Population expansion

[tris]

Does anyone have a formula for calculating population expansion? I need an approximate population for a colony on an otherwise uninhabited planet.

If you start with 700 colonists, what's the rough estimate of a population 150 to 200 years in the future? Add another influx of colonists (around 200-300) five years after the initial group. Immigration picks up the last 15 years of the time frame with maybe 25-50 new families arriving yearly.

This is not a massive fleeing-earth type of migration, so I'm not looking for huge numbers. I just need a roundhouse figure to give me a better feel for how the colony is progressing.

Thanks!

[journeyman]

tris,

You want to probably use the Malthusian growth model. See en.wikipedia.org/wiki/Malthusian_growth_model.


You might also like reading about the Reverend Thomas Robert Malthus, who came up with this and a whole lot more. He was a very controversial guy.

See en.wikipedia.org/wiki/Thomas_Robert_Malthus.

[tris]

Uh, journeyman, dealing with a numbers-challenged individual here. Got something a little simpler? I don't need exact figures, just a round house estimate of about how many people might conceivably be on this planet after 150 years since the initial incursion. The information on the link was fascinating, but way over my head in terms of finding a formula a x b = c type of thing. I appreciate the effort, though

[isabeau]

I think population expansion would depend on a number of factors. If they're colonizing an uninhabited planet, there could be disease or pathogens or toxins that have the potential to wipe out significant portions of the population.

Are your characters human? What is the ratio of male to female? How often do they procreate? What is the average lifespan?

Perhaps you can just pick a number that works for your story and find a way to justify it based on characteristics and elements of the world you created.

[journeyman]

I'm no Martin Gardner, but let me take shot at 'splaining the Malthusian population growth formula. I am no math genius and had abysmal experiences with advanced math in college. That was before I knew that I had ADD. Somehow the LORD has healed me and I've now got a couple of functioning brain cells I can use for math now. :-)

There's this incredibly neat number called 'e' that is used in calculating compound interest. It's also used in population growth. This repeating number is 2.718281828... but we can use this much of it to figure out population growth.

The formula is the total population for a given period is equal to the starting population times the product of 'e' to the power of the product of the growth rate times the given period.

It looks like:

total pop = starting pop * e^(rate * time)


The good news is you can do this with Windows Calculator by going to view and selecting the scientific calculator. You'll use the regular keys plus the function key 'x^y'.

There is a nice "Rule of 70" that shows that at a 1% growth rate over 70 years a population will double its original size. For 2% is will double its original population in 35 years. We'll use this example to show how the formula works.

First highlight the number for 'e', which is 2.718281828 and copy it in Windows by pressing Ctrl-c.

Next, start the Calculator program. You can do that by pressing the start buttion and press the Run option. Type in Calc and press enter. Calculator should pop up. If that doesn't work, go to the program menu, choose 'Accessories' and start Calculator from there. Go to the 'View' menu and select 'Scientific'.

Now we'll figure out the example for 1% population growth over 70 years. We'll assume we have a constant population growth and that we're starting with 100 colonists.

We'll figure out the exponent first which is the product of population growth rate times the period. In our example that would be .01 * 70. That works out to .7. Remember that number.

Now we go to the Calculator program, select 'Edit' and choose the 'Paste' option. That will paste the number 2.718281828 into Calculator's entry field.

Next we press the 'x^y' button and enter our exponent of .7 and press the '=' button. That gets us the number 2.0137527072324281694880993937531.

Multiply this number by 100 (our original number of colonists) and we get 201.37527072324281694880993937531. Feel free to round this up to 202, because factional folks don't exist in real life. :-)

As we go up in percentages, the number increase pretty rapidly. At two percent, the total population over 70 years with our original 100 colonists is about 406 for a 2% percent rate, 817 for a 3% rate, and 109,664 or so for a 10% rate.

This was pretty cool to contemplate today, especially the concept of 'e' . Saves a ton of work. :-)

It is amazing to find numbers like 'e' throughout nature and even intellectual pursuits. To me it shows the LORD's handiwork and it's always an occasion to worship Him when one of these crops up. I was blessed! :-)

Hope this helps!

[raregem]

My brain hurts.

[journeyman]

Your brain hurts? Lol! Mine is way past numb! :-)

[raregem]

Well, at least yours is numb...it means you're past the pain...for now. lol

[ryain]

I'm feeling dizzy . . . still very intresting! Good to know!

[renblack]

However, I do agree that the living conditions are major issues. How is medical technology? What type of families does the culture favor? Babyboomer families, or China's 1 kid per family? Is there inclination to relocate someplace else - such as return to Earth? Or is that not an allowed option for these people?

And I should hope the guy is controversial - The father of ultimate scarcity. Now what year was it that he declared that we would run out of food and all starve? lol. I try to have a bit more faith in God knowing how many people the world can sustain...Mankind just like playing the guessing game.

[raregem]

That's when God laughs at us, right, Ren? lol... We make our assumptions and He blows our minds.

[renblack]

Yep - definitive proof that God has a sense of humor.

[tris]

Have you seen the projections from the book The Birth Dearth that explains we don't have a population problem we have a distribution problem? Basically, giving every man, woman and child a five acre plot of land, you could easily fit the entire world population (yes for 2010) into North America and a little bit of South America.

Or to really blow your mind....st and everyone in a 3 foot by 3 foot square and the entire world population would fit inside the city limits of Jacksonville, Florida.

I'll take Journeyman's formula and let my hubby run it for me. I can't even add up our check book without making huge errors! (grins)

Meanwhile, a little more about the situation on the colony planet. No pathogens, except what we bring with us. Start with 800 colonists (of which approximately 1/3 don't make it through the first year). Not quite an equal mix of guys to gals and there's a pretty good mix of 30-45s and several 50-60s, plus a lot of young 20 somethings. Average size of the family unit is 8-10 kids.
Medical knowledge is pretty advanced, technology would be limited to what they could bring with them. But I must point out that 3/4 of the world today does not have access to our medical technology and they survive. Some even thrive under harsh conditions (La Paz, Bolivia, for example)

We lived in Ecuador for 10 years and all but two of our friends had their babies at home (and we're talking 10-14 kids in the same timespan) One dear friend delivered three of her children on her own. Not going to recommend it, but even basic medicine will go a long way under primitive conditions.

So am I looking at 100,000 colonists within a 150 year span or more like 10,000?

[metalikhan]

I'm also wondering how much natural disasters would impact the population expansion. Or how long it would be in any given population for territorial skirmishes to develop and decimate some portions of it.

Of the original colonists, what portion is actually able to bear children? That will also influence how slowly or rapidly the population will grow in a given span of time.

[tris]

Since there aren't any other colonists, no territorial skirmishes for now (still in the early stages of colonizing the planet and the immigration is pretty strictly controlled).

Natural disasters are mostly cold related, health related due to the thin atmosphere (at first... by the time the story takes place it's similar in composition to La Paz, Bolivia), work related accidents due to carelessness and equipment failure, and the occasional meteor (if you really want to push the envelope).

As for child bearing possibilities, 90% of the original colonists would fit that category.