The Population Reference Bureau provides an updated chart of total fertility rate for countries with very low fertility rates. The lowest total fertility rates among the measured countries are a TFR of 1.024 in China, 1.1 in Taiwan, and 1.163 in Bosnia and Herzegovina. Remember that a TFR of about 2.1 is required to keep population stable (not including immigration and emigration).

Comments
Alas, the correlation is almost perfect: The less able you are to care for a child the more children you have. Homo sapiens?