For the first 500,000 years of human existence the population growth rate was so slow (1.00004 per year) that if you lived in a village of 100 people then after 25,000 years there would be on average 101 people in your village.
The doubling time of the earths population is now 61 years. Even if you think there will be enough food and water for 2x the current population, you might still agree that at 4x the current population there will be mass starvation looming. I for one think that with GMOs and proper water management we can double our food supply. The current GMOs are not adequate but Monsanto thinks it can double the current food supply in about 60 years if we let them try. So far we aren't but that will change I suspect.
It seems very unlikely we could possible reduce population growth enough in a couple generations to stop the inevitable wars for resources.
Now how large will these wars be. Let's suppose they were larger than any human can even imagine. Lets say they killed half of the earths population. That severe. Then how long would it be till the next war? well about 61 years if we have the same doubling time.
So we will have wars that are so large that most of the population will die. If we don't then we will keep having wars.
I note that climate change is also dependent on the population growth, which is exponential. So Al gore is right about that too, but it's death by Mathusian population crash that awaits your grandkids.