PDA

View Full Version : Calculating population growth



Godskook
2011-05-18, 07:33 PM
Ok, I got a city, and I got a rough idea about how many founders are in it. Problem is, I need to figure out what the population would look like 100 years later. Worse, I can't use normal population growth, since founders are effectively immortal(children aren't).

snoopy13a
2011-05-18, 07:50 PM
Honestly, there's really no such thing as "normal population growth."

How large your population growth depends on:

1) Average generation time--> Basically, how long does it take the residents to mature and reproduce. A human villager may have several children by the time they are 25. A dwarf villager may still be a child at 25.

2) Average number of children per person--> How many children the average person has.

3) Immigration--> New residents moving in

4) Disease--> self-explantory

5) Wars--> Obviously, a war or two can decrease population size

6) Emmigration--> Residents moving out

7) Oppression--> Some regimes persecute citizens

8) Culture--> A culture that allows multiple wives will handle decreases in population due to war better than monogamous societies as the men who survive combat take multiple wives.

As you can see, there are many complex variables and there's really no way to find out an answer without more information.

NichG
2011-05-18, 09:05 PM
Of course you could just use average demographics and not worry about being precisely right. It's not the kind of thing most players will notice. They will notice however if you have extremely unrealistic numbers.

I think what I ended up using for a sandbox city-building game I ran once was a death rate of about 0.002 (average age of death = 41) to 0.004 (average age of death = 21) per month, and a base birth rate of about 0.005-0.01 per month among city-dwellers. Then I had various modifiers, e.g. if a druid was working there area there'd be a fertility bonus; if a cleric was curing disease, the death rate would go down, and so on.

Anyhow, if you take the low birth rate and the low death rate, it'd say that a city's population is multiplied by about 36.4. If you take the high death rate, its only a factor of 3. If you take the high birth rate and the low death rate, you get a very large expansion: a factor of 14000 (which would hit food shortages way before anything else happened).

So the answer can vary a lot. The immortality of the founders isn't going to mean much if you have the factor of 14000, but it might mean a lot if you have the factor of 3.

Dilb
2011-05-18, 09:59 PM
I'm guessing you want the following assumptions
a) the city is founded my immortal founders, who continuously have kids
b) the only population growth is due to children being born, who are not immortal
c) the only population decline is due to death

So it's a city on the moon or whatever, there's nowhere else to go and no one else to move in. Taking (from nowhere in particular) a birth rate of 0.04 per year, and a death rate of 0.02 per year, excel tells me that you get a population multiplier of 13, vs 7 without the immortal founders. Not really a big deal considering how rough all these estimates are.

It's kind of weird if the founders keep having kids the entire time, though. "Hey great-grandpa, how's your new baby coming along? Good to see burying grandpa, and great-uncle, and dad, and auntie, and all those second and third cousins, didn't put you off having a constant stream of kids".

Cyrion
2011-05-19, 09:01 AM
I'm reading Malthus' Essay on the Principle of Population at the moment, and his position was that a reasonable estimate for the upper bound of population expansion (remember he was writing in the early 1800's) is for the population to double every 25 years if there are no plagues, wars, etc. that control the population. So as a rough estimate, look at your current population and multiply it by 16 (2^4). If you like that number go with it or adjust it up or down as seems to fit the scenario.

Ormur
2011-05-19, 09:17 AM
In medieval cities the death rate was often higher than the birth rate and the population had to be replenished by immigration. D&D probably doesn't conform to that assumption but I think immigration and emigration are much more significant than natural population growth unless you have a city state with the surrounding areas or a very isolated city.

The economic conditions of the city would be the most important factor. In 100 years the city could go from being a backwater to being the capital of an empire or the hub of world trade and vice versa. At least in the modern world higher living expenses restrict natural growth in cities with a good living standard. People don't necessarily breed until they reach some Malthusian limit.

So my answer to the question would really be: just pick a number.

Jay R
2011-05-19, 11:16 AM
You can't answer this separate from that 100 years of history. The wars, plagues, and food supply have far more effect than anything else.

D&D rule complicate this, of course. How is the population affected by heal spells, Cure Disease, Raise Dead, etc.?

I recommend that you decide how many people you want there, and then build famines, plagues and wars to make it work.

Tvtyrant
2011-05-19, 12:42 PM
In a completely virgin land with tons of easy to access natural resources? Close to 200% (this has happened with European expansion onto certain islands). In a growing desert area like the Sahel without technological innovation? -10-20%

In your case I would suggest 10% per 25 years, since the most skilled work is going to go to the immortals and your keeping them all in the town. Towns in medieval times actually combined population decline with influxes from the countryside; its only in recent times that city populations grow faster then they die. Even then the fastest growing cities gain most of their population from influxes from small towns and rural areas.

