How many people need to be born every 8 years to sustain population?

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

• Welcome to WorldBuilding.SE! This looks like a good question, with a lot of thought put into it. The only detail I think you're missing is exactly how often new people join the town. With such a small population, and so few babies in each clutch, you may eventually start running into issues with in-breeding unless there are enough newcomers in the mix. – F1Krazy Mar 20 '19 at 22:22
• If you're going to strive for zero population growth the "raise a cohort of babies every 8 years" would certainly make the village seem a very surreal, communistic place with centralized planning and lack of flexibility allowing drama. Or you could set the stage so that one pregnancy is allowed at each death, which would automatically take care of accidental deaths and the death event could provide a focus for drama. – Patrick Hughes Mar 20 '19 at 22:27
• If your median age-at-death is 72, then you have (roughly) nine same-size cohort-equivalents...and each cohort is indeed about 22 folks. I think you're more likely to get the 16-year-olds pairing off unwisely as they rebel against their seemingly-inflexible parents. Predators tend to love small, isolated, conformist communities - it reduces their risk of being turned in. – user535733 Mar 20 '19 at 22:40
• I think 22 per 8 years sounds about right. And with a certain culture this would be manageable similar to how the polynesians for example dont overpopulate. – Demigan Mar 20 '19 at 22:40
• One thing to keep in mind here is the male to female ratio. If this were to "get out of wack" it could radically change the math. – SciFiGuy Mar 20 '19 at 23:30

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.

• 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.

• 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.

• 'They can not accumulate surpluses to be consumed later'. For a brief moment I had visions of a cannibalistic society, since you were talking about fertile women and children. – Justin Thyme the Second Mar 20 '19 at 23:45
• I was going to write my own answer but this pretty much covers all I was going to say, bar one point. The figures you quote here also assume that all women of child bearing age actually get pregnant, let alone even want to. Based on these numbers and assuming a fertile period between 16 and 40, women are only going to get between 3 and 4 turns through the windows which means that they pretty much ALL have to get pregnant during EVERY window to counteract the mortality rates you describe. Any infertile men or women further add to that burden. Your villagers had really better like being parents. – Tim B II Mar 21 '19 at 0:16
• @TimBII: They will have a window of one year to try and get pregnant every cycle, so they can make quite a few attempts... I actually thought about including some considerations about the difficulty of getting just about all fertile women pregnant in a specified year. – AlexP Mar 21 '19 at 0:45
• Who says health depends on genetics? Lmao. You literally say that you will live exactly as much as your parents. In reality, this depends on healthcare, climate (ecology/toxicity, temperature) and labour environment. There is certainly a genetic footprint in health but... is so small for most people with normal health. I wonder where you get this – Croll Mar 21 '19 at 10:02
• @Croll: I don't fully understand what you are talking about. What I said was that a small random population cannot escape inbreeding effects, that is, accumulation of genetic defects in later generations. Generally the minimum viable founding population is estimated around 4,000 people. This can be of course mitigated if the founding population is screened for genetic defects. – AlexP Mar 21 '19 at 10:44

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.

• The assumption of a pair-bonded society is completely unnecessary. Since it takes two to tango, every person will have to sire two offspring on average. You're allowed a much higher standard deviation in males than in females for obvious reasons. (Of course, this does assume that the split between males and females is even in your society. Interestingly enough, if this system is kept up long enough (think a millennium at the very least) it may actually drive in the direction of a non-even distribution...) – Jasper Mar 21 '19 at 10:07
• Almost any case will drive the ratio to very near 50/50. It would take a very odd mix of genetics and environment to have a naturally non-even ratio. Cultural effects, however (ie one child policy), can have a dramatic effect on ratio. – Michael Richardson Mar 21 '19 at 16:34
• @Jasper The 'pair-bonded' assumption was necessary for the 'equal ratios of men to women' assumption - one man bonds with one woman. All calculations are off if in fact one male mates with 22 females, and the sex ratio is so distorted that the female only has to propagate her own replacement. That is, there are 190 females to 10 males. In which case, 22 babies SURVIVE, but lots more males are born and then culled. – Justin Thyme the Second Mar 21 '19 at 22:55
• @JustinThymetheSecond You should make the lesser assumption, in that case: equal ratios of men and women. A non-pair nonded society with equal ratios of men to women still works out to the same math. (Conversely, a pair-bonded society with much higher male child death rate, for example, will work out to different math, as the females with no partner need to be replaced as well...) – Jasper Mar 22 '19 at 9:43
• @MichaelRichardson That bit was just a thought that "being able to reproduce only once every eight years" (which implies a woman can reproduce a very limited number of times) might possibly be enough to upset the balance. It was just a thought, though, and I don't have any knowledge of any species that has such a limitation. – Jasper Mar 22 '19 at 9:54

