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So, in a novel a buddy and I are working on, the gods created mankind 3000 years ago, their last act before they perished. The gods left behind several books containing all the knowledge a society would need to grow (agriculture, navigation, domestication of animals, crafting, fire, language, etc.), as well as an enchantment placed upon them that anyone that viewed them would instantly know how to read them.

That aside, we have one civilization that ended up on a peninsula to the far south of the continent. They have a massive desert to their north and nowhere else to go. This peninsula is approximately 58,000 sq km of livable land.

So, the question, assuming they began with a population of about 100 people, what would their population be 3000 years later?

We can assume they always have enough food and water to supply their people. The land they live on is very fertile and water is readily available. It should also be noted that over the years, the population has divided into four separate tribes. I'm not sure if this would have any affect.

Thanks for your time!

EDIT: Someone thought this might be related to farming and feeding a population, but this is not my concern. This place has more than enough food (farming, animals, fish, etc.) to feed their people. I'm more concerned with growth. I've added a comment below to address some of the follow up comments.

It should also be noted that I was assuming a "natural" population growth when I said they'd have enough food. They can't support a massive boom or overpopulation.

EDIT 2: People have pointed that there needs to be a limit to available food. So, guessing they would cultivate somewhere around 20% of available land, how would this affect population growth?

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  • $\begingroup$ This is going to require quite a bit conjecture, but for some foundation: What level of technology (agriculture, medical, education, etc, etc) did they have starting out, and how supportive of life is this peninsula (lush fields ripe for farming and some forest to support industry there, other geography...)? $\endgroup$
    – Ranger
    Dec 9 '16 at 18:19
  • $\begingroup$ Also there's a thing called "Minimum viable population" to avoid interbreeding issues with genetics. Assuming there's no effort to curb this (whomever can marry and mate with whomever), Wikipedia gives an outline of a normal minimum of 500 - 1,000. For this reason you might consider upping your initial count of 100. $\endgroup$
    – Ranger
    Dec 9 '16 at 18:20
  • $\begingroup$ - Their technology level is comparable with the Mayans, though somewhat more advanced in certain things (better farming, better language, better understanding of animals and nature). - So, 100 is not really a viable beginning. We could up it to 500 for sure. - I disagree about the duplication. They always have enough farmland, I don't think that's an issue. They also have tons of fishing, so food is not a problem. Feeding people is not the issue in question. $\endgroup$ Dec 9 '16 at 18:33
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    $\begingroup$ Do you really mean "58,000 sq ft" ? That is absurdly tiny, it means that (a) hunter/gatherer lifestyle is impossible even for a single family; (b) intensive agriculture is possible for a few people but not 100; (c) in a fishing everything becomes dominated by the how far (how many days travel distance) you're willing to go to "hunt" for fish. Feeding people is absolutely the issue in question. In long term, population equals to carrying capacity and the growth rate matters only for short term fluctuations. $\endgroup$
    – Peteris
    Dec 9 '16 at 19:26
  • $\begingroup$ Yeah, there are (rich) people with houses bigger than 58,000 sq ft. Buckingham Palace, for instance, is 828,820 ft² (per Google). $\endgroup$
    – jamesqf
    Dec 9 '16 at 19:32
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World population growth rate peaked at about 2.2% around 1970. Population growth can be calculated the same way as compound interest by $$P = P_0 (1 + r)^{t},$$ where $P_0$ is the starting population, $P$ is the final population, $r$ is the annual growth rate, and $t$ is the time in years.

Plugging in 100 people, 0.022 growth rate and 3000 years we get basically infinity people (2.2E30 to be exact). People can really breed when put to it. Even if you drop the growth rate to 0.5% (0.005), you still get over 3 billion people after 3000 years.

Since 3 billion people isn't what you are looking for, you are then limited by available food, and so limited by available farmland. In that case, this question is relevant. This is what limited humans historically. First people didn't farm, which limited their carrying capacity. Then they farmed in primitive ways, which still limited their carrying capacity. It wasn't until the agricultural revolutions spreading out of Europe in the 1800s that human population was really able to take off.

So in order to calculate your carrying capacity, you need to find out how many people can be fed, because your folks will breed themselves up to that limit in no time.

This paper suggests that lowlands Maya density was up to 700 people / square kilometer around major population centers, and around 300 people / square kilometer in other heavily farmed areas. On the other hand, areas of slash and burn cultivation were lower at 28-85 people /sq km.

If you have 58,000 sq km, then let us say that 25% is arable, and there are 100 people / sq km on average in the arable parts. Thus $58000\cdot .25 \cdot 100$ is 1.4 million people.

Solving the population grown equation backwards for a 1% growth rate, $$1400000 = 100\cdot (1+0.01)^t$$ becomes $$\log\left(\frac{1400000}{100}\right) = t \log(1.01)$$ so t = 959 years to reach that size.

So in a millenia, your people will be 1.4 million strong, having converted 25% of the region to agriculture.

