Population growth formula?

[Janx]

I wrote a program to do this a long time ago, and actually thought about writing a blog entry about the method I came up with.

Anyway, the method I devised is this:

Lookup the age category/life expectancy for the race involved.

Assume that for your population that there is an even distribution, across age.

If you had a pop. of 1000, and the life expectancy was 100, then that would be 10 people at age 1, 10 at age 2, etc. (math= pop divided by life expectancy)

Multiply this by the % of females in the population (50% for humans). This gets us 5 for a distribution.

Now look at the age categories, and figure out the breeding year range. This is basically the begining of adult hood, to the beginning of the last age bracket. Let's say for humans that's 20-80, which is 60 years. If you had to estimate, assume 1/2 or 2/3 of the life expectancy. This is the span.

Now folks don't crank out babies every year, it's simplest to statistically spread them over their breeding span. Divive the breeding span (60) by the age of maturity (20). We get 3. THat's basically 3 kids per person.

Multiply that by the first number, you get 15.

That means for a population of 1,000, whose life expectancy is 100 years, they will crank out 15 people next year. This seems plausible for humans.

Repeat that math for each year you want to pass.

The interesting mechanic is that a shorter lived race has a lower maturity, and they will basically crank out kids like candy.

Let's say you got 1,000 Kobolds that live to age 30, and mature at age 15.
1000/30*.5=16.67 population distribution
30/2=15 = breeding span
16.67*15=250baby kobolds next year


Now this formula is far from realistic or precise, but it's close enough, and the results compare well against real humans, and produces more babies for short lived races, less babies for long lived races. If you actually plug in real human numbers, it is remarkably close to American growth rate (at least it was when I designed it 15 years ago).

 

[pauljathome]

Thanks everyone, much appreciated
I want to know what a semi-realistic number is since it is important in this specific case.

Its probably worth emphasizing that semi -realistic numbers can vary
HUGELY depending on your assumptions as to fertility level, carrying capacity
of the land, etc, And the variance will go up greatly depending on the time.

If you're talking 100 years then there could still be easily be a spread of several
orders of magnitude between minimum reasonable numbers and maximum reasonable numbers. If you're talking a millenia or so then the spread becomes more or less "whatever you want it to be".

For example, assuming 100 people to start a 1% population growth would
give about 2 million after 1,000 years. A 2% growth would give 40 odd BILLION.

 

[Banshee16]

Most of the posts I've seen on this topic don't seem to have addressed death rates.

With no birth control, birth rates will be way higher, but so will infant death.

Yes, there are clerics, but those powerful enough to Remove Disease even once a day will be relatively rare. It requires a lvl 5 caster. Take a typical village of maybe 400 people, and the chances of having a level 5 cleric are not assured. Even if there is one, it's likely only one, and she can only cast the spell once per day.

So, if there's a bad flu, it could kill dozens of people while she can only save one a day.

Because travel is generally limited to walking or horseback, people might only be able to go 30 miles or so to the next village...so if there's a bad illness, a lot of people could die before help gets there.

Even if we look at Teleport, it requires a lvl 9 Wizard. So is it likely that the messenger will find one in the next village? Or might it be 3 or 4 days of walking before the messenger gets to help (assuming he isn't waylaid by bandits). Even if he gets help, the Wizard at lvl 9 can only bring 1, maybe 2 people with him.

On top of disease, there are other factors like murder. I'm reading a book about risk management at the moment, and one figure they mention is that the homicide rate in medieval england was 14 times higher than it is in the U.S......which itself has the highest homicide rate in the western world.

If most victims of murder tend to be young (as today) and less wealthy (as today), then they're possibly being killed before they can contribute to population growth.

Then, a fantasy world has got nasty monsters that tend to munch on the peasantry, in ways in excess of what peasants on Earth had to worry about.

I found a Wikipedia article which mentions that the growth rate among the poor was essentially zero for a long time......they were taxed heavily enough they couldn't afford big families, and their health was poor enough that they died in sufficient numbers to offset any growth by birth.

