Population growth

[Nathal]

Has anybody found a population growth calculator online that can deal with a population that beings with 100% immigrants? I'm creating a place where less than 100 people start anew in a rich and fertile land (in another plane), and I'm trying to figure out how many people would likely be living in that area 200 years later...

Population growth has proven much more complex than I thought. I checked out calculators like this http://www.lucidphoenix.com/dnd/demo/kingdom.asp ... but it assumes an indigenous population to start with, regardless of the age of the kingdom.

Any ideas?

 

[aco175]

I do not know of any calculators that can help, but I have thoughts that might. If this place of milk and honey is on another plane then people would come only if they can get to it easy enough or cheap enough. This also means that it is common enough knowledge on what is there.

Other factors to consider include how big it is, how many monsters are there, and what kind of weather it has. If everything goes in favor of wanting new people than I would guess a whole bunch would come, that is if their lord allows them to go.

Random guess after 200 years is around is 500k. Taking the immigrants to be human with average lifespans and population doubling every ten years. Throw in a few wars since good land and strangers make for that.

 

[der_kluge]

Does it have to be accurate? Can't you just make something up?

Are the 100 people of child-bearing age, or do they represent a cross-section of the population? Are 50 of them female, and 50 male?

The other complication is whether or not they can find a potential mate, and then have children. I suspect in a real population of 100 people, you won't end up with 50 couples. Likely a few will be gay, and a few will just have no interest in procreating, and a few will be unable to conceive, or the couple will be incompatible. So, to figure this one out, we'd need to know more (a lot more) about the population of 100 people.

And is this a group of 100 mormons and/or catholics, or a group of white anglo-saxon protestants? The former being more likely to have a lot more children, and the latter having 1, maybe 2 children.

And what are the conditions like? Is the environment inhospitable and dangerous? Could there be famine, or disease, or monsters which will weaken the population? In any population, the amount of food and resources available will always have a direct affect on how many children are born and/or survive. If I'm wealthy, I'm going to be more comfortable having more kids, but if I can barely feed myself, then having a child isn't something I'm going to be thinking about too much.

So, you mentioned a "rich and fertile" land, so we'll assume that conditions are good, and hospitable. Another is technology. If you just plop people down, they're going to be living in the stone age, regardless of their education level, because tools just aren't going to be readily available. That's going to make farming really difficult, especially if there aren't any domesticated animals to help, or contribute to the food supply.

Have I complicated this enough?

 

[der_kluge]

Random guess after 200 years is around is 500k. Taking the immigrants to be human with average lifespans and population doubling every ten years. Throw in a few wars since good land and strangers make for that.

What on earth are you smoking? 500,000 people, in 200 years? Are they multiplying like bunny rabbits? Unless you've got some huge influx of people coming in all the time, that's just impossible.

No, if a couple has 2 kids, and has a zero population growth, at most you'd have about 300 people, because that'd be three generations worth. As the original generation died, you'd have a new replacement of grandkids. No, it'd never really be more than about 300 kids, if each couple had 2 kids.

I mean think about it. 100 people to start. That's 50 couples. Each has 2 kids. That's 100 new people. That's generation #2. That's 20 years down. A generation is 20 years. That second generation of 100 people has 50 couples, and they each have 2 kids. That's 100 more kids. That's 300 people now, and 40 years. The third generation has 100 more kids, and the original generation (the grandparents of generation 3) begins to die off.

 

[drothgery]

No, if a couple has 2 kids, and has a zero population growth, at most you'd have about 300 people, because that'd be three generations worth. As the original generation died, you'd have a new replacement of grandkids. No, it'd never really be more than about 300 kids, if each couple had 2 kids.

The thing is, if the average woman has more than 2 kids, then you get a geometric progression. And that's not at all uncommon. A small group of colonists can grow into a large one very quickly if they've got a culture that encourages large families and the support structures to make sure an overwhelming majority of children reach adulthood.

 

[Nathal]

I was reading a bunch of webpages as I researched this, and I felt like I was going down into a rabbit hole. One early theorist, named Malthus of England wrote in 1798:

"It may be safely asserted, therefore, that population, when unchecked, increases in a geometrical progression of such nature as to double itself every twenty-five years. This statement, of course, refers to the general result, and not to each intermediate step of the progress. Practically, it would sometimes be slower, and sometimes faster."

