The increase of population is simply a projection from current figures, birth and death rates, and historical experience of other nations as they transitioned from agrarian to industrial societies. He is stating the projections absent any effects of climate change.
Now add the Sahara pushing North to the Mediterranean, West to the Atlantic, and South into the center of Africa. Yes, some areas will become wetter, but others drier. This is why climatologists switched from the term global warming to climate change: to emphasize the fact that different areas will experience different effects. Some will warm while others will cool, but on average the globe will warm.
When you combine increasing population with decreasing arable land area, you get mass famine, migration, and war.