Population growth formula
Posted 2nd September 2009 at 11:13 PM by 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).
The mortality rate is sort of effectively applied by virtue of the life expectancy. Since Kobolds have a short life expectancy, it is already assumed lots of kobolds are dieing.
I designed this formula years ago, when I had an elven nation that had lost a lot of people in a war, and time was passing, so I needed to know how big they would grow back to, after 100 years after the war (barring other cataclysms).
If you're just looking for a generic answer to "time passed, how many people are in this empire or city?" it is close enough for government work.
Hint: Applying multiple years is easier if you write a small program to loop through the math and add it all up...or just stick it in a spreadsheet.
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).
The mortality rate is sort of effectively applied by virtue of the life expectancy. Since Kobolds have a short life expectancy, it is already assumed lots of kobolds are dieing.
I designed this formula years ago, when I had an elven nation that had lost a lot of people in a war, and time was passing, so I needed to know how big they would grow back to, after 100 years after the war (barring other cataclysms).
If you're just looking for a generic answer to "time passed, how many people are in this empire or city?" it is close enough for government work.
Hint: Applying multiple years is easier if you write a small program to loop through the math and add it all up...or just stick it in a spreadsheet.
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