The Undying Lands were a realm inhabited by Ainur and the Elves.
The Ainur are effectively gods, who never die. The Elves are naturally immortal, and never die of old age. However they can have children - which leads me to believe that the population of the Undying Lands is constantly growing (possibly exponentially?).
Assuming that the Ainur don't alter the landscape or size of the Undying Lands, or use their godly powers to otherwise circumvent the inevitable:
At what point would over-population start affecting the inhabitants of the Undying Lands?
To answer this we would need to know the current population of the Undying Lands, which is a number I am struggling to find.
I am hoping to end up at a year, for example "roughly 5,000 years into the Fourth Age" or something similar.
For the purposes of "over population" I would consider any situation where there are more urbanized areas than rural areas (speaking about Elvish settlements as "urban" feels wrong, but it'll have to do right now). I am not after a date where the entirety of Aman is covered in Elves (although that could be interesting to work out), but I am more after a date where the population of the Elves has got to the point where some of them would realistically consider leaving because living space was becoming a serious issue.
In my question I am also ignoring any implications of the Ainur separating the Undying Lands from Middle Earth. For the purposes of this question it would be best to consider that the Undying Lands was still attached to Middle Earth, as it was just prior to the War of Wrath.