NichG
2011-05-19, 03:07 PM
I think it makes sense to combine the near-countryside with the town population for the sake of doing the calculation. Any medieval town is going to be supported by a network of farms, and your immigration is going to be mostly set by the growth rate of the farm populations anyhow.

I'm not sure of this, but I'd imagine that immigration in those situations is mostly from the local area, and a vanishing portion of it is truly distant immigration unless the town is very famous for something (e.g. gold rush dynamics).

Tvtyrant
2011-05-19, 03:15 PM
I wish I had Mercantilism in the 14th Century with me, it discusses farm to city dynamics in depth. But the biggest portion of the population the moved to towns was the second born son groups; men and women who had no inheritance of dowries moving to the city to try to find work. The ones that had trade skills did okay, those that were field hands tended to become a homeless population that moved from city to city during different work seasons. So when France started to produce silk there would be a lot of workers in Paris during the silk weaving season, and then they would move else where during the rest of the year. This was side by side with the permanent guilds.

MickJay
2011-05-19, 03:49 PM
I'm reading Malthus' Essay on the Principle of Population at the moment, and his position was that a reasonable estimate for the upper bound of population expansion (remember he was writing in the early 1800's) is for the population to double every 25 years if there are no plagues, wars, etc. that control the population. So as a rough estimate, look at your current population and multiply it by 16 (2^4). If you like that number go with it or adjust it up or down as seems to fit the scenario.

Of course, he didn't foresee effective contraception and family planning, which has led to a near-zero, or even negative population growth in many of the most developed countries (i.e. those with more food than needed, best available health care and so forth). I'm assuming, though, that OP's setting doesn't have those, in which case the model you proposed should work just fine.

Jay R
2011-05-20, 12:29 PM
I'm reading Malthus' Essay on the Principle of Population at the moment, and his position was that a reasonable estimate for the upper bound of population expansion (remember he was writing in the early 1800's) is for the population to double every 25 years if there are no plagues, wars, etc. that control the population. So as a rough estimate, look at your current population and multiply it by 16 (2^4). If you like that number go with it or adjust it up or down as seems to fit the scenario.

Malthus also said that the world would reach wide-spread cannibalism by the time it hits a population of 1 billion, because the food supply can't keep up.

In a world of seven Billion people, you can afford to be a little skeptical of his claims.

And in this case, his assumption don't apply, because the founders are immortal, and we don't know all the ramifications.

Do they give birth as often as humans? Immortal and fruitful adults could produce dozens of kids each in 100 years. Result: the population could have grown by a factor of ten or twenty.

Are they as sparing as Tolkien's elves? Elrond produced three children in several thousand years. Immortals might be very patient, and might not even have begun raising families yet.

Do they have D&D priests? What level? Healing, Raise Dead, Cure Disease and Neutralize Poison can really cut down the death rate, if available to everyone.

In short, we have no data to begin even as bad an estimate as Malthus's.

Now let's get into the issues that are not rooted in the fantasy system. Who are their neighbors? Are they belligerent? What is the food supply like? [Note that the priests can affect this, too.] Are there potential plagues?

The Roanoke colony disappeared in only three years.

So the population can be pretty much anything the DM wants it to be, from zero to 20 times its original population. The population could be one well-fed dragon, or hundreds of zombies and one evil high priest, or an orcish colony with hundreds of immortal slaves, or anything else you want.

Choose what works, and then decide how it got there.

Eric Tolle
2011-05-20, 01:00 PM
One should note that unless the immortality actually means "unkillable", the immortals will eventually die from accidents and other hazards' Depending on how dangerous the area of, average immortal lifespan would actually range from 300 to 3000 years. In any case, after a few veneration the effect of the immortals would be negligible compared to the birth and death rates of their descendants.

Anyway, for a crude estimate, take the birth/immigration rate and subtract the death/emigration rate to get the yearly growth rate. Divide this into 70 to get the time between population doublings. The average for the 20th century has been 2%, giving a doubling time of 30 years. In colonial areas this could be quite higher, up to 4-5%, whereas in medieval societies in general it could be around .1% or lower.

Godskook
2011-05-22, 12:47 AM
Wow, that's what I get for assuming a thread died.

Anyway, here's some facts:

Approximately 500 founders.
Among the founders, about a 2:1 gender ratio exists, favoring males.
Population is spread out fairly evenly among the various 3.5 races(Kobolds, Goblins, Hobgoblins, Humans, Bugbears, Elves, Dwarves, Gnomes, Halflings, Gnoll, Lizardfolk, Troglodyte and Orc), about 13 in total.
Minimum class level among founders is 8, max is 14, and is uniformly distributed.
Plenty of full-casters, artificers, and psionicists throughout, so magic is plentiful.
Aside from organics, all other resources are in rich supply locally. Assume organic resources are provided magically.
Population gets along very well, united by the common goal of ensuring the Tarrasque never wakes up again.

