How poor does Elven fertility need to be in order to keep the ratio of humans to elves constant?
I world-build for tabletop RPGs so I have Tolkien/DnD/Forgotten Realms like elves in mind. The assumptions are:
* The ratio of humans to elves in the world has been more or less constant.
* Humans live ~50 years and have 5-7 children per woman.
* Elves reach sexual maturity at 80-100 years of age and live for 600-800 years.
* Elves do not suffer infirmity until the very end of their lifespan.
* Elven reproduction is human-like. Human-Elven hybrids are possible, even somewhat common (~5% of the population in some areas).
So, how poor does elven fertility need to be to keep the human/elf ratio near constant? Additionally, what is an internally consistent "mechanism" to describe this in-world? Are elven women fertile one day a year? How to explain human-elf couple having at least 2-3 children over their time together? Do half-elves necessarily almost always have a human mother to make this consistent?
EDIT: Assume child mortality rates slightly lower than late medieval period for humans (magical healing is easily accessible in large cities but not in the frontier or countryside). For elves, child mortality rate may be part of the answer. My gut reaction is that elves tend to have easier access to magic in most settings so their child mortality rate should not be higher than humans if at all possible.
EDIT-2: Here is what I learned from the many great answers below:
* My assumption of 6 children in 50 years for humans is at best incomplete information, at worst inconsistent with the world I had in mind. 838
I now assume 1% annual growth rate for humans.
* Now, assuming elven reproductive period between ages 100-600, only 800 year old elves dying from old age that year, and 0.1% yearly mortality for all elves younger than 800; average elven woman needs to have 20 children over 500 years.
* So, while elven fertility per woman per year is poor, fertility per woman is unintuitively high! The average elf has 10 maternal siblings and will have 10 more during her lifetime. Does this mean small elven communities are highly inbred?
* The second part of the question about how to explain these numbers in-world while staying true to <PERSON>/DnD elves is still open. Here are the ideas I like:
+ Magical birth control.
+ 1 elven child at a time (credit: Agent_L) per elven couple. Elven women do not ovulate unless they are in a committed relationship and not already bonded with a child. This will give at most 5 children per elven woman. Perhaps, I just need to increase human mortality rate to keep them in check :( 838