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I am working on a species that ressembles humans beings and that, although slightly engineered in the sense that the evolutionary leaps are aided by genetic modification, they are left to go through the whole natural selection process on their own. Now I looked on this site and everywhere from research papers to more shady websites and found no information on world population estimates before 10,000 BC or population growth in the prehistoric era. I only found an article comparing humans to macaques as a "weed species". And it offers some idea as to population growth when looking at macaques, but I am not sure how accurate this is. Since I am trying to establish what the migration waves would have been so I can draw a pretty accurate migration (and hence ethnic) map of my intelligent species, I am trying to work out how to calculate population growth. Because Australopithecus conquered most of Africa and Homo Erectus went all the way to SE Asia and possibly even parts of Oceania, so that implies that in 7 million years the population was large enough it allowed migrations Out of Africa and in the first 3 it was also enough to cover the whole continent. Even if we started at… well basically a handful of individuals if not arguably just the one.

An important thing to note is that my generations are about half that of humans, with the individuals from those species living to about 30 years old once they reach adulthood (half of the 60 you'd expect in humans). So although generation numbers will stay the same, the time it will take will be halved.

The continent they start on is also much smaller than Africa and broken apart. It is basically an archipelago of large islands, and it is possible they start on very low ground with salt marshes in a cluster of smaller islands. I have attached a map and a zoom on the smaller islands.

Continent map

Zoom on the smaller atoll

So… how fast do you think they would spread, and how quickly would the population grow from a starting group of 20-200 individuals?

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  • $\begingroup$ 60 years expected life for a prehistoric man? I doubt it was that high even for the civilized Roman empire. $\endgroup$
    – L.Dutch ♦
    Sep 15, 2019 at 4:09
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    $\begingroup$ That's not exactly the topic, but one has to remember that in the stone age we are talking about the average age. The child mortality back than was extremely high. For each child that died during its first years, the average age would drop. But if you only count the individuals that lived long enough to reach adulthood, and they avoided being killed by predators, accidents or other humans, and didn't succumb to infection or died during child birth, you could live long enough to be called an old person even by today's standards. $\endgroup$
    – Tim Hansen
    Sep 15, 2019 at 5:05
  • $\begingroup$ A human generation is usually reckoned at 25 to 30 years. Should we understand that this species reaches sexual maturity at ten years of age? $\endgroup$
    – AlexP
    Sep 15, 2019 at 5:19
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    $\begingroup$ 20-200 is probably too small for long term survival in terms of avoiding effects of inbreeding, see the concept of a minimum viable population. $\endgroup$
    – Hypnosifl
    Sep 15, 2019 at 6:33
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    $\begingroup$ @Nierninwa: So plug in your numbers. Just remember that any prediction over a horizon longer than two or three centuries is useless -- they will run into resource limitations, they will catch a deadly epidemic, crops will fail seven years in a row etc. For example, the Plague of Justinian in the 6th century killed half the people in the Roman Empire. In the 17th century the population of Europe was only double of what it was at the height of the Roman Empire in the 2nd century. $\endgroup$
    – AlexP
    Sep 15, 2019 at 16:20

2 Answers 2

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Straightforward calculation

  • The initial number of females is N. You pick N. Ten, one hundred, one thousand, your choice.

  • The average life span is S. You pick S. Twenty, thirty years. Each year, an average of D = N / S females will die. (D stands for deaths.) Remember that this is the average life span; it must take into account horrible child mortality, famines, lions, tigers, death in childbirth etc.

  • The chance of a female of child bearing age having a daughter in any given year is F. For pre-industrial humans, this is between 1/8 and 1/6 (one child per pregnancy, one year of pregnancy + two or three years of nursing, one child in two is female).

  • The proportion of females of child bearing age is C. You compute this as (max_child_bearing_age − min_child_bearing_age) / S. For example, for humans, assuming average life span of 40 years, C would be (35 − 15) / 40 = 0.5.

  • Now you can compute the average numbers of daughters born in a year, B = C × F × N. (B stands for births.)

  • Now, if there are more deaths than births, your population is doomed. If there are more births than deaths, your population will expand.

  • Each year, the population increase is B - D. Substituting the values, we find that the annual population increase is (C × F − 1 / S) × N.