Tvtyrant
2011-05-22, 01:11 AM
Wow, that's what I get for assuming a thread died.

Anyway, here's some facts:

Approximately 500 founders.
Among the founders, about a 2:1 gender ratio exists, favoring males.
Population is spread out fairly evenly among the various 3.5 races(Kobolds, Goblins, Hobgoblins, Humans, Bugbears, Elves, Dwarves, Gnomes, Halflings, Gnoll, Lizardfolk, Troglodyte and Orc), about 13 in total.
Minimum class level among founders is 8, max is 14, and is uniformly distributed.
Plenty of full-casters, artificers, and psionicists throughout, so magic is plentiful.
Aside from organics, all other resources are in rich supply locally. Assume organic resources are provided magically.
Population gets along very well, united by the common goal of ensuring the Tarrasque never wakes up again.

Ew. That means tremendous inbreeding; since you have an average of 38 individuals to any one species. That makes 19 pairs, which means that they will start inbreeding at 3 generations or so. And then it becomes permanent. Humans can breed with elves and orcs, so make it more like 10 generations for them, which is safe. But the none-cross breeders are going to suffer without influxes. You have a 2:1 ratio of men to women; this means there are either 12 pairs per species or triads. Either way this increases the inbreeding.

Are the founders going to keep producing kids perpetually along with the rest of the population?

Godskook
2011-05-22, 02:49 AM
Ew. That means tremendous inbreeding; since you have an average of 38 individuals to any one species. That makes 19 pairs, which means that they will start inbreeding at 3 generations or so. And then it becomes permanent. Humans can breed with elves and orcs, so make it more like 10 generations for them, which is safe. But the none-cross breeders are going to suffer without influxes. You have a 2:1 ratio of men to women; this means there are either 12 pairs per species or triads. Either way this increases the inbreeding.

Are the founders going to keep producing kids perpetually along with the rest of the population?

1.Assume that magic can help with inbreeding issues, and/or that enough fresh genetic stock can be imported over time to compensate without altering the population size significantly.

2.Yeah, a lot of the founders are going to keep having kids. It took nearly 30 years before they realized they might be immortal, so before that, they were thinking along the lines of "gotta have kids to populate this city when we all die". So a baby boom like unto the one that happened shortly after WWII in the US.

Tvtyrant
2011-05-22, 03:07 PM
I would put it at a 50% increase the first 3 years (2 children in three years is not the highest possible but faster than that puts a lot of strain on the female body, as well as having one child still in need of constant attention while you also have a newborn). So around 800 in 3 years, and up to 1500 in 10. The greater part of the population is children though. Assuming no die off rate, the population climbs up to 2,000 by the time the 14 years rolls round. At this point the kids start getting it on (the oldest ones) so you get an additional 41 kids every other year or so, with an increase of 41 near entries into adulthood every year and a half if the population bred at a steady rate.

Assuming the mating pairs really concentrate on keeping their children safe and there aren't a lot of diseases floating around around 1 in 10 children will probably die (which is a really good rate historically). So this should be factored into each step. Basically the towns population will skyrocket until people stop having so many babies or something bad happens. The stop having babies one is likely within 20 years or so, when the rate will drop to a cultural number rather then a production rate (rather then "a child per so many years" there will be "three children" or "four children."

Godskook
2011-05-22, 04:53 PM
Except most of the population is non-human, which means altered birth rates, especially among the more traditionally belligerent races, like goblin/kobolds who give birth *far* more frequently.

Tvtyrant
2011-05-22, 05:12 PM
Except most of the population is non-human, which means altered birth rates, especially among the more traditionally belligerent races, like goblin/kobolds who give birth *far* more frequently.

I would, except that I have no idea how those give birth. A litter of Kobolds would change everything, but how big is the litter? How often do Goblins give birth? I don't know of any books that give that kind of information, so I just went with people.

Jay R
2011-05-23, 11:37 AM
Based on everything above, I'm making the following assumptions:

Current population of 167 females.
All current members of the population can breed for 100 years and plan to do so.
New members have a breeding life of roughly twenty years, starting at age 15.
50% of babies are female.

The problem is the magic available for healing, curing disease, and raising the dead. If one assumes no infant mortality and that all mortals die at age 70, then in 100 years, there will be over 120,000 people living there.

So what influences have we ignored? If 500 people are enough to handle the Tarrasque, then after there are ten times as many, there will be no particular compulsion to produce more. Furthermore, that large an increase involves clearing lots of new land each year. How do the neighbors feel about that? Even if it's a wilderness, there are animals being pushed out. They will push back.

Also, that fast a growing population will develop schisms within them. The different races that grew up in a crowded city won't be nearly as cozy as the founders were.

Any civilizations within a few hundred miles would look on such a city with alarm. Any wars due?

So I repeat: you can have pretty much any number you want, from 0 to 120,000 (or more - the breeding assumptions could be increased). What number serves your game?