Global population has always been controlled by the ability to provide food. And the only reason we can provide as much food as is currently produced is because of the increased use of phosphorus as a very important element (fertilizer) in growing food.
And phosphorus is not an infinite substance. Some people believe we will start to run out in about 50 years. Some say it will be 250 years. But everyone seems to agree that there is not an unlimited supply. And science has found nothing that will do what phosphorus will do. And animal and plants both depend on it.
SO we can cut back the population ourselves by limiting the number of kids we have, (which btw is going on now) or we can let nature take its course and millions of people around the world will starve to death.
But you can't sustain multi billions of people if you can't feed them.