There is a racial aspect to this decline too with growing birth rate in 3rd world countries and delcining birth of the industrial countries.
3rd World countries have such high birthrates 'cause people over there don't use (or even know about) contraception. Those countries also have the highest mortality rate in the world amongst infants (if they didn't have such high birth rates they'd be extinct in less than a century). When they'll become more developed they'll breed as scarcely as peopel from developed countries.
Also immigrants from other nations won't keep breeding at the same levels they do now. Catholics in the US used to have more kids at the start of last century and many were predicting that the whole US would soon become Catholic. Guess what? It didn't happen.
Do you really see africa being a developped continent in the next 200 years? they've been colonized for 100 and independent but closely helped for about 50... the only thing that changed is that now instead of tribal systems, they have corrupt governments, add to this a population growing faster than these country can possibly handle and you don't have the reciepy for rapid developpment of the infrastructures and of the cultural morals of the people there... your birth rate is still gonna be high for a long time.
Err the Catholic migration from last century was from developped countries and it basically stopped on it's own. The US is currently more trending to being overun by south/central america and Asia than anything else. Again i'm not saying this in a bad way, just that the migration flux are more consistant due to the discrepancy in the quality of life, and although you may think that migrants addapt and start having the same birth rate as the local country, if the flow of migrant keeps the same, you'll still have a gradual change in the population of the country. Take this to a much larger scale and you get a country that is basically colonized. (great example, because it is out of proportion, is the US.... white people invaded indian land... the country is a white country now, not an indian one... well all I say is that white people are the indians of the future, they have the attractive land with opportunity, and many many people are gonna migrate there thus in the long run changing the population.
Now a case could be made for the US that the migration will stop from the americas at one point.... but do you really think that any south american country will in our lifetimes have a migratory appeal greater than the one of the US? I doubt it. same as I doubt that Europe will be less appealing than it currently is for africa and the middle east.