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So I'm doing some worldbuilding for a small, isolated village on the coast. The winters are harsh, but making sure everybody has enough food generally isn't an issue because they have good trade with an outside source, and they are community-led so they make sure nobody gets left out in the cold (literally or metaphorically). New people will join the town every now and again, but not often enough to really impact the population.

I think the population is small - maybe two hundred people - and the average person reaches about 65-70. So my question is, how many kids have to be born to sustain this in a zero population growth model?

I had the idea that the town tries to synchronise births so that every child has friends their own age to play with and learn from, and I thought every 8 years or so made some sense - the 8-year-olds could start learning a craft, and the 16-year-olds could teach the 8-year-olds, whilst the 24-year-olds start to couple off and have their own babies. How large would each "clutch" of babies have to be?

I did some quick maths and got maybe 20-25, but I'm not sure how accurate this is. My reasoning was 8 (number of years)/70 (average lifespan) * 200 (population) = ~22.

If anybody has a more solid idea I'd love to hear it! And if you think this is a really stupid idea then let me down gently please haha

Your calculation is correct assuming that all children born live to be 70. But that is not the case even with the most modern health care. So you may want to up the number of babies a bit, to account (1) for infant mortality, (2) for the tendency of young males to do stupid things which get them killed, and (3) for the general premature mortality due to diseases and accidents.

Here are two tables grouping the population by age cohorts; first assuming that all babies born live to 70, and then assuming a more natural population pyramid.

Age cohort
----------
 0 to 7 22 32
 8 to 15 22 27
16 to 23 22 22
24 to 31 22 20
32 to 39 22 20
40 to 47 22 20
48 to 55 22 20
56 to 63 22 19
64 to 71 22 18
---------- ---- ----
Total 198 198

A random isolated village of 200 people surviving long term would be a clear sign of divine favor.

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  Unless the initial population was chosen extremely carefully by in-depth genetic screening there will be severe inbreeding effects after a handful of generations, raising the mortality. (Note that there are only about 40 to 44 women aged 16 to 47 at any given time.)

  
  
  

  For example, in (the pre-modern principalities which would eventually coalesce into) Romania, a significant fraction of the women (and a smaller fraction of the men) married into neighbouring villages, so that there was some exhange of genetic material. This had also the positive effect of creating wider social networks.

  
  


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  With such a small population the village is prone to demographic shocks. One good sized war, or one Tartar raid, or one epidemic and the population pyramid may be skewed irretrievably.

  
  
  

  Consider for example what happens if the Tartars come and abduct half of your 20 women aged 16 to 31. Or consider what happens if the Thirty Years' War comes and kills two thirds of your men aged 16 to 47.

  
  

Grouping births into clutches every eighth year has the massive drawback that almost all women of reproductive age suddenly find themselves busy with babies at the same time.

• In a real village of about 200 people, with 4 births per year, you have about 8 to 10 women out of the workforce at any given moment, for a total non-working population of about 40 souls (8 to 10 women and 30 to 32 small children), or 20%.




• With this grouping, every eighth year a whopping 32 women go out of the workforce for two or three years, for a total non-working population of about 60 souls, or 30%. True, in non-fertile years the non-working population drops to around 15%, but this is a village, they cannot accumulate surpluses to be consumed later.

22 is right. At 22 you do not have much cushion for downside risk, like people dying young. But that might be OK. Maybe there is not much downside risk of that sort.

I would be interested to read a story set in this world. I feel like it must be set in the future - infant and child mortality is nil, life expectancy is reliably long, women start having babies late in their reproductive life, and they have control over pregnancy such that they can time births all together. That last one is why it is in the future because most societies still cannot reliably pull that pregnancy control piece off.

Also "community led" sounds interesting to me. Maybe that is the secret. Good luck with your story.

As others have said, mathematically 22 is right, but fails to account for early deaths.

But there is a much simpler answer. Every 8 years the number of babies you produce is the number of people needed to raise the current population to 200 (or some similar suitable number). This will be approximately the same as the number of people that have died since the previous birth time.

If things haven't been going well, you need a larger number than 22, and if people have been healthy, a smaller number will be fine.

And again, as others have pointed out, it would be good to occasionally add some fresh genetic material to the gene pool (which would also reduce the number of babies required at the next birth time).

I am trying to get my head around ALL the math.

Assuming this is a pair-bonded society, for a stable population, each female has to give birth to two children - one to replace her, and the second to replace her mate.

That means the female gets pregnant twice - once when she is 15, and once when she is 23 (or 23 and 31).

So 11 fifteen year olds get pregnant from 11 fifteen year old boys, and 11 twenty three year old females get pregnant from 11 twenty three year old boys.

And no one gets pregnant in between.

So either every male and every female have sexual intercourse on only two occasions, or this community has very good and enforced birth control or enforced abortion, neither of which you mention. That puts it in a very modern context.

Alternatively, there was a society that pretty much matched this one - Sparta.

One thing that is seldom mentioned about Sparta, was that it was intensely homosexual in nature, and the only sex between male and female was for reproduction that was strictly proscribed.

It was a very interesting society.

Having sex only twice in your life?

Be very careful of that which you wish, as the Law of Unintended and Unforeseen Consequences can sometimes be very brutal.