But...also according to this site:

"Demographers typically measure human population growth rates as annual growth rates. They calculate the annual birth rate per 1,000 people, and the annual death rate per 1,000 people. For example a birth rate of 18 per 1,000 people, and a death rate of 8 per 1,000 people, gives a net gain of 10 people per 1,000. This is then expressed as a 1% growth rate.

So, at a constant annual growth rate of 1% a human population will double roughly every 70 years, and at a constant 2% a population will double roughly every 35 years. You could just as easily calculate the population tripling or quadrupling times, but demographers prefer to use doubling times.

To attain the 25 year population doubling time used by Malthus, a population would have to sustain a growth rate of 2.8%."

The same site (http://members.optusnet.com.au/exponentialist/DoublingMech.htm) goes on to read:

"Constant Growth Rate versus Variable Growth Rate

Note that a variable positive growth rate (known as variable compound interest) will also result in doubling your population, which is why our global population has been growing exponentially (see below). It is a common fallacy to assume that a constant growth rate is required for exponential growth. This is what Malthus had to say in "A Summary View on The Principle Of Population", published in 1830:

"The immediate cause of the increase of population is the excess of the births above deaths; and the rate of increase, or the period of doubling, depends upon the proportion which the excess of the births above the deaths bears to the population."

Logic alone should be enough to show that, if a constant 1% growth rate doubles a population in 70 years, and a constant 2% growth rate doubles a population in 35 years, then a population which experiences variable growth rates falling from 2% to 1% will double somewhere between 70 and 35 years. "

In other words Population grows geometrically rather than arithmetically.

...

Anyway, I'm thinking that of my original 100 immigrants from Earth (from wales in the 13th century), that the average birth rate was 7 children per women in her lifetime. Average life expectancy was 60 due to some bit of magic. It seems to simple to me to double the population every 25 years without knowing the death rate. With magic, I am certain there would be excess of the births above deaths, so a high growth rate could be expected...

I'm looking at a region about 240,000 square miles.

 

[Nathal]

Does it have to be accurate? Can't you just make something up?

I could, and probably would save myself a headache if I did. But I'm at once curious about this and absolutely terrible at anything beyond basic math...a real predicament.

I was thinking of just assuming a growth rate of over 2% and doubling the population every 25 years. 25,600 people in 200 years....if I did that right...

 

[Evilhalfling]

I just came out of my urban planning methods class and thought I would take a stab at it.

Basicaly Popt100 = (rate of births(over 10 yr) - rate of deaths(over 10 yr) +1 )POWER 20 * intial population.

it is taken to the 20th power because there are 20x10 year intervals in 200
your intial population = 100
to do this properly you need to know the # of people in each age cohort, then apply matrix algebra.

trying to get a simple estimate, death rate .33 (one third of population dies every 10 years)

the .32 death rate was calculated from a class example problem. The birth rate was actually .35 the final population is 148.

If you change the bith rate - to .44 which was as high as I could get it with a normal age distribution then your total is 1033. someting like 4.3 children per couple of reproductive age.

Edit Nevermind i was still calculating over 10 yr interval

 

[mythusmage]

Population tends to expand to fit a land's carrying capacity absent mechanisms that curtail such growth. A land's carry capacity depending on numerous factors, such as soil, precipatation, temperature, plant life, and technology. Very often population will expand to a territory's apparent carrying capacity, only to decline to fit the actual carrying capacity. Often precipitously. See the Anazasi of New Mexico for an example.

For a good example of what can happen when a technologically advanced people colonize a virtually empty land take a look at the demographic history of colonial America and the early United States. While both Europeans and American Indians were recovering from devastating die offs at the time, it was the Europeans who recovered fastest and so were able to provide a constant supply of colonists who would, eventually, overwhelm the aborigines.

Currently the fastest growing areas have a growth rate of around 2.3% per annum. In a land empty of people the growth rate could yet much higher. At, say, a growth rate of 4.6% every 20 years the population can add up in 10 generations. Note that this rate does include fatalities. (Note that I am likely grossly underestimating population growth.)

Update: At a growth rate of 5% over 200 years at 20 years per generation our 100 colonists would see about 63% growth for a population of 163. At a 10% growth rate the same period of time would see the population expand to 264 people.

And I just realized I screwed things up. I'll get back to this later.

 

[mythusmage]

As I promised...

Using a basic calculator I just dug up, after a century at an annual population growth of 1% we get some 270 people. For 2.7 times as many people as we had at the start. My fingers are aching, so I'm not going to do a full three centuries. I'm sure somebody could do it on their computer, but I'm not that good on these things.

At a 2% growth rate there's going to be a lot more people.

Hope this helps.