it's not a hard conclusion to reach that there is a finite number of human beings that can be supported by planet earth, and that the closer we get to this limit the worse the quality of life will be as there's less to go round.
exactly what that number is, and more importantly what quality of life we as a species will accept before taking action is a different story.
Not anything to really worry about because global overpopulation scare stories are a long way from the truth. Human population growth is far smaller than it was predicted ot be back in the 80s, at quite an alarming shortfall.
The futures problems will not be overpopulation, but a massive ageing population and a dwindling worker base. immigrants will become massively valuable, they already are.
We are currently about 7.6Bn. By the 2050s we will be about 10Bn, but the growth quickly tapers. Probably about 11Bn by 2100