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I did the spreadsheet method. Assumptions are based on the number 16 for symmetry and biological plausibility.

  1. Reproductive age starts at 16 and ends at 48.
  2. Nonreproductive age is 49 thru 80.
  3. Population will include children <16, reproductive age 16 thru 48, elders 49 thru 80
  4. A woman will have 16 children over her 32 reproductive years.

  5. Each year 0.5 of the reproductive age population produces 0.5 children.

  6. For each the row 16 prior (-the row 17 prior) moves into the reproductive column and is subtracted from child column. The same for elders and for deaths.

Note these are not hard numbers; people do not necessarily all drop dead at 80. They can be considered the peaks of a bell curve normal distribution.

xcell rows

Using these numbers I find the population cracks 1,000,000 between year 116 and 117.

A real world comparison shows this to be pretty fast.

http://family.jrank.org/pages/837/Hutterite-Families-Fertility.html

In 1954, Joseph W. Eaton and Albert J. Meyer published their landmark study on Hutterite fertility. They documented that from 1880 to 1950, the Hutterites grew from 443 to 8,542 persons. This represents an annual increase of 4.12 percent, which appears to be the world's fastest natural growth rate. Documenting an average family size of slightly over ten children, Eaton and Meyer established the Hutterites as the demographic standard and estimated that maximum fertility for humans is twelve to fourteen children.

That said the Hutterites did not have the benefit of modern medicine and probably suffered higher child and mother mortality than your moderns would.


In case anyone is interested, this rate of reproduction cracks 1 billion at 230 years and 1 trillion at year 337. Hopefully they find some way to power things down.

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