Well, perhaps you don't read enough. Japan has a negative population growth rate, and its not a western country. China, South Korea, Taiwan, etc have lower birth rates than many western countries.

And westerners traditionally were about 15 percent of the world population till the 17th century A.D. Emigration to the fertile Americas allowed western populations to grow to about 30 percent of the world population (so for all the population explosion in Asia and Africa, western populations have grown at double their rates).

My source is Angus Maddison's data.