Population Growth for a colony

[mallet]

Hi guys,

 

I'm looking for any information, ideas, websites, programs, etc... that might help calculate the growth of a population over time.

 

The background is, a human colony ship went off course during it's trip to a new world and ended up setting down on an entirely different planet then they planned on. Cut off from resupplies and any contact with Earth they have spent the last x years building a new society on this earth-like planet.

 

So I am trying to establish that if they started with 1000 people, what would the population probably be in, say, 100 years? or 300 years?

 

What happens to those totals if they only had 500 people to start, or 3000?

 

Does anyone know a good (and fairly realistic) formula to calculate this out? Or even better a program that does the calculations for you?

 

Thanks!

[ajackson]

Re: Population Growth for a colony

 

Hi guys,

 

I'm looking for any information, ideas, websites, programs, etc... that might help calculate the growth of a population over time.

Depends on a lot of factors, but it's typically an exponential growth curve. You might get a factor of ten increase in fifty years, a hundred years is more likely, and of course it's possible that the colony will remain static, shrink, or die out entirely. So, after three hundred years, I would expect 3-6 factor of 10 increases, or a population between 1 million and 1 billion.

[Kraven Kor]

Re: Population Growth for a colony

 

Well, some guesswork might do the trick...

 

But first, some things to consider. What supplies are with them on the ship? What is the environment of the planet they landed on? What about extraterrestrial microbes, bacteria, viruses? What range of human knowledge was on the vessel - was it meant to start a colony, or simply add to another?

 

Under ideal circumstances a woman can (this sounds horrible but bear with me) pump out a child each year, but most women would beat you to death if you suggested they be essentially permanently pregnant.

 

A safe bet would say 3 children per woman per generation, and given ideal circumstances few of those would die per generation.

 

So, number of women survivors at start, multiply by 3, then multiply by how many generations have passed (this is assuming approx. 50% of children born per generation are female.)

 

If there was high death tolls, from any cause, or harsh conditions, lower that to 1 or 2 surviving children per woman. If they were doing any kind of accelerated breeding programs - be it child quotas or test tube babies or whatever - then increase it a bit.

[McCoy]

Re: Population Growth for a colony

 

You could probably do this with a spread sheet.

 

Critical factors are

• How many women are in the first generation
  
• How many daughters do each woman have that grow up and bear children themselves
  
• At what age do the daughters start having their own children
  

 

For an example, let's suppose your crew of 1000 was equal male and female, your parent generation is 500 women who have an average of four children apiece, no sex selection is practiced, and 15% of the children either die in childhood, "never marry," or are barren for some other reason.

 

*pulls up calculator* F1 generation is 850 fertile women.

 

Now frontier societies girls grow up into women quickly, so let's say they start having children at sixteen and two thirds, or six generations per century.

 

F2 generation is 1445 fertile women.

F3 round to 2456

F4, 4175

F5, 7097

F6, 12065

 

Now, some decisions need to be made about how dangerous your planet it, and the society you want to build. Frontier planet, might be rare for people to live beyond 50 years, the last three generations might still be alive, 23337

fertile women. If building a population for the planet is a priority, men may only live half as long as women are barred from any "risky" profession. So let's say men die off twice as fast, the population is two women for every man, and the total population at the century mark is thirty-three thousand people, a small city by modern standards.

 

Feel free to vary the assumptions, it's your planet.

 

A smaller group to start with could cause a "genetic bottleneck," and increase the risk of genetic defects. Look for albinism and cleft palate to be more common in your population, possibly as well as some mild forms of autism or even retardation. You might look up Prader-Willi syndrome and Williams syndrome, these might be guidelines if you want to fix a particular mutation in the population. (I'm thinking that males with visible birth defects might be prevented from reproducing, but females not, YMMV, it's your world and society.)

[Sundog]

Re: Population Growth for a colony

 

I think you're being too conservative, KK.

 

A common trend in "frontier" areas (the US West and Australia during the 19th Century, for instance) is large families. The reason those areas stayed frontier and didn't fill up fast was due to equally high death rates - mostly due to disease. Unless you're talking about dropping colonists with no supplies and no support, we can reasonably expect death rates only slightly higher than in modern periods, thanks to vaccination, barrier nursing and modern germ theory, which combined tend to kill epidemics before they start. These need little in the way of high-tech - it's just a better understanding of the problem that makes all the difference.

 

In the 19th century, 50% child mortality rates were not uncommon. I would be surprised at a 10% rate with a colony planted with modern technology, let alone where medicine has reached by the time we have the capacity to reach another inhabitable world.

 

So, if a family in the NA West had eight kids, four would reach breeding age. In a modern colony, seven would manage that feat (on average, of course).

 

My best guess? 150% increase in population per generation, 200% in the initial generation (before the first settlers start to drop off due to age).

[Lawnmower Boy]

Re: Population Growth for a colony

 

I think you're being too conservative, KK.

 

A common trend in "frontier" areas (the US West and Australia during the 19th Century, for instance) is large families. The reason those areas stayed frontier and didn't fill up fast was due to equally high death rates - mostly due to disease. Unless you're talking about dropping colonists with no supplies and no support, we can reasonably expect death rates only slightly higher than in modern periods, thanks to vaccination, barrier nursing and modern germ theory, which combined tend to kill epidemics before they start. These need little in the way of high-tech - it's just a better understanding of the problem that makes all the difference.

 

In the 19th century, 50% child mortality rates were not uncommon. I would be surprised at a 10% rate with a colony planted with modern technology, let alone where medicine has reached by the time we have the capacity to reach another inhabitable world.