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).

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.

Everyone here is answering the wrong question.

"How many kids have to be born every 8 years?" is WRONG.

Because it doesn't really matter how many are born in a given timespan, what counts is how many are born to each mother. [Which means the relevant timespan is the 30-40 years a woman is fertile]

Assuming relative monogamy, the fertility rate for a stable population is about 2.2
That is every mother hat to birth on average 2.2 children (between 2.1 and 2.5 depending on the level of medical care and general helath of the population). 2 is because the mother has to birth 1 women to be her successor-mother 1 man to replace the dad (who won't birth anythining) and then .X to account for premature deaths (premature here means before they give birth themselves)

Also the thing with the cluthes is unnecessary. If it's important/interesting to your story/world, go ahead and do it, it's realistic enough, but there is no actual need for it. First of all, some kids are way slower than others, making a more individual education more important, and secondary, since your small town will probably fall back to mechanical jobs like woodworking, huntil etc. an individual training for each job is way more important than general education, which means that the " 18 yr olds teach the 15 yr olds" won't help too much.

• Given a fixed population size of 200 the number of people in the fertile region depends on the mean lifespan (and population distribution). Thus answering the question of how many people need to be born in a given timespan, is an equivalent question to how many people must be born to each mother. Additionally, it's the question that the OP wants answered. They want to know how big each clutch would be. Given your answer then they would then have to back calculate that number. That calculation requires pretty much the same math as just getting the estimate directly. – Rick Mar 21 '19 at 12:24

Your culture isn't stable. There's a flood. 9 people get killed. Do you have an inbetween clump? Do you shorted the breeding period until you are back to 200? Do moms who have already had their 2 kids have a third?

Genetically your community isn't stable. You will have serious inbreeding problems. This translates into the unpleasant reality of a much larger increase in miscarriages, and kids with birth defects, and kids with genetic problems that make them die early.

A community of 200 is of necessity a primitive community, at best in a blacksmith pig iron tech level. At that level in our culture, you needed on average 4-5 kids per woman to break even. (My mom started grade 1 in a class of 32. She graduated from grade 8 in a class of 20. The other 12 died. TB, farm accidents mostly. That was 1920)

Women die in childbirth. Men are more likely to die in farm accident, or conflict. Your population demographic isn't even. I would expect that the 50-60 cohort would be 1/3 of the 20-30 cohort. You need to make a model of this on a spreadsheet.

At 4 kids per woman, and assuming a breeding time from age 16 to age 40, you need a kid every 6 years. But how many people do you know of who take 2 or more years to get pregnant once they have decided to try? Answer: Lots. So you have a 6 year interval on average, but the births are likely spread out over 2-3 years.

One way you can do this is to have women nurse their offspring for an extended period of time. Hard to get pregnant while nursing.

Another way is to have a cycle of plenty and famine. If your body fat drops below a certain point (about 9% I think) women stop menstruating. When you are that thin, you have other problems too. This in turn would shape society. Women are cherished, protected.

Option:

More communities. Many communities, several day's walk apart. At a certain age a boy goes walkabout. For a year he goes from community to community, and at the end of that year settles in one. Perhaps during that time he acts as a stud too. This reduces the inbreeding problems. It is also a way to more quickly spread the effects of a disaster on one town.

Or at a certain age, girls journey to the nearest town, and marry there.