How much could a population of 100 grow in 1000 years?

Question

My theoretical scenario has a isolated population of 100 placed in a temperate fertile environment, with little to no negative factors affecting growth such as war, radiation, predators, disease etc. Considering this, how much would this community's population be expected to grow within a thousand years?

Answer 1

It really depends.

We could assume the maximum rate of increase:

• Assuming once females hit puberty they have a child every year until menopause giving us a 40 year period ie for every female there are an extra 40 people (we can assume 50/50 male to female).

So in theory, have your population increasing 20 fold (assuming monogamy) every generation, lets take an average of about 30 years between each generation (realistically it would be spread over a 40 year period). So we have 1000 years ($T$), a generation every 30 ($t_{g}$). Giving us $ \frac{1000}{30} = 33 + \frac{1}{3} $ generations. We start with 100 people ($P_{0}$), multiply this by 20 ($\frac{dP}{dg}$) every generation:

$$ P_{0}*(\frac{dP}{dg})^{\frac{T}{t_{g}}} = 100 * 20^{1000/30} = 2.33\times 10^{45}$$

I don't suppose I need to tell you that this is a very big number and I hope this illustrates that we need more information about your society. Fertility rates depend on culture, it would depend on many different things:

• Is there some religious factor where having more children is good?
• Are your people open about sex, monogamous?
• How big is your divide between the upper and lower classes?
• 1000 years without war, disaster or disease? That is an impressive record for humans.

All these factors could change the fertility rate. However in the past the fertility rate has been related to the mortality rate, the higher the mortality rate the more children each family would have so that, chances were, at least one would live to carry on the family name. Assuming this trend still holds we can assume modern day average family sizes of around about 1.7 children per family. The average age of mothers lies in the 25-34 age band assuming this is an even spread we can say use a generation gap of 30 years again. So lets use our other equation and stick those number in: $$ 100*1.7^{\frac{1000}{30}} = 4.8\times 10^{9} $$ Giving us a population of 4.8 billion. This, however, is fraught with assumptions and generalisations. It doesn't have anything to account for mortality rate, the capacity of the land to feed this many people, cultural factors etc etc.

However the formula there can be used as a guide, you can choose your own fertility rates, generation gap and such to guide you. Without more information about your world we can't really give you any more than generalisations.

Answer 2

After 1000 years the number would be zero, as 100 humans is likely below the Minimum Viable Population.

Even assuming that there are 50 healthy breeding pairs, any offspring after a couple of generations would encounter a serious genetic bottleneck, resulting in various health issues. Death through natural causes such as falling off a cliff, underlying conditions, etc, will further reduce this poll. Depending on the level of medical technology, infant mortality might also be high. The humans might also not have adequate tools to harness the fertile environment, reducing the number of individuals the colony could support.

Hopelessness is also a big factor. Those 100 humans might get demoralised knowing that they can't escape this place, and as a result could simply give up.

Answer 3

Carrying capacity

1000 years is enough for a population to reach the carrying capacity of that isolated environment, no matter how small or large it is.

There is a certain level of population for a given environment, resources and level of technology that is stable - where it doesn't increase due to resource constraints, and any local excess of population generally is "spent" on resource conflicts.

1000 years is a very long time. Given available resources (while the population is much lower than the carrying capacity), every century population can easily increase tenfold (~2.3% annual growth rate) and even much more. 100 * 10^10 is far greater than the current population of the earth, so assuming that your environment is planet-sized or smaller, there's more than enough time to fill that environment up to its capacity - assuming that your population doesn't go extinct while it is yet very small.

Answer 4

According to this handy population calculator, the number would be almost 15 million (assuming there's enough resources to supply those people with what they need) at a growth rate of 1.2%.

Others will be better at math than me, but there's a handy equation at the Wikipedia Population Growth page

Answer 5

The existing answers are pretty good, but there's a whole bunch of variables that haven't been mentioned yet. (As usual, I went full ham on this, so TL;DR at the bottom)

What is this community?

This is a big one. Your community could be colonists, sent to colonize some distant land/planet/whatever. If that's the case, they would most likely be 50 virile breeding pairs, hand-picked to produce the largest possible second generation, in order to increase the colony size as quickly as possible. If that's the case, you can assume a high starting growth rate, and a much higher end population.

But, they could also just be 100 people chosen completely at random. And if that's the case, then you will have to think about:

Demographics.

The demographics of your starting 100 people (let's call them Gen I) will have a profound effect on the number of children they have (Gen II), and that in turn will directly affect the population's growth rate for the remaining 1000 years. Change one male to a female, for example, and the ensuing butterfly effect could affect your final population by a significant, and possibly surprising margin.

@Masterzagh already noted that the ratio of men to women will affect the side of Gen II: the further you get from 50:50, the less potential breeding pairs there are, and the smaller Gen II will be. But there are a few other factors as well:

• Sexuality: I don't know the exact proportion, but chances are that at at least one member of Gen I will be homosexual or asexual. That obviously reduces your number of initial breeding pairs.
• Compatibility: Maybe you have a 50:50 male/female ratio, but who's to say that gives you 50 breeding pairs? Some of them may not be interested in any of their potential mates. Some of them might pair up but decide they don't want kids. Depending on how fast Gen I pairs up, you could have people who are left out because the people they liked were already taken and/or "friendzoned" them, or because they're not attracted to the ones who are left. Or...
• Age: What's the age spread of Gen I? If they're all, say, 18-30, you're golden. The wider the age spread, the more problems you're gonna have, not necessarily in terms of "X is menopausal, Y is 13, etc", but in terms of the age gaps between potential pairings. If this is bad enough, you're in trouble.
• Other Priorities: This might sound like a weird one, but bear with me. I'm assuming Gen I are starting a brand new colony in an area where previously, there was nothing. So at least some of them will be busy actually building that colony. You'll have people constructing buildings and infrastructure, people growing crops, people setting up systems of governance and drafting laws, people scouting the land, and so on. And some of these people may end up "married to the job", and simply not have the time to settle down (or the energy to enjoy doing so).
• Prior Relations: Depending on the circumstances of how Gen I came together to start a colony, it's entirely possible that some of them are related to one another. And that, of course, throws some of your potential breeding pairs right out of the window.
• Technology Level: A futuristic colony is going to have a much lower mortality rate than a medieval colony, because of advances in medicine, general safety, and so on. On the other hand, they also have access to contraception, meaning lower birth rates. So it's kind of a 50/50.

Combine all these factors together and you might even find yourself hitting what's called a "population bottleneck", where you don't have enough people for your colony to be self-sustaining without resorting to in-breeding. And as @fractalwrench already noted, having ninja'd me... that's very bad.

And all that is just the start. Once you've got your Gen II, assuming you haven't hit the bottleneck, you'll have to move on to Gen III, then Gen IV, and so on. And from there, as I mentioned earlier, your population will gradually spiral upwards and become very difficult to predict. It could go anywhere from the millions up to the billions. It's almost impossible to say. But it will be influenced greatly by that initial burst of population growth.

TL;DR:

• Depending on who those 100 people are, your final population could be anywhere from 0 to in the billions.
• You will want to think really long and hard about who those 100 people are. Literally the fate of your entire 1000-year civilization depends on it.

Answer 6

Using some assumptions

start with 50 women
1/2 born are women
women from age 10 to 50 will bear one child each year
everyone dies at 50 and no one dies before 50

After just 200 years that is over 90 trillion

After 1000 years like 15 * 10^60
Would need a very large planet