Population Mechanics

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cadbrowser
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Population Mechanics

Postby cadbrowser » 2012-03-26 11:03am

Is there anyone that can point me to a simulator that allows a user to start off with "X" amount of people, set the life expectancy, and average birth cycle, and then run it for a set amount of generations to see how it effects population size?

I'm trying to do it mathmatically but I'm afraid that I am failing at it.

Thanks.

:banghead:
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HMS Conqueror
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Re: Population Mechanics

Postby HMS Conqueror » 2012-03-26 04:35pm

I don't know of a calculator that does this but the maths is quite simple if you use birth rate rather than life expectancy.

dP/dt = (B-D)*P

B - birth rate per person per unit time
D - death rate per person per unit time

Make sure it's not per 1,000 or whatever dumb thing epidemiologists do.

Now this equation needs to be integrated, giving P = P(0)*e^((B-D)*t)

P(0) is initial population

t is time, and must be expressed in the same units as B and D.


It becomes more complicated if B and D change over time. Also IRL there isn't a trivial relationship between death rate and life expectancy. However in a steady state (perhaps what you're interested in?) D = 1/life expectancy, and B = children per woman over lifetime/life expectancy.

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Executor32
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Re: Population Mechanics

Postby Executor32 » 2012-03-26 11:40pm

Searching Google for 'population simulator' gave me this, which is similar to what you're asking for.
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cadbrowser
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Re: Population Mechanics

Postby cadbrowser » 2012-03-27 08:33am

Ahh, cool; thanks a bunch. Let me see if I can do this. Yes, steady state is what I'm looking for.

It's for a hypothetical scenario; and for it; I am wanting to make sure the math works or is plausible.

I have designed a 3D model wherein there are 65,000 residential units capable of housing 4 people a piece as a bunker setting in a post-apocolypic Earth. Now, my original idea was to take 16,250 mated pairs with 2 children each (one male, one female) for a total of 32,500 as a base. Or the 16,250 mated pairs that are near the age (25) to have children.

And then restrict 2 births per couple (one male; one female) (as a controlled agent) (cause anything less than 2 causes the group to go extinct based on the model you sent me).

I am wanting to have available 4 generations at any given time that is alive; also, birth rates appear once every 27 years (appx).

Assume 0 infant mortality rates due to technological advancement, genetic prescreening, and etcetera.

It didn't allow me to manipulate the annual increase in adult mortality to below 6% so that poses a bit of a problem. According to the model with the above parameters set (minus the starting population cause it wouldn't let me set that).

It appears that there is a stable population ~250 to 300 year mark wherein the 25 age groups that are represented (from 0 to 125) are all at 4%.

So it looks like my idea is doable; but I need to either decrease the amount of starting pairs so I can maintain a limit of 260k total population or slightly lower.

If (in my world) the upper age limit is 125 and there is a birth rate of every 25 years, then that would mean I'd need to accomodate 5 generations instead of 4. If I ignore the advances in mortality rates due to the nature of the idea behind the shelter itself, then I could max the upper age limit at ~100 and keep my 4 generation spread.

Maybe make it towhere the advances in medicine are mostly attributed to keeping the infant mortality rate at 0; and not advancing the adult mortality rate. I think that'd work better.

Is there anything I am overlooking or totally "effing" up?

I'm going take my numbers and your equations and plug them in as well.
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"Cheerleaders are dancers who have gone retarded." - Sparky Polastri
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cadbrowser
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Re: Population Mechanics

Postby cadbrowser » 2012-03-27 08:45am

Oh...one other thing I guess would be important to note. If these individuals that were selected were sampled from every country to diversify the genetics to select from, would the 16,250 number be sufficient enought to prevent the "kissin cousin" issue?

I thought I read in Popular Science many years ago that the minimum population needed for a "generation ship" was like 15,000. As I said this was many years ago...so please correct me if I'm wrong.

Thanks in advance for your help.
Financing and Managing a webcomic called Geeks & Goblins.


"Of all the things I've lost, I miss my mind the most." -Ozzy
"Cheerleaders are dancers who have gone retarded." - Sparky Polastri
"I have come here to chew bubblegum and kick ass...and I'm all out of bubblegum." - Frank Nada

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Ziggy Stardust
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Re: Population Mechanics

Postby Ziggy Stardust » 2012-03-27 01:54pm

cadbrowser wrote:Oh...one other thing I guess would be important to note. If these individuals that were selected were sampled from every country to diversify the genetics to select from, would the 16,250 number be sufficient enought to prevent the "kissin cousin" issue?

I thought I read in Popular Science many years ago that the minimum population needed for a "generation ship" was like 15,000. As I said this was many years ago...so please correct me if I'm wrong.

Thanks in advance for your help.


There is no clear consensus on what the minimum viable population for humans might be. For example, there is a lot of evidence that there were far fewer than 15,000 humans left alive on the planet after the Toba catastrophe. Hell, there is one theory that North America was colonized by as few as 70 people, originally, though I would take that claim with a massive grain of salt.

And careful genetic screening and the use of a sperm bank could significantly reduce the effects/dangers of inbreeding (read this). Indeed, estimates of population size for animals have trended downwards in recent years among conservationists due to increased knowledge of genetics, demographics, and various environmental factors. Here is a good study on the subject (though it focuses on non-humans).
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cadbrowser
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Re: Population Mechanics

Postby cadbrowser » 2012-03-28 09:46am

Ah yes, I do remember reading something about the Toba catastrophe. Thank you for reminding me about that. I will look at those links too. Hopefully I can from work...lol (since that's where I am!).

That's what I was hoping for with the sperm bank and etcetera.

Again...Thank you.
Financing and Managing a webcomic called Geeks & Goblins.


"Of all the things I've lost, I miss my mind the most." -Ozzy
"Cheerleaders are dancers who have gone retarded." - Sparky Polastri
"I have come here to chew bubblegum and kick ass...and I'm all out of bubblegum." - Frank Nada


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