 

So, if a family in the NA West had eight kids, four would reach breeding age. In a modern colony, seven would manage that feat (on average, of course).

 

My best guess? 150% increase in population per generation, 200% in the initial generation (before the first settlers start to drop off due to age).

I think your neonatal death rates are stretching things a little. Population dynamics are a complicated historical science. Historically, human population increase has been darn near flat: from perhaps 1e4--1e5 in 10,000BC to roughly 1e9 in 1800. This has been attributed to the end of periodic famines and introduction of public health measures such as having authorities enforce "this area for pooing, this area for drinking" rules, hence a fall in neonatal mortality. It now seems more likely to be linked to increasing economic opportunities for young familes. (See below.) It produced a population surge that moved around the world, but which has proven transient. Most populations change rates have now fallen back to basically static levels. (I'm assuming that the exceptions will prove the rule eventually.)

There is no longer any doubt that, specific causes aside, this wave has revealed that reproductive choice has always been the most active factor in determining population change rates.

We have also discovered some basic rules at work here from historical cases. Nineteenth century Ireland, and to a lesser extent France, show a stable to negative population growth. This is linked to the same brute average ages of marriage as in modern society. (27+ for women, 30+ for men). We'll call this the Irish model. Socially, you get married after your parents die.

The medieval European model shows a slow doubling rate (100 years or so). It is linked to marriage at c. 23 for women, 27 for men. Socially, you get married when your parents are too old to work.

The "American" model, also seen throughout the world during the great surge, sees marriage at c. 19 for both sexes, or perhaps earlier. Socially, you get married when you are old enough to establish an independent household. This model results in a doubling rate of 40 years, which you can work out to be an annual growth rate of 2.3%. (I think. I might be misremembering numbers, and my brain is refusing to divulge old calculus again.) If you plug those numbers into actual populations, you'll see it leads to a surprisingly high pregnancy rate. I'll have some words about that below.

You'll see now from my "social factors" how models can be linked to the availability of resources, in particular farmsteads.

 

Now, about pregnancy rates: first, we cannot use historical data on family sizes, because they are not telling us what we need to know. If you believe this data, everyone has a mother and a father. That seems obvious, until you realise that we are being told that before 1950 there were no adoptions; no "Palin manoeuvres" (women raising their daughter's/sister's/cousin's/university buddy's illegitimate children); no masters of households impregnating every women unlucky enough to live under their roof and handing them off to their wife to raise; in fact, no irregular households at all. The American case is particularly, blindingly irregular. We know from records that Britain got rid of its copious quantity of abandoned/orphaned children by shipping them to America as slaves. Er, I mean, "indentured servants." Yet you won't find any of them in the genealogical records. Why? Because they are included with the children of the household. Usually the clue is that these are the children who do not get much of the inheritance, but genealogists can't detect this, and, frankly, aren't interested in doing so.

 

So we turn to medical science, and find that it is frustratingly vague. I don't know why. All we need is for a few million women to have unprotected sex every day for their entire reproductive lifetimes, and count the number of pregnancies. I honestly don't know why we don't have more volunteers. But we do have indirect indices of likely fertility/attempt from infertility clinics, some idea of how frequent miscarriages might be, and various scientific findings about postnatal infertility periods that guide us to a very rough notion that the 40 year doubling rate is the highest really plausible one. This raises the question of how the 20 year doubling rates seen in colonial America was achieved, which is especially interesting because it is this data that one Reverend Thomas Malthus used to scare the pants onto us in 1796. My own explanation for this is more hanky-panky (only with numbers, this time), which don't add up.

But that's a topic for another day. Short answer, in the presence of ample resources that make women choose to have children, a doubling time of 40 years may be reached.

[Chris Goodwin]

Re: Population Growth for a colony

 

The Toba catastrophe is believed by some scientists to have reduced the entire human population to between 1,000 and 10,000 breeding pairs.

[Clonus]

Re: Population Growth for a colony

 

I think you're being too conservative, KK.

 

A common trend in "frontier" areas (the US West and Australia during the 19th Century, for instance) is large families. The reason those areas stayed frontier and didn't fill up fast was due to equally high death rates - mostly due to disease. Unless you're talking about dropping colonists with no supplies and no support,

.

 

Which he more or less is. The OP was a situation where all they would have is what happened be on the ship when it landed. No new supplies, no immigrants. Diseases aside, other limiting effects on population growth are food supply (it's probably going to be difficult to establish a viable agricultural base in alien soil), environmental issues (a significant gravity variance will make pregnancy...tricky, and alien spores raise anaphlaxis issues) and social issues (how many women from a modern society really want to be baby machines even when they can count on their children making it to adulthood?)

 

GURPS Space uses a 2.3% growth per year model until the planet starts to get a bit crowded. In general 500 settlers is the minimum to avoid serious inbreeding issues. If we're talking less than ten thousand, there will probably be some noticeable genetic homogenization.

[ajackson]

Re: Population Growth for a colony

 

GURPS Space uses a 2.3% growth per year model until the planet starts to get a bit crowded.

 

Aka x10 per century, or x2 per 30 years.

[Basil]

Re: Population Growth for a colony

 

In theory, the rate of population increase counting only births depends on the average number of female children per female (called F), and the average time between the birth of a female and the birth of her female child/children (called G--generational time).

 

The rate = ln(F)/G

 

If the death rate is independent of the size of the population, then multiply the above rate by (1-death rate).

 

This is more accurate with a fairly large population: with a population in the low thousands it's only approximate.