What is a reasonable amount of population growth for 900 years?

Others have looked at this from various theoretical points of view. I want to look at it from the point of view of our own Earth's history, and what would be the impact if your population followed the same growth rate seen on Earth. Do note that for the purposes of this answer, I am ignoring the minimum viable population; in the real world, that's something you'd have to consider, and your 500 humans might not be large enough starting out particularly if they aren't selected based on genetic criteria for a maximally genetically diverse population and that diversity is carefully managed and monitored.

The Real Population Problem on the blog Do The Math comes in handy, as it gives population graphs and growth rates for the human population during different eras in a convenient form. The numbers are basically (all numbers are approximate, obviously):

• From 10000 BC to 3000 BC: about 0.03% population growth per year
• From 1000 AD to 1700 AD: about 0.12% per year
• From 1700 AD to 1870 AD: about 0.41% per year
• From 1870 AD to 1950 AD: about 0.82% per year
• From 1950 AD to 2000 AD: about 1.7% per year

Here is an alternative graph (Kremer and Vermillion) which shows the period 2500 BC to 2000 AD. Notice the negative population growth around 1300 AD, and that it dips to right around zero on several occasions. The dip around 1300 AD might be explainable by the beginnings of the Little Ice Age and the Bubonic plague, although strictly speaking that is speculation on my part.

The thesis posed in the Do The Math post to explain the jumps in growth rate is:

We can perhaps attribute the 1700 jump to the Renaissance and scientific progress. We learned to wash our hands after wrestling with our pigs, and that diseases were not caused by bad vapors conjured by impure thoughts. The jump around 1870 corresponds to the Industrial Revolution, in which coal transformed the production of steel (providing agricultural tools), rail transport of commodities, and began to mechanize agriculture in a limited way. 1950 marks the Green Revolution: full-scale petrolification of agriculture, accompanied by massive fertilizer campaigns using natural gas as the chemical feedstock.

This leads to a rather simple thesis: the surplus energy presented to us by fossil fuels allowed us to feed people more easily the world over. The bounty of fossil-fuel-turned-food encouraged an explosion in birth rates, as happens for virtually all organisms given similar circumstances. It's so blindingly obvious that I am embarrassed to have belabored the point as long as I have.

We can also use these numbers to answer your question with a reasonable degree of accuracy. For example, for a Middle Ages level society, the human population will grow at about 0.12% every year on average. (If you want this to be realistic, don't forget to throw in the occasional boom year as well as the occasional plague or die-off due to a few years of crop failure!) Starting with 500 humans and letting 900 years pass, we end up with $$ 500 \times 1.0012^{900} \approx 1471 $$ or let's round that off to 1,500 humans. Not a whole lot. Under those conditions, your colony is extremely vulnerable to die-off; a single serious disease can easily take out a large fraction of your entire population.

If instead we use the current era, during which we have gone to the Moon, (even human) spaceflight is so routine that it often isn't reported in the news, energy has been plentiful, intercontinental travel and trade is something the world could barely survive without, and so on, then the same calculation becomes $$ 500 \times 1.017^{900} \approx 1.94 \times 10^9 $$ or just under two billion people.

The above calculations assume no significant leaps in technology or society during the interim period as described by the blog post. For a reasonably developed society and over such a long period of time, this appears an unrealistic assumption. If we instead take the 900 year period from 1100 AD to 2000 AD and use the above figures, then the calculation becomes slightly more involved, but significantly more realistic.

• 600 years from 1100 AD to 1700 AD at 0.12%: $ 500 \times 1.0012^{600} \approx 1027 $
• 170 years from 1700 AD to 1870 AD at 0.41%: $ 1027 \times 1.0041^{170} \approx 2059 $
• 80 years from 1870 AD to 1950 AD at 0.82%: $ 2059 \times 1.0082^{80} \approx 3957 $
• 50 years from 1950 AD to 2000 AD at 1.7%: $ 3957 \times 1.017^{50} \approx 9192 $

for a final population of about 9,200 people. Frankly this sounds low, but that's part of the problem with the exponential function: it works slowly at first and with small inputs, then takes to the skies when the input grows. Note that the first doubling took about 600 years, whereas the last doubling happened in less than 50 years.

You can plug these equations into a spreadsheet and play with the numbers to see if you can get the effect you are after. For example, if instead of starting with 500 people at year 1100 AD we start with 10,000 people and calculate over the same period, the result becomes quite different:

• 600 years from 1100 AD to 1700 AD at 0.12%: $ 10000 \times 1.0012^{600} \approx 20535 $
• 170 years from 1700 AD to 1870 AD at 0.41%: $ 20535 \times 1.0041^{170} \approx 41170 $
• 80 years from 1870 AD to 1950 AD at 0.82%: $ 41170 \times 1.0082^{80} \approx 79125 $
• 50 years from 1950 AD to 2000 AD at 1.7%: $ 79125 \times 1.017^{50} \approx 183807 $

The population grows by the same factor in both cases (about 18x) but since the starting population size is larger, the resulting population also obviously is larger.

Looking at your median age at death of 60 years, we can also look at life expectancy variation over time and conclude that this is similar to a Medieval Britain (approximately 500 - 1500 AD) level of society (at age 21, life expectancy was to a total age of 64 years). Our handy-dandy table above doesn't include specific figures covering that period, but around 0.1% population growth per year appears to be a reasonable extrapolation based on the data we do have. That also appears to match reasonably well with the Kremer and Vermillion graph posted on the History Stack Exchange. In the present day, we see such life expectancies primarily in Africa south of the equator, and slightly longer life expectancies in Russia, including Asian Russia. The effect of diseases on life expectancy is particularly pronounced in Africa, however; according to World Health Organization data as quoted on Wikipedia, the life expectancy in Botswana and Zimbabwe would more than double were it not for HIV/AIDS. Current day countries which have a life expectancy of exactly 60 years at birth are Kenya, Rwanda and Afghanistan (again WHO data, dated 2012). Perhaps interestingly, neither of these show a large difference between genders; they are all listed as 59 years for men and 61 years for women.

It is also important to keep in mind that the population growth rate is going to be heavily impacted by culture as well. If the culture is one that encourages people to have lots of children, the overall population growth rate obviously goes up; if the culture actively or passively encourages people to have fewer children (as for example is the case with China's family planning policy), the number will be lower or could even lead to a population decrease over time. A population that reduces in size over the long haul is obviously not sustainable, but in extreme situations it could become necessary to take such measures in order to avoid even worse consequences of resource overshoot. The culture can also, of course, change over time; 900 years is a fairly long time for any society when looking at it in terms of a human lifespan.

You can decide on population growth rates for different periods and perform the same types of calculations yourself to get population sizes even down to per year if you are so inclined. If you do, I encourage you to make sure that there are die-offs as well; there are going to be years when quite a number of people die, especially in a society that doesn't have access to the advanced health care technology of today, and those are going to make a major dent in the population curve. For further added realism, consider demographics as well (maybe it is a disease that kills off the young more than the adults; also considering that you don't have many people who are actually old). The effects of such a die-off could last for decades before the population pyramid is somewhat back in shape.

posted almost 10 years ago

Canina‭

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