I haven't seen the official statistics on eunuchs, but I'm guessing there maybe a host of other factors, that would contribute to a negative decline in birth rates, among the nations.
I have heard it said, that when nations rise above third world status, population declines. Shift in focus goes from family and farming to working and chasing the dollar.
Or maybe it has to do with the quality of rock music. It appears rock music peaked in the 60's as well as birth rates, than a slight rebound in the 90's (thanks to Nirvana), after Kurt Cobain died the birth rates have been falling ever since. Make better rock music, or birth rates will continue to decline.
International Planned Parenthood Federation Expands Programs With $1.7 Million Gift From Bill & Melinda Gates Foundation