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!)