Let's assume a post apocalyptic scenario, specifically a world which's sentient population was critically reduced due to a series of calamities, such as a sudden climate change chain reaction caused by unchecked pollution and the failure of any safeguards put in place against it, leading to extreme weather in the following era.

What's the minimal population that could make reaching at least 1 billion individuals in about 500 years plausible?

For additional context let's also assume that the planet's environment remained mostly habitabile with minimal adaption and countermeasures (gas masks, supplements and the like) required, that there wasn't much of a technological regression (the residual technology would be akin to that of the mid 21st century earth) and that sufficient resources remained (the latter two thanks to caches and repositories that were put in place in the case of such a scenario).

Let us also assume human-like reproductive rates.

And finally let us assume that ideology wise they'd be very focused on survival and repopulation efforts.

  • $\begingroup$ Could you tell us about the normal reproductive habits of your species, there's not enough to go on at present. What are the hazards, what's the birth/death rate etc.. $\endgroup$ Dec 16, 2022 at 9:31
  • $\begingroup$ @AngryMuppet is this better? $\endgroup$ Dec 16, 2022 at 9:49
  • $\begingroup$ You should specify their ideology, which may be crucial for your story. If their mindset is modern Western then we need a few billions as growth rate is negative. For high level of growth you would need a pre-modern mindset, where having at least half dozen of kids was default and in accordance to the will of God (gods, ancestors, whatever). My POV is that modern ideologies are not sustainable from evolutionary perspective and can only thrive for a few centuries under very favorable conditions, so you should except a reasonable population rebound, but with different ideology. $\endgroup$
    – Shadow1024
    Dec 16, 2022 at 10:16
  • $\begingroup$ @Shadow1024 alright, ideology wise they'd be very focused on surviving and repopulating $\endgroup$ Dec 16, 2022 at 10:45
  • $\begingroup$ @JuimyTheHyena Then I'd agree with Nepene answer, if anything I'd add that 3% is still not the ceiling, so you can have much more bumpy road with a few population collapse on the way and anyway achieve 1 billion. $\endgroup$
    – Shadow1024
    Dec 16, 2022 at 10:52

3 Answers 3


To answer you have to come up with some estimate of population growth rate, let's say in percent per year.

Right now most industrialized nations in the world have negative growth rates if you don't count immigration, or they will soon have negative growth rates given their population distribution. (Namely, too few young people.)

Estimating population growth historically is difficult because we don't have very good numbers for population more than 300 years or so ago. In that time, growth rates appear to have hovered around 0.5% per year. Such a growth rate gives plausible population numbers for most of history. Of course there have been ups and downs.

(From a creationist perspective, if Noah's Flood was approximately 4500 years ago, then to get from 8 people to 8 billion in 4500 years would require a growth rate of about 0.46%, which is consistent with observed rates.)

The fastest growing countries today have growth rates of around 3% to 4%. So such numbers are possible.

A lot depends on how difficult conditions are. If we assume that after the disaster the environment is mostly undamaged, that the world is wide open and empty, that modern technology can be rebuilt much more quickly than it took to develop it the first time, and that there are stored supplies to get the people (or whatever) through the difficult starting times ... growth rates could easily be very high, 5% or 6% or more. If we make opposite assumptions, that conditions are hard and people are struggling to survive, the growth rate could be very low.

In general, the formula is going to be: x * r^500 = 1e9, where x is the initial population and r is the growth rate. Solving for x gives 1e9/r^500.

At 5%, to reach a billion people in 500 years requires an initial population of less than 1 person mathematically, so realistically 2 people. Of course if you start with only 2 people that creates problems of genetic diversity, especially if whatever catastrophe killed everyone off resulted in chromosomal damage.

At 4%, 3 people. Again, genetic diversity becomes an issue.

3% -> 381 (as Nepe says), say 300 to 400

2% -> 50,108, say about 50,000

1% -> 6,907,376, say about 7 million

0.5% -> 82,597,922, or about 80 million

If there was such a catastrophe on Earth in the next century or so and the population was reduced to hundreds, there could be problems with genetic diversity. There'd be a lot of inbreeding, which would probably result in high death rates for the first few generations until the worst mutations were bred out of the system. That might mean a lower growth rate for a century or so. Or it might simply mean that people have more children to make up for the high child mortality rate.


Two to four hundred people

The countries with faster reproductive rates have slightly over 3% population growth per year. We can calculate what population you would get from 500 years of 3% growth with 1,000,000,000 / 1.03^500 and we get 381. That's fairly close to the lower bound of people that can realistically produce a new human population, about 160 people. and the population will lose some adaptivity to environmental issues if there's less than 2500-5000, but humans are good at overcoming environmental issues.

So, assuming some weak growth early on while adapting, a couple hundred is the minimum you need to reach a billion later on.

If you want to mitigate inbreeding issues, just have them grab a sperm bank's supplies early on. That might give them a few hundred or thousand samples to add some diversity.

  • $\begingroup$ That is surprisngly low, thank you very much for your answer $\endgroup$ Dec 16, 2022 at 10:46
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    $\begingroup$ I think your math is off - you've calculated the result if a population started at 1 billion and decayed 3% per year, but that's slightly different than starting small and growing 3% per year. The total you want is 1,000,000,000 / 1.03^500 ~= 381. Still quite small, all things considered. $\endgroup$
    – Cadence
    Dec 16, 2022 at 11:22
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    $\begingroup$ This problem goes a bit beyond simple math. 250-500 individuals are required to avoid incest and 2500-5000 are required to maintain evolutionary potential (phys.org/news/2018-03-populations-pair.html). $\endgroup$
    – Matthias
    Dec 16, 2022 at 11:42
  • $\begingroup$ I added both your comments. $\endgroup$
    – Nepene Nep
    Dec 16, 2022 at 12:33
  • $\begingroup$ As long as you are not concerned about the genetic homogenetic composition of the population. $\endgroup$ Dec 16, 2022 at 20:17

This depends largely on how many people survived, and the breeding rate of these beings, (the fact that you refer to them as a “sentient population” rather than humans suggests to me that they are nonhuman?). Assuming a humanlike breeding rate and the conditions you describe, then these beings could easily reach several billion in 500 years.

However, as I said, it depends…

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    $\begingroup$ I modified the question a bit, is this better? $\endgroup$ Dec 16, 2022 at 9:49

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