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It's a trend seen repeated around the world: as a country's development progresses, its reproduction rate falls. Most developed nations are at or below their replacement rate already, as are a number of developing nations (China and Brazil among them). Without immigration, these countries will see population declines.
Sub-saharan Africa is the main laggard in the trend:
It seems to me that, outside of Africa, there is no big population "scare". This is a relief, because coercive population control requires horrendous intrusion on civil liberties--something we absolutely do not want. The goal of nations in the future will likely be to aim for population stability.