# How Many Generations for Elves to Match All Other Races in Population?

So Elves and their long lives are well-known to be a fantasy trope but I wanted to determine how long it would take for the Elves to achieve dominance not through magic or wisdom but sheer numbers.

Hopefully I have everything here that is needed to determine the answer. Each of these races has enough land and food to continue these levels of growth for hundreds of years- ideally that is the scale which is needed for the answer- if not I have some work to do. If Elves end up not being numerically superior then that'll need fixing too. The main goal is the Elves need enough numbers to match all the other races.

• Humans have the birth rate, fertility rate, mortality rate, and life expectancy of the modern day USA. Their starting population is 3 million.

All races share the human birth rate, fertility rate, mortality rate, and life expectancy unless stated otherwise.

• Elves have the birth rate of humanity but a different life expectancy: they mature at a rate similar to a human until they hit 25 years or so at which point they slow down to 1/5th the aging rate. They can reach up to 500 years old. They have a starting population of 0.5 million.
• Dwarves have a birth rate of humanity but a different life expectancy: they mature at a rate similar to a human until they hit 50 years or so at which point they slow down to 1/10th the aging rate. They can reach up to 100 years old. They have a starting population of 1.5 million.
• Rat-Men have humanity's birth rate but half humanity's life expectancy. They mature at the same rate as a human. Their starting population is 2 million.
• Stone-men have half humanity's birth rate but twice a human's life expectancy. They mature at the same rate as a human. Their starting population is 1 million.

All of these races share the same reproductive lifespan as humanity. That is to say any that mature at the same rate as a human and can reproduce as though they are a human of that age. The babes all share the same birth period of nine(ish) months.

The ones that mature more slowly can reproduce at the equivalent human rate. For example an Elf that has had 30 years pass would be able to reproduce as though they were a 26 year-old human. 25 normal years and then 5 years at the reduced rate to only add up to 1.

To recap I am assuming the Elves eventually will start winning in terms of population against every other race. That isn't being questioned- or if it is then I need to mess with the numbers. The question isn't IF the Elves can match the other races in population but WHEN they have sufficient numbers that their population matches all the other races combined.

(Also hey guys and gals- glad to be back on Worldbuilding. I finally have a World I'm consistently working on!)

• Do the demihumans have menopause? How long is their reproductive life? For example life expectancy for a woman might be 80 but her ability to have babies ends at 50. Aug 6, 2021 at 11:59
• "Reach up to x years old" is not a particularly useful metric--average life expectancy would be much more practical for calculations. Humans can reach up to 120 y/o, which would make the average probably live longer than the Dwarves, who, if their absolute oldest get 100, would have an average life expectancy of around 60 years if it's modeled similarly to humans Aug 6, 2021 at 17:00
• @Willk Menopause and reproductive cycles do not really matter. What we need are fertility and mortality rates. Aug 6, 2021 at 18:46
• When you say 'Humans have the birth rate and life expectancy of the modern day' do you mean global average or some country/group of countries' average? This is important because many developed countries have below-replacement fertility rates and their population is projected to decline (see Japan and most EU countries). Aug 6, 2021 at 18:50
• Tolkien's elves had their children early in life, so that old elves like Galadriel would not have more.
– Mary
Aug 6, 2021 at 23:33

Assuming exponential growth instead of something more resource-limited (and reasonable) like a logistic growth model, the populations with the highest growth rate will eventually have the highest population.

Modeling this as exponential growth, the formula $$f(x) = a(1+r)^x$$ can be used, where $$a$$ is the initial population, $$r$$ is the growth rate (births-deaths), and $$x$$ is the number of intervals (years in this case).

So, I created a table:

Here, I made several assumptions, notably that death rate directly relates to life expectancy (for the rat-men I doubled human death rates, for the elves I divided them by 6.5). This is unrealistic, and probably not the right way to do it, but it's good enough to get a ballpark estimate. This gives us something like this:

In this simplified example, the Elves overtake the Humans around the year 300, while the Rat-Men rapidly approach critical mass and run the risk of collapsing into a black hole.

• I love all the work you put into this, thanks for that., I am a little uncertain of your numbers. For example, the CDC says (cdc.gov/nchs/data/vsrr/vsrr012-508.pdf) the TFR for the USA is 1,637 births per 1000 women and is well below the 2,100 births required to sustain the population. How are you getting your numbers and how can an answer be determined without know the breakdown of males vs females? If the CDC says 2,100 births per 1,00 women is required to sustain the population, that seem to suggest that we should see a decline over time. Aug 7, 2021 at 0:28
• @JonSG I think this answer is based on global statistics. Aug 7, 2021 at 2:13
• @JonSG I am using global average stats. 18.5/1000 as per Wikipedia. This represents the amount of people who will be born by any given group of 1000 average people per year. Knowing male/female ratio is also irrelevant in this (primitive) calculation. It is simply assumed 50% of people born will be women Aug 7, 2021 at 3:16
• The question specifically asks for all births relative to humans who have births per USA. Aug 7, 2021 at 15:58
• @JonSG well, in that case the human population and all the others modeled after it die out. US birth rates are below replacement levels, and the country relies on immigrants to keep demographics healthy. Aug 7, 2021 at 16:25

You are basically asking us to determine for which value of $$t$$ the equation $$P(t)=P_0e^{rt}$$ calculated for elves is greater than the corresponding equation calculated for all the other races.

$$r$$ in the equation is the rate of growth, which you didn't specify. And even the birth rate differs enormously between countries in our era, for example Japan and Niger. Once you have made up your mind on its value, just set up a spreadsheet, using a different columns for each race and check when (and if) the population of elves becomes larger than the other.