They spread through out the world for dominance. They can’t do that staying in their birth place. Their main objective is Sharia all over the world! They have many children, so it probably will happen eventually.
Not so much, anymore.
Total fertility rate by country:
Iran - 1.9
Egypt - 2.8
Algeria - 2.8.
Bahrain - 2.1
Bangladesh - 2.2
Saudi - 2.6
Turkey - 2.0
Tunitia - 2.3
Some Muslims countries are still considerably higher, but even most of those are trending down, often quite sharply.
There is a huge bulge of young people in Muslim countries, but it's temporary. There just simply is no population explosion anymore in the Muslim world.
This is very similar to the demographic change in western societies, just some decades later.
US TFR, BTW, is 1.9.
There are some real surprises in the TFR numbers. Lots of Americans think of Mexico as very prolific. Actual TFR: 2.2, not far ahead of the US.
http://data.worldbank.org/indicator/SP.DYN.TFRT.IN