A long article discusses the fall in birth rates in Muslim-majority countries. It's still dreadfully high in some, but quite a few are now comparable with Western birth rates. It needs a lot of reading and digesting - for instance a graph appears to show that even where there are far too many children, they are all intended. This is contrary to a claim I've just read elsewhere, that up to half of pregnancies in the Third World are unwanted and half of these end up in abortion. Although, I suppose, the genital mutilators could be expert abortionists in their day jobs.
http://www.hoover.org/publications/policy-review/article/118261