Medieval demography - Wikipedia, the free encyclopedia

Altogether, I'm willing to bet that growth rates would be very, very small, even in a fantasy world with access to magical healing.

Banshee

 

[S'mon]

For a medievalesque population with effectively unlimited land in a temperate climate, I typically use a growth rate of doubling every 50 years.

Maximum population will vary from around 30 per square mile (medieval Britain, mostly rugged, lots of hills and moors) to 118 per square mile (medieval France, mostly good farmland). Around 10 per square mile is borderland, or a very marginal area like the Scottish highlands. Much below 10 per square mile is wilderness. Hunter-gatherers tend to be around 1-5 per square mile, less in extreme enviroments (eg harsh deserts), more in extremely fertlle areas (eg the Pacific coast salmon runs). For fertile river valley wheat farmland around 200 per square mile is possible. Rice allows a much higher density.

 

[S'mon]

I found a Wikipedia article which mentions that the growth rate among the poor was essentially zero for a long time.

Historically the very poor have usually had negative population growth, due to not having enough to eat. Population growth was driven by those with assets.

 

[Umbran]

Most of the posts I've seen on this topic don't seem to have addressed death rates.

With no birth control, birth rates will be way higher, but so will infant death.

That's why you commonly phrase this as a growth rate (this can factor in birth, death, immigration, and emigration all in one number) - usually something like one percent per year. I think the peak measured global growth rate for the real world is something like 2.2%, reached a few decades ago. Locally, the number can be much higher.

 

[Umbran]

Now look at the age categories, and figure out the breeding year range. This is basically the begining of adult hood, to the beginning of the last age bracket. Let's say for humans that's 20-80, which is 60 years.

Eh, no. Even in our modern world where we have major medical support humans don't generally breed at age 80, or even 60. Human males are fertile later into life, but the risk to the child increases after age 40 or so, as does the risk to the mother.

 

[Nikosandros]

Eh, no. Even in our modern world where we have major medical support humans don't generally breed at age 80, or even 60. Human males are fertile later into life, but the risk to the child increases after age 40 or so, as does the risk to the mother.

True. Also, humans can breed at a much earlier age than 20.

 

[N0Man]

As much as it may not be what you really want to hear, the previous answer of "as many as you want" is really the single best answer here. Population growth formula is not going to follow some exact formula, especially for 1,000 years. It will vary on such a ridiculous number of factors given that amount of time.

In 1,000 years, you might see the following (and likely, multiple times each):

• Plagues or diseases that could slow growth or create negative growth.
• Wars that could reduce populations.
• Poor weather that produce poor crops and slow growth.
• Famine or other food source losses that could reduce growth or create negative grwoth.
• Culturual changes that might either increase or reduce the average age that mothers give birth.
• Outbreaks of crime, violence, or a harsh leader or other power that kills, sacrifices, enslaves, or otehrwise takes citizens out of the child-bearing cycle.
• Periods of economic growth or recession.
• Natural disasters.
• Mass exoduses to or from the city.

On Earth, in 1,000 years, we have had some incredibly large cities that have sprung up from practically nothing, ancient cities that have become ghost towns, and some of these ancient ghost towns have even been reborn and become big important cities once again.

You might want to rethink your question in terms of how big of a city do you want this to be, relative to the world, and what's areasonable number of people for a given city.

However, I will say that an often overlooked major factor in population growth is not just how many kids a family will have, but the age at which mothers begin having children. Younger mothers leads to higher population growth.

In fact, in the real world, there is the school of thought that best way to slow down population growth to sustainable levels is to provide better educational opportunities for women, because that is apparently the #1 most contributing factor in how old mothers are when they have their first child, which in turn is one of the top (if not the top) factor in overall growth.

 

[N0Man]

True. Also, humans can breed at a much earlier age than 20.

That's also true... the notion of waiting until over the age of 18 is a pretty modern notion. Wives might be 13, 14, or 15 a mere century ago.

The real irony is that supposedly modern teens reach physical maturity at a *much* faster rate than during those times as well.