This "demographic transition" to lower birth rates began in Western Europe in the 19th century and later spread to North America, then Latin America, Asia and now Africa. In 1955, the birth rates per woman in Yemen, Iran, Bangladesh, Nigeria, Brazil and China were, respectively, 8.3, 7.0, 6.8, 6.5, 6.1 and 5.6. Today they are 5.1, 1.7, 2.7, 5.2, 1.8 and 1.7. Notice: The poorer a country has remained, the slower the fall.
Birth rates have gone down because of prosperity, not poverty. Everywhere it has occurred, it has followed a fall in child mortality and famine and an increase in income and education. The wider availability of contraception has been necessary, even vital, for this shift, but it has not been sufficient.
Read full in The Rational Optimist blog.