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  • $\begingroup$ So, if we say 20-30% of their land is cultivated for farmland. How would this affect population growth? $\endgroup$ Dec 9 '16 at 19:41
  • $\begingroup$ @user3491276 Edited with results. $\endgroup$
    – kingledion
    Dec 9 '16 at 19:52
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On Growth

Assumptions: using data from here

  • 50% of children are girls
  • at age of ~20, a woman starts having children
  • The chance to die from childbirth is ~20% and 1/4 of the time both mother and child died.
  • 1/3 of all children die before the age of 5.
  • There are typically enough men for all women to get pregnant.

On average, a woman dies after 5 pregnancies, resulting in on average 3,8 children.

2,53 of these survive childhood.

1,29 of them are girls.

So each girl born gives rise to 1.29 new girls.

Thus there is an increase in the female population with 1.29 each generation (~ 25 years) and one can assume that there is a similar amount of men as there are girls.

3000 years = 120 generations 1.29 ^ 120 = 18,653,710,652,522 girls per original girl..

So, well, 3000 years is a long time. If food is unlimited they can easily reach billions and above.

What will happen is that food and living space runs out. If food really is endless overpopulation will spark massive epidemics killing lots of people and increasing the mortality rate dramatically. That is unless they develop advanced medicine during those 3000 years.

On Sustainable Population:

According to this, the carrying capacity of the land using various methods are as follows:

  • Hunter-Gatherer 0.1 person / km2
  • Dry Farming 1-2 person / km2
  • Irrigation 6-12 person / km2

This translates to 5,800 people sustained by hunting and gathering. This population will be reached by the above growth in about 9 generations or about 225 years. At this point population growth will stagnate unless they start farming the land.

If about 20% is farmable, they could increase the carrying capacity to about 23,000 people. This would be reached in just 3-4 generations or 100 years after begining to farm the land in full.

If they also invent irrigation, they could both increase the yeilds and increase the farmable area. Lets say they irrigate 30% of the land. This allows 160,000 people. This amount will be reached in 5-6 generations or 150 years.

Given that there are probably plateus between each stage before new inventions and cultural changes occur, you could add 250 years between each stage.

This would make the population cap out at ~160,000 after a little less than 1000 years. Keep in mind that the devastating effect of wars and the like will increase with farming technology, destroying 100 km2 of irrigated farmland will cause 10,000 people to starve the coming year.

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  • $\begingroup$ In the EDIT, I mentioned that they have enough food to support "normal" population growth. They don't have unlimited food. I see that we need to determine exactly how much of that 58,000 sq km is farmable land. $\endgroup$ Dec 9 '16 at 19:35
  • $\begingroup$ @user3491276 The calculation in my post is based upon the upper class during medieval times. As such it is not assumed they have unlimited food - but that few die from starvation. Factors that possibly mitigate an exponential population boom would be fewer children per female (unlikely unless contraceptives exist or sex is prohibited) and the various problems that come from reaching the limit sustainable by the land (increasing mortality). $\endgroup$
    – Sesdun
    Dec 9 '16 at 19:45
  • $\begingroup$ @user3491276 I added a bit on sustainable population size given various types of farming and sustenance. $\endgroup$
    – Sesdun
    Dec 9 '16 at 20:11
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Depends on the technological level

As your initial population is very small, in the first part (first millenium give or take a few hundred years), the demographics will be rapidly growing in the face of abundant land and food, lack of competition, and comparably advanced technology - animal husbandry and agriculture can provide abundant food while pastures and fresh farmland are available.

Then it will stabilize to the carrying capacity, and for the final 1500-2000 years the population will be mostly somewhere close to the capacity suited for technology of the time - the carrying capacity of the same plot of land grows as people get more effective with agriculture. 3000 years is long enough for major advances, but how far they will get mostly depends on your story.

You can simply look at real world analogues to where the population level converges at each technology level. Given the key data (58000 sq km peninsula with fishing), I'm going to take Denmark as an example (43000 sq km) and multiply by 1.33. [P.S. - maye I shouldn't have multiplied, as Denmark's arable land rate seems extraordinarily high].

Non permanent farming (pasturing animals, fishing, hunting/etc) tech level can support some 100k people in that area. It will take many generations to reach that capacity (e.g. 1000 years assuming an average population doubling every 100 years), but they will inevitably get at least there unless they go extinct.

Iron age agriculture (which seems to be implied in the described tech that is "left to them") can get you to something like 500k - Denmark allegedly did, that may be exaggerated, but you're larger than Denmark. It must be noted that sea is a major "farm" in this case; pure farming requires more land for this population.

Medieval advances will allow you to get a million (again, as Denmark did) - mostly by more exploitation of nature and long term infrastructure development; replacing forests with farmland, irrigation, draining swamps, etc.

~1800s improvements seem to be highly reliant on introducing more effective species (e.g. potatoes) imported from Americas, so they might be or not be feasible in your world. Still, if your civilization is set at that level, then 2+ million would be reasonable.

Modern agriculture (tractors, chemical fertilizers) can feed 8+ million people in that area.

Futuristic agriculture (stacked hydroponics, etc) can go an order of magnitude higher, to 100 million maybe - if we're talking 3000 years from a technologically good starting point would be feasible, but is that what you want?

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