All theory and speculation. However, the links I provided show real historical data that the world population has continued to increase and shows absolutely no signs of slowing.
The links you posted are just as much "theory and speculation" about the future and are based on old assumptions that are proving NOT to be true. It not only "show signs of slowing" but of reversing course. The non-replacement fertility rate is a "sign of slowing." If you don't have young people in their reproductive years around then no one can have babies. That's a biological certainty. That will cause a population decrease as the old die off, a biological and mathematical certainty. Just because that is inconvenient to the Chicken Little crowd doesn't make it less true. The population explosion doomers are just as shrill and dense as the anthropomorphic global warming doomers.