  • Which means that after n years the numbers of females in the population will be (1 + (C × F − 1 / S))n × N.

  • Notice that the increase is exponential, which, over long time spans, makes it extremely sensitive to initial conditions.

  • Example:

    • Let's assume that the average life span S is 23 years, females become fertile at 15 years of age (giving C = (23 − 15) / 23 = 8/23), and the chance F of a fertile female to have a daughter in any given year is 1/8. The yearly increase will then be C × F − 1 / S = 8/23 × 1/8 - 1/23 = 0. The population is stable.

    • Now let's keep everyting the same but let's increase the average lifespan a little, making it 23.002 years (that's just 18 hours more). The natural increase is a miserable factor of about 1.00001 per year -- the population increases by about one thousandth of one percent per year. But here is the power of the exponential increase: in one million years the population will increase by a factor of 52,500. If you started one hundred females, after one million years you will have 5,250,000 females.

What have we learned?

  • The most important lesson which we have learned is that making predictions about the distant future is an exercise in futility. Increasing the average life span of our population by just 0.002 years (and we cannot even today measure the average life span with such great precision) meant moving from a stable population to an expansion by a factor of 52,500 over a million years. Decreasing it to 22.998 years would have meant extinction in a million years.

  • But we have also learned that we can make predictions over shorter time spans. For example, returning the initial example and increasing the average life span to 24 years would gives us an increase by a factor of 2 every 130 years. This is obviously not sustainable over centuries (it would give an increase by a factor of 180 over a millennium!) but it gives an idea of the population pressure experienced in two or three centuries.

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  • $\begingroup$ Juicy answer worth an upvote, but I wonder if the model makes still sense when the increase in lifetime is shorter than the pregnancy duration. $\endgroup$
    – L.Dutch ♦
    Sep 15, 2019 at 8:24
  • $\begingroup$ @L.Dutch: Of course it still makes sense. Those are averages, they tell you nothing about individuals. Consider the example population with an average life span of 23 years. If the child lives to the age of one year, their average lifespan would be in the thirties. If the child lives to the age of two, they would expect to live in the forties. Consider, for example, imperial Rome in the second century. The life expectancy at birth was around 25 years. But very very few people actually died in their twenties; they either died in infancy, or they died in their fifties or sixties. Average. $\endgroup$
    – AlexP
    Sep 15, 2019 at 8:30
  • $\begingroup$ @L.Dutch: And, yes, for small populations you will see great variation around the average. If on the average you get 0.25 children per fertile woman each year, and you only have 7 fertile women, you won't actually get 1.75 children per year. On the average, three years out of four you will get two children, and one year out of four you will get one child. But this is on the average. You have 6.25% chances to get two years in a row with only one child; 1.5% chances to get three years in a row with only one child... Small populations are fragile and may succumb to blind bad luck. $\endgroup$
    – AlexP
    Sep 15, 2019 at 8:40
  • $\begingroup$ Thanks a lot for this, I guess it answers my question… although it seems difficult to plan how they would spread over 200,000 generations. I guess my other issue is how much space would they take and how fast would they conquer new territories. I assume it's just a case of trying to keep the population density constant… $\endgroup$
    – Nierninwa
    Sep 15, 2019 at 15:53
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    $\begingroup$ Most wild animals do not expand to cover the world. They are kept in check by competing species, natural barriers and the like. Some versatile wild animals, on the other hand, will quickly expand to cover available land. If all you want to do is a possible, and by no means necessary, estimation then you could guess that the area occupied by the population doubles, for example, every 1000 years. If the initial areal of the species covered 100 square kilometers, then they will cover 16 million square kilometers in 17,287 years. (Compute how many doublings are needed, i.e., base 2 logarithm.) $\endgroup$
    – AlexP
    Sep 15, 2019 at 19:53
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What you probably need is a simple math equation that can give you a hint of how fast the populations will grow. I'm not a mathematician, so this was all I could find: https://en.wikipedia.org/wiki/Logistic_function#In_ecology:_modeling_population_growth

Also found these links. Don't know if they can be of any help or if you have already checked them out:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3997431/

https://genographic.nationalgeographic.com/human-journey/

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